**2. Capacitive coupling in solar-photovoltaic installation**

The region between PV modules and PV structure essentially acts as an insulator between layers of PV charge and ground. Most shunt capacitive effects that may be ignored at very low frequencies can not be neglected at high frequencies for which the reactance will become relatively small due to the inverse proportionality with frequency *f* and, therefore, a low impedance path is introduced between power elements and ground.

This effect is present in PV installations because of the high frequency switching carried out by the converters stage, which arises different capacitive coupling between modules and ground. Thus, the capacitive effect must be represented as a leakage loop between PV arrays, cables and electronic devices and the grounding system. By means of this leakage loop, capacitive currents are injected into the grounding system creating a GPR along the PV installation which introduces current distortion, electromagnetic interference, noise and unsafe work conditions. For this reason, an accurate model of these capacitive couplings are requiered for PV installations.

#### **2.1 Equivalent electric circuit for ground current analysis**

Depending on the switching frequency, the harmonics produced may be significant according to the capacitive coupling and the resonant frequency inside the PV installation.

Power electronic devices, as used for DG, might be able to cause harmonics. The magnitude and the order of harmonic currents injected by DC/AC converters depend on the technology of the converter and mode of its operation (IEC Std. 61000-4-7, 2010, IEEE Std. 519-1992, 1992). Due to capacitive coupling between the installation and earth, potential differences imposed by switching actions of the converter inject a capacitive ground current which can cause significant electromagnetic interferences, grid current distortion, losses in the system, high-

Several renewable system installations analyses have been reported (Bellini, 2009, Conroy, 2009, Luna, 2011, Sukamonkol, 2002, Villalva, 2009), where most theoretical analysis and experimental verifications have been performed for small-scale installations without considering capacitive coupling. Power electronics models and topologies also have been studied, but without considering the amount of losses produced by the capacitive current that appears due to the switching actions (Zhow, 2010, Chayawatto, 2009, Kim, 2009). In (Iliceto & Vigotti, 1998), the total conversion losses of a real 3 MW PV installation have been studied considering reflection losses, low radiation and shadow losses, temperature losses, auxiliary losses, array losses and converters losses. The latter two factors sum a total of 10% of the rated

noise level in the installation and unsafe work conditions (Chicco et al., 2009).

power where part of these losses is due to the capacitive coupling that was neglected.

**2. Capacitive coupling in solar-photovoltaic installation** 

**2.1 Equivalent electric circuit for ground current analysis** 

low impedance path is introduced between power elements and ground.

and safety conditions.

requiered for PV installations.

Therefore, for an accurate study of power quality, it is important to model DG installations detailing the capacitive coupling of the electric circuit with the grounding system, which are detailed for PV installations and wind farms in Sections 2 and 3, respectively. These models allow analyzing the current distortion, ground losses and Ground Potential Rise (GPR) due to the capacitive coupling. The combined effect of several distributed generation sources connected to the same electric network has been simulated, and results have been presented together with solutions based on the proposed model to minimize the capacitive ground current for meeting typical power quality regulations concerning to the harmonic distortion

The region between PV modules and PV structure essentially acts as an insulator between layers of PV charge and ground. Most shunt capacitive effects that may be ignored at very low frequencies can not be neglected at high frequencies for which the reactance will become relatively small due to the inverse proportionality with frequency *f* and, therefore, a

This effect is present in PV installations because of the high frequency switching carried out by the converters stage, which arises different capacitive coupling between modules and ground. Thus, the capacitive effect must be represented as a leakage loop between PV arrays, cables and electronic devices and the grounding system. By means of this leakage loop, capacitive currents are injected into the grounding system creating a GPR along the PV installation which introduces current distortion, electromagnetic interference, noise and unsafe work conditions. For this reason, an accurate model of these capacitive couplings are

Depending on the switching frequency, the harmonics produced may be significant according to the capacitive coupling and the resonant frequency inside the PV installation. Moreover, every PV array is considered as an independent current source with a DC current ripple independent of the converter ripple. These ripple currents are not in synchronism with the converter and produce subharmonics in the DC circuit which increase the Total Harmonic Distortion in the current waveform (THDI) (Zhow et al., 2010).

