Simple Technique Reducing Leakage Current for H-Bridge Converter in Transformerless Photovoltaic Generation

Abstract

Given their structural arrangement, photovoltaic (PV) modules exhibit parasitic capacitance, which creates a path for high-frequency current during zero-state switching of the converter in transformerless systems. This current has to be limited to ensure safety and electromagnetic compatibility. Many solutions that can minimize or completely avoid this phenomenon, are available. However, most of these solutions are patented because they rely on specific and often complex converter topologies. This study aims to solve this problem by introducing a solution based on a classic converter topology with an appropriate modulation technique and passive filtering. A 5.5 kW single-phase residential PV system that consists of DC-DC boost stage and DC-AC H-bridge converter is considered. Control schemes for both converter stages are presented. An overview of existing modulation techniques for H-bridge converter is provided, and a modification of hybrid modulation is proposed. A system prototype is built for the experimental verification. As shown in the study, with simple filtering and proper selection of switching states, achieving low leakage current level is possible while maintaining high converter efficiency and required energy quality.

I. INTRODUCTION

Photovoltaic (PV) modules are the structural basic unit for PV systems, comprised of PV cells. Modules can be connected in series and in parallel to form large structures called PV arrays. This feature allows the development of scalable systems, from small-scale domestic applications ranging from a few kilowatts to large-scale power plants with capacities in orders of tens to hundreds of megawatts. The first category is especially popular because of the declining costs of installation and system components. Government support in the form of subsidies and green tariffs has driven development in many countries. This process initiated an ongoing growth in the field of PV power converters. Many new solutions emerged, including converter topologies, monitoring systems, and control algorithms. Power converters for PV applications have become a dedicated group with many specific functions integrated in their control structures. Well-established and inherently embedded features, such as maximum power point tracking (MPPT), anti-islanding, ride-through grid disturbances, current harmonics compensation, and advanced synchronization, were either developed or highly improved. Efficient energy processing is the most important design criteria in every energy conversion stage because of the relatively low efficiency of modules (between 14% and 18% for commercially available polycrystalline modules). Therefore, minimizing the number of these stages has become reasonable by considering highly efficient systems has become reasonable. Initially, this process was performed mostly by eliminating the low-frequency transformer, which, despite providing galvanic isolation and voltage level adjustment, is characterized by high cost and relatively low energy density. The introduction of high-frequency transformers with a much higher energy density was inevitably associated with the addition of a DC-DC conversion stage with numerous passive and active components. Therefore, transformerless systems, with their primary design guideline, became popular. Transformerless systems demonstrate reduced cost and size compared with conventional systems. However, major issues exist with regard to the operation of such systems. First, lack of galvanic isolation of these systems imposes some concerns about safety issues. Unfortunately, PV modules exhibit non-negligible parasitic capacitance, which is formed between the module substrate and its grounded frame. For transformerless systems, this phenomenon creates a capacitive link between the grid and the PV modules, which can provide a path for high-frequency current component formed by the switching action of the converter. This current closes its path through the ground, thereby compromising human safety and causing additional electromagnetic interference problems [1], [2]. Second, the lack of galvanic isolation allows a DC current component to be injected to the grid, which is limited or restricted in many grid codes [3].

In the following sections, problems related to the operation of transformerless converters are explained. Subsequently, a novel technique for minimizing the leakage current phenomena is presented, and experimental verification is provided.

 

II. COMMON-MODE VOLTAGE AND CURRENT

Common-mode voltage vCM is defined as the mean value of converter terminal voltages vA0 and vB0, i.e., voltages of each leg referenced to the negative DC terminal (see Fig. 1), which for single-phase converters is equal to:

Fig. 1.Grid-connected H-bridge converter.

To obtain high efficiency, a modulation scheme that allows unipolar switching (i.e., adopting zero-voltage states) has to be utilized. However, if zero-voltage states are applied in the pulse-width modulation (PWM) scheme, converter terminals become effectively shortened for a fraction of a switching period, thus introducing unwanted vCM variations. A variation is not an issue, unless a galvanic connection between PV array and the grid exists, which is the case for transformerless systems.

