Harmonic Distortion in Renewable Energy Systems: Capacitive Couplings

Renewable energy systems such as wind farms and solar photovoltaic (PV) installations are being considered as a promising generation sources to cover the continuous augment demand of energy. With the incoming high penetration of distributed generation (DG), both electric utilities and end users of electric power are becoming increasingly concerned about the quality of electric network (Dugan et al., 2002). This latter issue is an umbrella concept for a multitude of individual types of power system disturbances. A particular issue that falls under this umbrella is the capacitive coupling with grounding systems, which become significant because of the high-frequency current imposed by power converters. The major reasons for being concerned about capacitive couplings are: a. Increase the harmonics and, thus, power (converters) losses in both utility and customer equipment. b. Ground capacitive currents may cause malfunctioning of sensitive load and control devices. c. The circulation of capacitive currents through power equipments can provoke a reduction of their lifetime and limits the power capability. d. Ground potential rise due to capacitive ground currents can represent unsafe conditions for working along the installation or electric network. e. Electromagnetic interference in communication systems and metering infrastructure. For these reasons, it has been noticed the importance of modelling renewable energy installations considering capacitive coupling with the grounding system and thereby accurately simulate the DC and AC components of the current waveform measured in the electric network. Introducing DG systems in modern distribution networks may magnify the problem of ground capacitive couplings. This is because DG is interfaced with the electric network via power electronic devices such as inverters. These capacitive couplings are part of the electric circuit consisting of the wind generator, PV arrays, AC filter elements and the grid impedance, and its effect is being appreciated in most large scale DG plants along the electric network (García-Gracia et al., 2010).


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.

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.
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.

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: where I o is the diode saturation current, V the terminal voltage of a module, n the ideal constant of diode, V T 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. I sc is the short circuit current of a module under a given solar irradiance. I d is the diode current, which can be given by the classical diode current expression. The series resistance R s represents the intrinsic resistance to the current flow. The capacitive coupling of PV modules with the ground is modelled as a parallel resistance R pv and capacitor C pv 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 R g . 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 R ac_cable , L ac_cable and C ac_cable are the resistance, inductance and capacitance of the AC underground cables, R g_es is the ground resistance at the substation and L filter and C filter are the parameters of the LC filter connected at AC terminals of the inverter. The inclusion of R pv and C pv 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 1 12 According to the equivalent DC circuit shown in Fig. 2, i 1 (t) and i 2 (t) are the current of mesh 1 and mesh 2, respectively, v in (t) is the injected voltage by the converter, v 2 (t) the voltage at node 2 and v pv (t) is the voltage between PV module and ground and represents the parameter under study. Parameter C c represents the capacitive coupling between cables and ground and R c and L c are the resistance and inductance of the cable, respectively. In some simplified models of PV installation (Villalva, 2009, Kim, 2009, Bellini, 2009, the capacitance C pv and resistance R pv 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 (R g = 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  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. 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

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. 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 www.intechopen.com

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. 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. 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 R WG and L WG make reference to the resistance and inductance, respectively, of the synchronous wind generator. R g is the ground resistance at the wind turbine location while R q_es is the ground resistance of the electrical substation belonging to the wind farm under study.
C rectifier and C ac_cable are the capacitive couplings of the rectifier side and underground cable, respectively, with ground. R ac_cable and L ac_cable make reference to the resistance and inductance, respectively, of the synchronous wind generator. L filter and C filter are the dimensions of the filter. L TR is the equivalent impedance of the power transformer and L source the thevenin impedance of the source. The variables v WT (t) and v source (t) are the voltages at wind generator node and network grid source, respectively. The input voltage v in (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 v in (t) and the network grid v source (t) are the following   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 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 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(IEEE 80- , 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. www.intechopen.com

Impact on distribution networks of DG ground current contribution
The distribution network considering DG, shown in Fig. 12, has been modelled to analyze the effects of wind farms and PV solar installations ground current contribution to the network. The DG is based on capacitive coupling models of a 1 MW PV solar installation and a 1.4 MW wind farm with the electric parameters shown in Table 1 and Table 2, respectively. This distribution network feeds two loads through a multi-terminal ring topology. These loads are connected to bus 2 and 5 with a rated power of 500+ j 25 kVA each one. In steady state conditions, the wind farm generates a total active power of 1370 kW, and the PV solar installation delivered 940 kW to the distribution network. To analyse the capacitive coupling effect over the ground current in DG systems, it has been noticed the voltage and current waveforms seen at node 5 through the capacitive coupling of the line.  Table 3. Electric parameters of the network grid.
In node 5, the phase voltage waveform meets the standard regulation of harmonic distortion (THD=5.4%) with a fundamental component of 8.72 kV, as shown in Fig. 13. Although voltage waveform meets standard regulations, it has been observed an important ground current contribution through the admittance of the underground cables. The ground voltage waveform has a considerable magnitude with peaks reaching 7 V, as shown in Fig. 14. Likewise, the ground current measurement due to the capacitive coupling of these underground cables is also significant as shown in Fig. 15  These observations point to the importance of controlling the capacitive coupling in load installations connected to networks with DG. Otherwise, end users equipments can be exposed to malfunctioning and lifetime reduction due to the capacitive ground current. Moreover, GPR can reach values of unsafe work conditions.

Conclusions
The capacitive coupling models lead to an accurate approximation to the response of distribution network against the frequency spectrum imposed by the switching action of the converters at DG. This approximation is not feasible using simplified models because of the bandwidth limitation for high frequencies.
According to the distribution network under study, a high ground current contribution to grid provided by DG has been detected. Therefore, some preventive actions can be applied to network design stage in order to solve this problem, such as: -Connection of the PV array to the grounding systems by means of an inductor. The latter element represents high impedance for harmonics current and subsequently reduces the capacitive ground current in the installation. -Insertion of capacitors between the DC terminals and ground avoids the injection of harmonic current to the PV array, as shown in Fig. 13b, and thereby the noise level and GPR between PV modules and ground is minimized. -Adjustment of the firing pulses frequencies and control strategies to reduce or avoid resonance and capacitive currents by analyzing the ground current with the proposed model. -Insertion of high-pass filters on the distribution network to avoid end users equipments to be exposed to a high amount of ground current.