The typical maximum harmonic order h = 40, defined in the power quality standards, corresponds to a maximum frequency of 2 kHz (with 50 Hz as fundamental frequency) (IEC Std. 61000-4-7, 2002). However, the typical switching frequency of DC/DC and DC/AC converters, usually operated with the Pulse Width Modulation (PWM) technique, is higher than 3 kHz. Hence, higher order harmonics up to the 100th order, can be an important concern in large scale PV installations where converters with voltage notching, high pulse numbers, or PWM controls result in induced noise interference, current distortion, and local GPR at PV arrays (Chicco et al., 2009).

A suitable model of capacitive couplings allows reproducing these harmonic currents injected not only into the grid, but also into the DC circuit of the PV installation that would lead to internal resonant, current distortion and unsafe work conditions where capacitive discharge currents could exceed the threshold of safety values of work (IEEE Std. 80-2000, 2000). The capacitive coupling is part of the electric circuit consisting of the PV cells, cables capacitive couplings, AC filter elements and the grid impedance, as shown in Fig. 1, and its effect is being appreciated in most large scale PV plants.

Fig. 1. Model of PV module, PV array and capacitive coupling with PV structure.

Harmonic Distortion in Renewable Energy Systems: Capacitive Couplings 265

d () 1 1 · () · () <sup>d</sup> *c c v t it it*

d () · · () · () d ·( ) · ·( ) ·

According to the equivalent DC circuit shown in Fig. 2, *i1(t)* and *i2(t)* are the current of mesh 1 and mesh 2, respectively, *vin(t)* is the injected voltage by the converter, *v2(t)* the voltage at node 2 and *vpv(t)* is the voltage between PV module and ground and represents the parameter under study. Parameter *Cc* represents the capacitive coupling between cables and

In some simplified models of PV installation (Villalva, 2009, Kim, 2009, Bellini, 2009), the capacitance *Cpv* and resistance *Rpv* are considered like infinite and zero, respectively. Then, the capacitive coupling with the grounding system is totally neglected. Even ground

The PV arrays are connected to a DC system of 700 V, and the power is delivered to an inverter stage based on four inverters of 125 kW in full bridge topology and operation frequency of 3.70 kHz. The underground cables, which connect the PV arrays to the inverter

The electrical parameters of the capacitive coupling between PV arrays and grounding system are shown in Table 1 and have been adjusted according to the field measurement in order to simulate the response of the capacitive coupling model accurately against the

Element Parameter Value

Filter LC Inductance Lfilter 90 µH

Table 1. Electric parameters for the solar PV installation capacitive grounding model.

*cs g pv pv c s g pv pv*

*vt v t*

1 2

1 2

*i t i t*

*pv*

Operation voltage 700 Vdc Capacitance CPV 1x10-9 F Resistance RPV 1x107 Series Resistance RS 0.30

Resistance RC 0.25 /km Inductance LC 0.00015 H/km Capacitive coupling CC 1x10-4 F/km

Capacitance Cfilter 0.756 mF

Positive sequence impedance 0.3027 + *j* 0.1689 /km Zero sequence impedance 0.4503 + *j* 0.019 /km Zero sequence susceptance 0.1596 mS/km

Thevenin voltage 20 kV Thevenin impedance 0.6018+*j* 2.4156 Ground resistance Rg 1.2

*tC C* (4)

(5)

2

*g*

 

*R*

resistance of the PV installation is not considered (*Rg* = 0).

harmonics injected by the operation of the converters.

PV array

DC cable

Underground cable

Power grid

stage, have been included through their frequency dependent model.

2

ground and *Rc* and *Lc* are the resistance and inductance of the cable, respectively.