PV modules generally consist of the encapsulated semiconductor structure and aluminum grounded frame. Such arrangement naturally creates capacitance CPV between these elements and ground, which varies significantly with environmental conditions, particularly humidity of the modules. The values are usually expressed relative to array power and can range from several nF/kW up to few μF/kW [4], [5]. The current that flows in the presence of this capacitance is called common-mode current iCM or leakage current. Its path goes through the PV module, ground connection, and converter output filter (Fig. 1). Common-mode current iCM introduces electromagnetic interference, grid current, distortion, and potential electric hazards. Leakage current is also caused by grid voltage variations; however, because of its low frequency (relative to the switching frequency), its value becomes insignificant. Leakage current phenomena can be modeled as follows: Given that differential voltage of the converter is equal, then

and by neglecting the grid voltage contribution to the leakage current, terminal voltages vA0 and vB0 can be expressed in terms of vCM and vDM as

and

This corresponds to the converter representation shown in Fig. 2(a). Assuming equal inductor values in both converter legs (balanced system), the differential voltage has no effect on the leakage current. Therefore, the converter can be modeled as shown in Fig. 2(b). Reducing the value of the leakage current to an acceptable limit requires minimizing the common-mode voltage variation during the switching period of the converter. The vCM waveform depends on the modulation schemes and the value of DC-link voltage VDC.

Fig. 2.Simplified converter model for leakage current analysis.

Several methods can be employed to minimize this problem. The simplest one is to adopt a modulation technique that does not allow for any zero-voltage states. Unfortunately, using this method decreases efficiency and increases the size of a grid-side filter. The second method involves disconnecting the converter from the PV array (either on the DC or AC side) during zero-voltage states [6], [7]. In this manner, the common-mode voltage still varies, but a path for leakage current flow does not exist. This solution implies utilizing additional switches, but it has been widely adopted for transformerless PV topologies by many power electronics companies [3], [7]. The three most commonly recognized topologies are H5 by SMA, HERIC by Sunways, and FB-DCBP by Ingeteam. These solutions are difficult to implement in new products because of existing patents. Moreover, as shown in [8], some topologies with additional bypass switches may also cause vCM variations during low-voltage ride-through (LVRT) operation, which has recently become of interest for PV systems.

Another solution is to change the topology of the DC-AC converter from classical H-bridge to half-bridge diode clamped topology because of their fixed connection between PV array and ground. The half-bridge diode clamped topology does not require any additional elements but needs at least two times higher DC-link voltage to operate normally.

 

III. PROPOSED SYSTEM

Another approach has been taken to avoid restrictions related to the abovementioned topologies. It focuses on modulation techniques that reduce CM voltage variations for the converter rather than techniques that modify the existing topology itself. In addition, small common-mode filters are necessary to maintain a low RMS value of the leakage current below 300 mA (limit set according to VDE0126-1-1 standard). In addition to minimizing the leakage current, the PV converter has to fulfill many important requirements to be suitable for high-performance industrial applications. The most desirable features can be depicted as [9].

A. Power Circuit

The power stage of the proposed 5.5-kW system is shown in Fig. 3. The system consists of DC-DC (boost topology) and DC-AC (H-bridge) converters, which are considered simple, robust, and relatively cheap. A diode bypassing DC-DC stage is adopted to conduct a current in case the PV voltage exceeds the DC-link voltage. Moreover, the power circuit of the converter was extended with two additional common-mode filters [10], which are necessary to limit the maximum value and slew rate of a leakage current. Common-mode inductive filter Lcm is placed at the input stage of the boost converter. It limits the slew rate of a leakage current, and it turn reduces its RMS value. The second filter is composed of two capacitor banks at the output stage of the H-bridge. Each bank is connected between two legs and corresponding DC terminals (positive or negative), which results in four additional capacitors: CA-, CA+, CB-, and CB+. The role of these capacitors is to close the path for a leakage current during zero-voltage states of the converter. However, these capacitors create a resonant tank, along with line inductors Lline and parasitic capacitance, which may lead to oscillations when fast vCM change occurs, as will be shown in the next section.

