**3. Capacitive coupling in wind farms**

Wind energy systems may contribute to the distribution network voltage distortion because of its rotating machine characteristics and the design of its power electronic interface. As presented in Fig. 6, wind energy system designs incorporate a wide range of power electronic interfaces with different ratings (Comech et al., 2010).

Fig. 6. Wind turbine configurations.

because of the capacitive coupling modelled. Thus, a 1 MW PV installation as modelled in Fig. 2 presents 12.50 kW of losses due to the capacitive couplings or leakage loop between

Frequency (Hz)

Fig. 5. Resonance frequency of the PV installation without capacitive coupling (dashed line)

Wind energy systems may contribute to the distribution network voltage distortion because of its rotating machine characteristics and the design of its power electronic interface. As presented in Fig. 6, wind energy system designs incorporate a wide range of power

**(b)**

GB

PV modules and ground.

Impedance

and considering capacitive couplings (solid line).

electronic interfaces with different ratings (Comech et al., 2010).

(a)

GB

**(c)** 

**3. Capacitive coupling in wind farms** 

Fig. 6. Wind turbine configurations.

GB

 |Z| (

)

Fig. 6a shows the fixed-speed wind turbine with asynchronous squirrel cage induction generator (SCIG) directly connected to the grid via transformer. Fig. 6b represents the limited variable speed wind turbine with a wound rotor induction generator and partial scale frequency converter on the rotor circuit known as doubly fed induction generator (DFIG). Fig. 6c shows the full variable speed wind turbine, with the generator connected to the grid through a full-scale frequency converter.

These power electronic interfaces are rated as a percentage of the machine power, hence larger systems are accountable for higher distortions. Recent investigations based on wind energy systems suggests that frequency converters (with a typical pulse width modulated with 2.5 kHz of switching frequency) can, in fact, cause harmonics in the line current, leading to harmonic voltages in the network (Conroy & Watson, 2009).

Moreover, most simplified models of wind farms consider a simple series impedance model for underground cables that connect wind turbines with the network grid. Thus, capacitive couplings with ground through cables are not considered for different frequencies components.

To simulate wind farms harmonic distortion behaviour accurately, it is important to model cables by their frequency dependent model. The equivalent circuit for the capacitive coupling model of wind farms is shown in Fig. 7.

Fig. 7. Capacitive coupling model for wind farm.

Notice that, otherwise the capacitive model of solar installations, the wind turbine is directly connected to the rectifier side of the converter. The capacitive coupling seen by the DC bus through the wind turbine is composed of the path between the rectifier side and ground because of the high harmonic current component imposed by the switching actions, whereas the capacitive coupling seen through the grid is represented by the inverter side, the filter and the underground cable. The equivalent electric circuit of the wind farm capacitive coupling model is shown in Fig. 8.

In this figure, parameters *RWG* and *LWG* make reference to the resistance and inductance, respectively, of the synchronous wind generator. *Rg* is the ground resistance at the wind turbine location while *Rq\_es* is the ground resistance of the electrical substation belonging to the wind farm under study.

Harmonic Distortion in Renewable Energy Systems: Capacitive Couplings 271

harmonic 70 has a magnitude of 17.54 V, as shown in Fig. 9a. Moreover, the multiples of the switching frequencies are also considerable respect to the fundamental component, as shown in Fig. 9b*,* where the harmonic component 138 (7000 Hz) and 210 (10500 Hz) are

The ground current waveform measured at the wind farm is shown in Fig. 10a, and the FFT analysis concerning this waveform is performed in Fig. 10b. Consistently with the voltage waveform, the dominant harmonic component in the ground current fits the switching frequency of the converter. That is harmonic component 68 with 503% of the fundamental component magnitude which is 168 mA. Thus, the magnitude of harmonic 68 is 844.9 mA.

approximately 145% and 98%, respectively, of the fundamental component magnitude.

Element Parameter Value

Power grid Thevenin voltage 3.5 kV

The multiples of the switching frequencies are also significant, as shown in Fig. 10b*,*  however harmonic component 140 (7000 Hz) appears higher than in the ground voltage waveform near to 200% while harmonic 210 (10500 Hz) is less dominant, 56% but still high

These simulation results indicate that ground current in wind farms can be considerable according to the values expressed in (IEEE 80-2000, 2000) for the range of frequencies expressed at Fig. 10a. Therefore, care is then needed to ensure that ground current is within

This issue is one of the most significant advantages of considering capacitive coupling models for wind farms, which allows implementing further corrective actions to mitigate

The capacitive coupling model detects the expected resonant frequency of the wind farm at 11.0 kHz with an impedance magnitude Z of 77.8 while simplified models does not detect

Table 2. Electric parameters for the wind farm capacitive grounding model.

enough in comparison with the fundamental component.

the adverse effect of ground current over safe conditions of work.

a resonant frequency for this wind farm configuration, as shown in Fig. 11.