*pv pv s g pv pv*

*CR R R CR*

<sup>1</sup> · () · () · ·( ) ·

*t CR R C R CR R C R*

*pv g pv g g g*

*vt R R R R R*

#### **2.2 Behavior of the PV installation considering capacitive coupling**

Normally, numerous PV modules are connected in series on a panel to form a PV array as it is shown in Fig. 1. The circuit model of the PV module (Kim et al., 2009) is composed of an ideal current source, a diode connected in parallel with the current source and a series resistor. The output current of each PV module is determined as follows:

$$I = I\_{sc} - I\_d = I\_{sc} - I\_o \left[ \exp\left(\frac{V + I \cdot R\_s}{n^\* V\_T}\right) \right] \tag{1}$$

where *Io* is the diode saturation current, *V* the terminal voltage of a module, n the ideal constant of diode, *VT* is the thermal potential of a module and it is given by *m*·(kT/q) where *k* the Boltzmann's constant (1.38E-23 J/K), *T* the cell temperature measured in K, *q* the Coulomb constant (1.6E-19 C), and *m* the number of cells in series in a module. *Isc* is the short circuit current of a module under a given solar irradiance. *Id* is the diode current, which can be given by the classical diode current expression. The series resistance *Rs* represents the intrinsic resistance to the current flow.

The capacitive coupling of PV modules with the ground is modelled as a parallel resistance *Rpv* and capacitor *Cpv* arrangement which simulates the frequency dependency on the insulator between PV modules and the grounding system. The PV structure is connected to the grounding system represented in the model by the grounding resistance *Rg*.

Taking into account that the converter represents a current source for both DC circuit and AC circuit of the PV installation, an equivalent circuit is deduced to analyze the capacitive coupling effect over the current and voltage waveforms.

The equivalent circuit of both DC circuit of the PV installation and AC circuit for connection to the grid as seen between inverter terminals and ground is illustrated Fig. 2. In the AC circuit *Rac\_cable*, *Lac\_cable* and *Cac\_cable* are the resistance, inductance and capacitance of the AC underground cables, *Rg\_es* is the ground resistance at the substation and *Lfilter* and *Cfilter* are the parameters of the LC filter connected at AC terminals of the inverter.

Fig. 2. Capacitive coupling model for the DC and AC electric circuit of a PV installation.

The inclusion of *Rpv* and *Cpv* on the PV equivalent circuit allows representing the leakage path for high frequency components between PV modules and ground. This DC equivalent circuit is represented by the following continuous-time equations, at nominal operating condition

$$\frac{\text{d}\dot{i}\_1(t)}{\text{d}t} = \frac{1}{L\_c} \cdot v\_{in}(t) - \frac{R\_c}{L\_c} \cdot i\_1(t) - \frac{1}{L\_c} \cdot v\_2(t) \tag{2}$$

$$\frac{\mathrm{d}i\_{2}(t)}{\mathrm{d}t} = \frac{1}{\mathrm{C}\_{c}\mathrm{\{R}\_{s} + \mathrm{R}\_{\mathrm{g}}\}}i\_{1}(t) - \left[\frac{1}{\mathrm{C}\_{c}\mathrm{\{R}\_{s} + \mathrm{R}\_{\mathrm{g}}\}} + \frac{\nu}{\mathrm{C}\_{pv}\cdot\mathrm{R}\_{pv}}\right]i\_{2}(t) + \frac{1}{\mathrm{C}\_{pv}\cdot\mathrm{R}\_{pv}\left(\mathrm{R}\_{s} + \mathrm{R}\_{\mathrm{g}}\right)}\upsilon\_{2}(t) \tag{3}$$

Normally, numerous PV modules are connected in series on a panel to form a PV array as it is shown in Fig. 1. The circuit model of the PV module (Kim et al., 2009) is composed of an ideal current source, a diode connected in parallel with the current source and a series