Fig. 3.Proposed system with H-bridge and boost converters, common-mode filter, and modeled parasitic capacitance CPV.

B. Control Scheme of the DC-DC Converter

The boost converter control is responsible for the extraction of the maximum available power of the PV plant (Fig. 4). The structure is obtained by the MPPT algorithm, which properly references the converter input voltage (PV voltage). For this study, perturb and observe (P&O) algorithm was used because of its simplicity [11]-[14]. The sign of a new step in voltage is selected based on the measurement of the change in power and previous perturbation in the PV voltage, with respect to which this change occurred. To achieve improved dynamics and a small steady-state error, variable step size referencing was implemented, which is simply based on the rate of the change of power with respect to applied voltage step [15]. When an actual operating point is far from the maximum power point (MPP), even a small perturbation in voltage results in a large change in power (large dppv/dvpv).

Fig. 4.Control scheme for the DC-DC boost converter.

Therefore, a large step size can be set to reduce the time taken to achieve MPP. However, when dppv/dvpv is close to zero, no significant change in power will occur, and therefore, the step size is small, which reduces unnecessary oscillations and improves efficiency. Reference change in the PV voltage is realized by a PI controller, which provides a reference value for the inductor current. An inner-loop PI controller is responsible for maintaining the current by calculating a proper duty cycle for the converter switch.

C. Control Scheme of the DC-AC Converter

The control scheme for a DC-AC part, which is presented in Fig. 5, consists of two cascaded loops. The external voltage loop controls the power flow in the system by stabilizing the DC-link voltage. Reference DC-link voltage vDC* is compared with the measured vDC value. The vDC voltage is distorted by a 100-Hz AC oscillation. This oscillation distorts the DC-link voltage δvDC error signal because the vDC* has a constant DC value. The vDC PI regulator, which generates referenced grid current amplitude iline,max, cannot eliminate the phase error. Thus, to prevent the transmission of 100 Hz distortion on iline,max, a low-pass filter with 30 Hz cutoff frequency is applied to δvDC. The internal current loop is responsible for the system power quality by controlling the grid current. The unity power factor operation can be achieved if reference grid current iline* is in phase with line voltage vline. For this purpose, synchronization with vline is required. Among many methods [16], a phase-locked loop (PLL) based on second-order generalized integrator (SOGI) is utilized to generate vline angle θ [17]. The SOGI is used to generate an in-quadrature signal of vline required in a single-phase system to provide transformation into the synchronous reference frame. Reference grid current iline* is compared with measured iline, and error is delivered to the proportional multiresonant (PMR) controller [18,19]. The PMR is composed of proportional gain and resonant integrator.

where Kp and Ki are the gains for proportional and resonant part, respectively, ω is the vline fundamental frequency, and h is the odd harmonic order of iline. Such structure can track input phase-angle θ without a steady-state error with specified (e.g., 3rd, 5th, 7th, and 9th) higher current harmonics compensation by simply adding parallel connection—to the fundamental PR controller—resonant terms for specified hω frequencies.

Fig. 5.Control scheme for the H-bridge converter.

 

IV. MODULATION TECHNIQUES FOR THE H-BRIDGE CONVERTER

A. State of the Art

The PWM technique used to generate output voltage vAB of the converter highly influences its losses, quality of extracted energy, and, in a certain case, leakage current level. Three well-known modulation techniques for the H-bridge converter are described below to perform a comparative study. With no additional filtering, only bipolar PWM is suitable for the transformerless PV systems, but at the expense of efficiency. Next, an improvement in the hybrid modulation is presented, which ensures unipolar change in common-mode voltage vCM (either from 0 to VDC/2 or from VDC/2 to VDC). Thus, icm current reduction occurs, whereas high current spikes and oscillations generated in the presence of passive filters are avoided. Taking into consideration data sheet parameters for particular transistor and diode (see Section V for details) a per-unit switching loss calculation is also provided. Calculations were performed only for a relative loss evaluation, and detailed values are not shown. Power losses were calculated across only one switching period with a bipolar PWM set, which is the base for the comparison. Results are summarized in Table I.