Operation voltage 3.5 kV Operation frequency 50 Hz Nominal power 1400 kVA Stator winding resistance 0.01196 pu Stator leakage reactance 0.1966 pu

Nominal power 1800 kVA Switching frequency 3500 Hz Topology 6 pulses Capacitive coupling 0.8 uF

Q factor 10 Cut-off frequency 1000 Hz Nominal power 530 kVA

Positive sequence impedance 0.09015+*j* 0.0426 /km Zero sequence impedance 0.0914 + *j* 0.03446 /km Zero sequence susceptance 0.327 mS/km

Thevenin inductance 0. 231 mH

Wind generator

Full converter

Filter

Underground cable

safe limits of work.

*Crectifier* and *Cac\_cable* are the capacitive couplings of the rectifier side and underground cable, respectively, with ground. *Rac\_cable* and *Lac\_cable* make reference to the resistance and inductance, respectively, of the synchronous wind generator. *Lfilter* and *Cfilter* are the dimensions of the filter. *LTR* is the equivalent impedance of the power transformer and *Lsource* the thevenin impedance of the source. The variables *vWT(t)* and *vsource(t)* are the voltages at wind generator node and network grid source, respectively. The input voltage *vin(t)* is the voltage injected into the grid by the inverter side.

Fig. 8. Equivalent electric circuit belonging to the wind farm capacitive coupling.

The state variable representing this model can be deduced in a similar way as expressed in Section 2. Nonetheless, the effect of capacitive couplings in wind farms is more significant at the inverter circuit through the power grid where the circuit of the filters and cables exert an important influence over the ground currents.

The continuous time equations that describe the transfer function between the input voltage *vin(t)* and the network grid *vsource(t)* are the following

$$\frac{d\dot{i}\_1(t)}{dt} = \frac{1}{L\_{filter}} \cdot \left(v\_{in}(t) - v\_2(t)\right) \tag{6}$$

$$\frac{dv\_2(t)}{dt} = \frac{1}{\left(\mathbf{C}\_{flhr} + \mathbf{C}\_{\text{ac\\_cable}}\right)} \cdot \left(i\_1(t) - i\_3(t)\right) \tag{7}$$

$$\frac{di\_3(t)}{dt} = \frac{1}{L\_{fac\\_cable}} \cdot \left(v\_2(t) - i\_3(t) \cdot R\_{ac\\_cable} - v\_3(t)\right) \tag{8}$$

$$\frac{dv\_3(t)}{dt} = \frac{i\_3(t) - i\_4(t)}{C\_{ac\\_cable}}\tag{9}$$

$$\frac{di\_4(t)}{dt} = \frac{v\_3(t)}{L\_{TR} + L\_{source}}\tag{10}$$

The electric parameters related to the capacitive coupling model of Fig. 8 are shown in Table 2. In Fig. 9a, the ground voltage measurement is shown while in Fig. 9b the FFT analysis for this waveform is shown. It is observed that the harmonics components near the switching frequency are considerably higher than the fundamental component. Harmonics components 70 (3500 Hz) is 575% of fundament component magnitude which is 3.05 V. That means that

*Crectifier* and *Cac\_cable* are the capacitive couplings of the rectifier side and underground cable, respectively, with ground. *Rac\_cable* and *Lac\_cable* make reference to the resistance and inductance, respectively, of the synchronous wind generator. *Lfilter* and *Cfilter* are the dimensions of the filter. *LTR* is the equivalent impedance of the power transformer and *Lsource* the thevenin impedance of the source. The variables *vWT(t)* and *vsource(t)* are the voltages at wind generator node and network grid source, respectively. The input voltage *vin(t)* is the

*vWG(t) LTR vsource(t)*

*Cfilter*

The state variable representing this model can be deduced in a similar way as expressed in Section 2. Nonetheless, the effect of capacitive couplings in wind farms is more significant at the inverter circuit through the power grid where the circuit of the filters and cables exert an

The continuous time equations that describe the transfer function between the input voltage

<sup>1</sup>

<sup>2</sup>

\_ () 1 () () *filter ac cable dv t it it dt C C*

<sup>3</sup>

( ) <sup>1</sup> () () ( ) *ac cable*

*di t vt it R vt*

3 34

*dv t i t i t dt C*

<sup>4</sup> <sup>3</sup> ( ) ( )

The electric parameters related to the capacitive coupling model of Fig. 8 are shown in Table 2. In Fig. 9a, the ground voltage measurement is shown while in Fig. 9b the FFT analysis for this waveform is shown. It is observed that the harmonics components near the switching frequency are considerably higher than the fundamental component. Harmonics components 70 (3500 Hz) is 575% of fundament component magnitude which is 3.05 V. That means that

*di t v t dt L L*

\_ () () ()

*ac cable*

*TR source*

*filter di t v t vt*

\_

*fac cable*

() 1 () () *in*

2

23 \_ 3

1 3

*dt L* (8)

*Rg\_es*

*dt L* (6)

(9)

(10)

*i 3(t)*

*Cac\_cable*

*<sup>4</sup> i (t) 1(t)*

*v2(t) v3(t)*

*i*

(7)

*Cac\_cable*

*Lfilter Rac\_cable Lac\_cable*

*i 2(t)*

*L Converter source*

voltage injected into the grid by the inverter side.