*<sup>s</sup> sc d sc o*

where *Io* is the diode saturation current, *V* the terminal voltage of a module, n the ideal constant of diode, *VT* is the thermal potential of a module and it is given by *m*·(kT/q) where *k* the Boltzmann's constant (1.38E-23 J/K), *T* the cell temperature measured in K, *q* the Coulomb constant (1.6E-19 C), and *m* the number of cells in series in a module. *Isc* is the short circuit current of a module under a given solar irradiance. *Id* is the diode current, which can be given by the classical diode current expression. The series resistance *Rs*

The capacitive coupling of PV modules with the ground is modelled as a parallel resistance *Rpv* and capacitor *Cpv* arrangement which simulates the frequency dependency on the insulator between PV modules and the grounding system. The PV structure is connected to

Taking into account that the converter represents a current source for both DC circuit and AC circuit of the PV installation, an equivalent circuit is deduced to analyze the capacitive

The equivalent circuit of both DC circuit of the PV installation and AC circuit for connection to the grid as seen between inverter terminals and ground is illustrated Fig. 2. In the AC circuit *Rac\_cable*, *Lac\_cable* and *Cac\_cable* are the resistance, inductance and capacitance of the AC underground cables, *Rg\_es* is the ground resistance at the substation and *Lfilter* and *Cfilter* are

Fig. 2. Capacitive coupling model for the DC and AC electric circuit of a PV installation.

The inclusion of *Rpv* and *Cpv* on the PV equivalent circuit allows representing the leakage path for high frequency components between PV modules and ground. This DC equivalent circuit is represented by the following continuous-time equations, at nominal operating

> d () 1 <sup>1</sup> · () · () · () <sup>d</sup> *<sup>c</sup> in c cc i t <sup>R</sup> v t it vt*

d () 1 <sup>1</sup> <sup>1</sup> · () · () · () d ·( ) ·( ) · · ·( ) *cs g c s g pv pv pv pv s g i t i t i t v t t CR R CR R C R C R R R* 

1 2

1 22

*tL L L* (2)

(3)

the grounding system represented in the model by the grounding resistance *Rg*.

the parameters of the LC filter connected at AC terminals of the inverter.

1

*V IR II I I I*

· · exp ·

*T*

(1)

*nV*

**2.2 Behavior of the PV installation considering capacitive coupling** 

resistor. The output current of each PV module is determined as follows:

represents the intrinsic resistance to the current flow.

coupling effect over the current and voltage waveforms.

condition

2

$$\frac{\mathrm{d}v\_2(t)}{\mathrm{d}t} = \frac{1}{C\_c} \dot{v}\_1(t) - \frac{1}{C\_c} \dot{v}\_2(t) \tag{4}$$

$$\begin{split} \frac{\mathrm{d}\upsilon\_{pv}(t)}{\mathrm{d}t} &= \frac{R\_{\mathrm{g}}}{\mathrm{C}\_{\mathrm{c}}\mathrm{r}(R\_{\mathrm{s}} + R\_{\mathrm{g}})} \dot{\imath}\_{1}(t) + \left( \frac{R\_{pv} + R\_{\mathrm{g}}}{\mathrm{C}\_{pv} \cdot \mathrm{R}\_{pv}} - \frac{R\_{\mathrm{g}}}{\mathrm{C}\_{\mathrm{c}}\mathrm{r}(R\_{\mathrm{s}} + R\_{\mathrm{g}})} - \frac{R\_{\mathrm{g}} \cdot \mathrm{pv}}{\mathrm{C}\_{pv} \cdot \mathrm{R}\_{pv}} \right) \dot{\imath}\_{2}(t) \dots \\ &+ \frac{R\_{\mathrm{g}}}{\mathrm{C}\_{pv} \cdot \mathrm{R}\_{pv} \cdot \mathrm{(R\_{\mathrm{s}} + R\_{\mathrm{g}})}} \upsilon\_{2}(t) - \frac{1}{\mathrm{C}\_{pv} \cdot \mathrm{R}\_{pv}} \upsilon\_{pv}(t) \end{split} \tag{5}$$

According to the equivalent DC circuit shown in Fig. 2, *i1(t)* and *i2(t)* are the current of mesh 1 and mesh 2, respectively, *vin(t)* is the injected voltage by the converter, *v2(t)* the voltage at node 2 and *vpv(t)* is the voltage between PV module and ground and represents the parameter under study. Parameter *Cc* represents the capacitive coupling between cables and ground and *Rc* and *Lc* are the resistance and inductance of the cable, respectively.

In some simplified models of PV installation (Villalva, 2009, Kim, 2009, Bellini, 2009), the capacitance *Cpv* and resistance *Rpv* are considered like infinite and zero, respectively. Then, the capacitive coupling with the grounding system is totally neglected. Even ground resistance of the PV installation is not considered (*Rg* = 0).

The PV arrays are connected to a DC system of 700 V, and the power is delivered to an inverter stage based on four inverters of 125 kW in full bridge topology and operation frequency of 3.70 kHz. The underground cables, which connect the PV arrays to the inverter stage, have been included through their frequency dependent model.

The electrical parameters of the capacitive coupling between PV arrays and grounding system are shown in Table 1 and have been adjusted according to the field measurement in order to simulate the response of the capacitive coupling model accurately against the harmonics injected by the operation of the converters.


Table 1. Electric parameters for the solar PV installation capacitive grounding model.

Harmonic Distortion in Renewable Energy Systems: Capacitive Couplings 267

(a)

(b) Fig. 4. Simulation result of the capacitive coupling model: (a) voltage waveform between PV

Simulation results indicate that ground current in large scale PV installations can be considerable according to the values expressed in (IEEE Std. 80-2000, 2000). In the range of 9-25 mA range, currents may be painful at 50-60 Hz, but at 3-10 kHz are negligible (IEC 60479-2, 1987). Thus, the model allows the detection of capacitive discharge currents that

Because of large scale installations are systems with long cables, the resonant frequency becomes an important factor to consider when designing the AC filters and converters operation frequency. The proposed model accurately detects the expected resonant frequency of the PV installations at 12.0 kHz with an impedance magnitude Z of 323.33 while simplified models determine a less severe resonant at a frequency value of 15.50 kHz

This latter resonant frequency is misleading and pointless for the real operating parameters of the installation. The total DC/AC conversion losses obtained from simulations is 5.6% when operating at rated power, which is equivalent to 56.00 kW. Through the proposed model, it has been detected that a 22.32% of the losses due to the DC/AC conversion is

array and grounding system and (b) FFT analysis of the voltage waveform obtained.

exceeds the threshold of safety values at work.

with a Z of 150.45 , as shown in Fig. 5.

The frequency response of both capacitive coupling and simplified model for the DC circuit of a PV installation operating at nominal operating condition is shown in the Bode diagram of Fig. 3. The capacitive coupling model presents a considerable gain for waveforms under 108 kHz in comparison with the simplified model which has a limited gain for this range of frequencies. Hence, the capacitive coupling model is able to simulate the leakage loop between PV module and grounding system for high frequencies, unlike the simplified model.

Fig. 3. Bode diagram for both capacitive coupling model (solid line) and simplified model (dashed line) for the DC circuit of a PV installation.

The PV installation modelled consists of 184 PV arrays connected in parallel to generate 1 MW. Both circuits have been modelled to analyze the mutual effect raised from the capacitive couplings between the electric circuits and the grounding system, at rated operating conditions. The simulation has been performed using PSCAD/EMTDC [PSCAD, 2006] with a sampling time of at least 20 µs.

The current and voltage waveforms obtained from the proposed model together with the FFT analysis are shown in Fig. 4a and Fig. 4b. The THDI and THDV obtained from simulations are 26.99% and 3725.17%, respectively, where the DC fundamental component of current is 88.56 mA, and the fundamental voltage component is 8.59 V. The frequencies where most considerable harmonic magnitudes are the same of those obtained at field measurement; 3.70 kHz, 11.10 kHz, 14.80 kHz and 18.50 kHz within a percentage error of ±27.42% for fundamental component and ±15.35% for the rest of harmonic components.