*Crectifier*

important influence over the ground currents.

*vin(t)* and the network grid *vsource(t)* are the following

*Rectifier circuit*

*Inverter circuit*

Fig. 8. Equivalent electric circuit belonging to the wind farm capacitive coupling.

*vin(t)*

*Rg*

*RWG LWG*

harmonic 70 has a magnitude of 17.54 V, as shown in Fig. 9a. Moreover, the multiples of the switching frequencies are also considerable respect to the fundamental component, as shown in Fig. 9b*,* where the harmonic component 138 (7000 Hz) and 210 (10500 Hz) are approximately 145% and 98%, respectively, of the fundamental component magnitude. The ground current waveform measured at the wind farm is shown in Fig. 10a, and the FFT analysis concerning this waveform is performed in Fig. 10b. Consistently with the voltage waveform, the dominant harmonic component in the ground current fits the switching frequency of the converter. That is harmonic component 68 with 503% of the fundamental component magnitude which is 168 mA. Thus, the magnitude of harmonic 68 is 844.9 mA.


Table 2. Electric parameters for the wind farm capacitive grounding model.

The multiples of the switching frequencies are also significant, as shown in Fig. 10b*,*  however harmonic component 140 (7000 Hz) appears higher than in the ground voltage waveform near to 200% while harmonic 210 (10500 Hz) is less dominant, 56% but still high enough in comparison with the fundamental component.

These simulation results indicate that ground current in wind farms can be considerable according to the values expressed in (IEEE 80-2000, 2000) for the range of frequencies expressed at Fig. 10a. Therefore, care is then needed to ensure that ground current is within safe limits of work.

This issue is one of the most significant advantages of considering capacitive coupling models for wind farms, which allows implementing further corrective actions to mitigate the adverse effect of ground current over safe conditions of work.

The capacitive coupling model detects the expected resonant frequency of the wind farm at 11.0 kHz with an impedance magnitude Z of 77.8 while simplified models does not detect a resonant frequency for this wind farm configuration, as shown in Fig. 11.

Harmonic Distortion in Renewable Energy Systems: Capacitive Couplings 273

3.000 3.005 3.010 3.015 3.020

Time (s)

(a)

Frequency (Hz) 0 4000 8000 12000

(b)

Fig. 10. Simulation result of the capacitive coupling model: (a) waveform between wind farm electric circuit and ground and (b) FFT analysis of the ground current obtained.



Ground current (kA)

Magnitude

(% of fundamental component)

600

450

300

150

0

0.0000

0.0005

0.0010

Fig. 9. Simulation result of the capacitive coupling model: (a) voltage waveform between wind farm electric circuit and grounding system and (b) FFT analysis of the voltage waveform obtained.

2.000 2.005 2.010 2.015 2.020

Frequency (Hz) 0 4000 8000 12000

(b)

Fig. 9. Simulation result of the capacitive coupling model: (a) voltage waveform between wind farm electric circuit and grounding system and (b) FFT analysis of the voltage

(a)

Time (s)



0.000

Voltage (kV)

Magnitude

(% of fundamental component)

600

450

300

150

0

waveform obtained.

0.025

0.050

Fig. 10. Simulation result of the capacitive coupling model: (a) waveform between wind farm electric circuit and ground and (b) FFT analysis of the ground current obtained.

Harmonic Distortion in Renewable Energy Systems: Capacitive Couplings 275

In node 5, the phase voltage waveform meets the standard regulation of harmonic distortion

3.80 3.81 3.82 3.83 3.84 3.85 3.86

(b) Fig. 13. Simulation result of the distribution network: (a) phase voltage waveform and (b)

Time (s) (a)

(THD=5.4%) with a fundamental component of 8.72 kV, as shown in Fig. 13.

Thevenin voltage 15 kV Thevenin inductance 17.938 Shortcircuit power 12.54 MVA

Positive sequence impedance 0.6969 +*j* 0.492 /km Zero sequence impedance 5.945 + *j* 7.738 /km Zero sequence susceptance 2.13 µS/km

Element Parameter Value

The electric parameters of the network grid are shown in Table 3.

Power grid

Underground cable


Voltage (kV)

Table 3. Electric parameters of the network grid.

FFT analysis of the waveform obtained, at node 5.

Fig. 11. Resonance frequency of the wind farm model without considering capacitive coupling (dashed line) and with capacitive couplings (solid line).