#### **2.3 Additional information provided by the PV installation capacitive coupling**

The model considering capacitive coupling between PV modules and grounding system of the installation leads to an accurate approximation to the response of the PV installation against the frequency spectrum imposed by the switching action of the inverters. This approximation is not feasible using simplified models because of the bandwidth limitation shown in Fig. 3 for high frequencies.

The frequency response of both capacitive coupling and simplified model for the DC circuit of a PV installation operating at nominal operating condition is shown in the Bode diagram of Fig. 3. The capacitive coupling model presents a considerable gain for waveforms under 108 kHz in comparison with the simplified model which has a limited gain for this range of frequencies. Hence, the capacitive coupling model is able to simulate the leakage loop between

PV module and grounding system for high frequencies, unlike the simplified model.

Fig. 3. Bode diagram for both capacitive coupling model (solid line) and simplified model

The PV installation modelled consists of 184 PV arrays connected in parallel to generate 1 MW. Both circuits have been modelled to analyze the mutual effect raised from the capacitive couplings between the electric circuits and the grounding system, at rated operating conditions. The simulation has been performed using PSCAD/EMTDC [PSCAD,

The current and voltage waveforms obtained from the proposed model together with the FFT analysis are shown in Fig. 4a and Fig. 4b. The THDI and THDV obtained from simulations are 26.99% and 3725.17%, respectively, where the DC fundamental component of current is 88.56 mA, and the fundamental voltage component is 8.59 V. The frequencies where most considerable harmonic magnitudes are the same of those obtained at field measurement; 3.70 kHz, 11.10 kHz, 14.80 kHz and 18.50 kHz within a percentage error of ±27.42% for fundamental component and ±15.35% for the rest of

**2.3 Additional information provided by the PV installation capacitive coupling** 

The model considering capacitive coupling between PV modules and grounding system of the installation leads to an accurate approximation to the response of the PV installation against the frequency spectrum imposed by the switching action of the inverters. This approximation is not feasible using simplified models because of the bandwidth limitation

(dashed line) for the DC circuit of a PV installation.

2006] with a sampling time of at least 20 µs.

harmonic components.

shown in Fig. 3 for high frequencies.

Fig. 4. Simulation result of the capacitive coupling model: (a) voltage waveform between PV array and grounding system and (b) FFT analysis of the voltage waveform obtained.

Simulation results indicate that ground current in large scale PV installations can be considerable according to the values expressed in (IEEE Std. 80-2000, 2000). In the range of 9-25 mA range, currents may be painful at 50-60 Hz, but at 3-10 kHz are negligible (IEC 60479-2, 1987). Thus, the model allows the detection of capacitive discharge currents that exceeds the threshold of safety values at work.

Because of large scale installations are systems with long cables, the resonant frequency becomes an important factor to consider when designing the AC filters and converters operation frequency. The proposed model accurately detects the expected resonant frequency of the PV installations at 12.0 kHz with an impedance magnitude Z of 323.33 while simplified models determine a less severe resonant at a frequency value of 15.50 kHz with a Z of 150.45 , as shown in Fig. 5.

This latter resonant frequency is misleading and pointless for the real operating parameters of the installation. The total DC/AC conversion losses obtained from simulations is 5.6% when operating at rated power, which is equivalent to 56.00 kW. Through the proposed model, it has been detected that a 22.32% of the losses due to the DC/AC conversion is

Harmonic Distortion in Renewable Energy Systems: Capacitive Couplings 269

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

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,

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

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

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

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

leading to harmonic voltages in the network (Conroy & Watson, 2009).

the grid through a full-scale frequency converter.

coupling model of wind farms is shown in Fig. 7.

Fig. 7. Capacitive coupling model for wind farm.

coupling model is shown in Fig. 8.

the wind farm under study.

components.

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 PV modules and ground.

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