TABLE IPWM TECHNIQUE COMPARISON

1) Bipolar PWM: The scheme of the basic switching technique for the H-bridge converter is shown in Fig. 6. Switch pairs SA1, SB2, SA2, and SB1 are controlled in a complementary fashion. Therefore, two output voltage vconv levels can be obtained: -VDC and +VDC. The common-mode voltage is nearly constant because zero-voltage state does not exist. The common-mode voltage varies only with low frequency grid voltage, but neither these changes nor dead-time influence are considered in this paper. The RMS value of leakage current icm is very low. The turn-on sequence for the positive line voltage can be presented as DA2+DB1, SA1+SB2, and DA2+DB1, where letter D denotes a freewheeling diode. Unfortunately, because of bipolar switching, this scheme imposes high voltage stress and high inductor current ripple, which is associated with additional losses.

Fig. 6.Switching states and common-mode voltage vCM waveform for the bipolar modulation (switching states SA2 and SB2 are negations of SA1 and SB1, respectively).

2) Unipolar PWM: Setting a reference signal for every converter leg independently and with 180° phase shift results in a zero-voltage state in the middle of each switching period, which, in turn, results in unipolar transition between “active” states that correspond to three values of converter output voltage vconv: -VDC, 0, and +VDC. Hence, switching frequency is effectively doubled. Unipolar switching also reduces dv/dt stress on the system. Both features reduce the size of the filtering components. In terms of the turn-on sequence, i.e., DA2+SB2, SA1+SB2, SA1+DB1, SA1+SB2, DA2+SB2, the switching losses are the same as in the bipolar modulation (Psw =1 pu). Although more transitions per switching period exist, only one device changes state in each of them. Therefore, the effective number of switching becomes the same. Despite having natural advantages over bipolar modulation, this scheme is far less suitable for any transformerless PV application because every switching action is “mirrored” in the vCM voltage, which changes between 0, VDC/2, and VDC, as shown in Fig. 7. This phenomenon causes high icm current to flow, which disqualifies unipolar PWM from this application.

Fig. 7.Switching states and common-mode voltage vCM waveform for unipolar modulation (switching states SA2 and SB2 are negations of SA1 and SB1, respectively).

3) Conventional Hybrid PWM: The idea of hybrid modulation is based on switching both legs independently and with different frequencies. The first leg is modulated with low fundamental grid frequency, whereas the second leg operates with the normal high switching frequency. Similar to the unipolar scheme, three voltage levels can be obtained. In terms of the switching pattern (Fig. 8), turn-on sequence DA2+SB2, SA1+SB2, DA2+SB2 is similar to the unipolar modulation, except for the lack of the zero-voltage state in the middle of a switching period. The switches of leg B change their state every half-cycle of the line voltage. For this reason, switch losses are two times lower (Psw=0.5 pu) than that of previous schemes. The common-mode voltage also varies between 0, VDC/2, and VDC but with superimposed square-shape waveform with the frequency of the vline voltage (50 Hz in this case). Very fast voltage changes every half of the cycle result in high current spikes combined with large oscillations because of the LC resonant tank formed both by filtering components and parasitic capacitance of a PV array. Therefore, this technique also cannot be utilized in a transformerless system.

Fig. 8.Switching states and common-mode voltage vCM waveform for the conventional hybrid modulation (switching states SA2 and SB2 are negations of SA1 and SB1, respectively).

B. Modification of a Hybrid PWM

As discussed in the previous section, none of the modulation techniques can be suitably used in simple transformerless PV applications. Despite constant vCM, bipolar modulation results in poor efficiency because of high switching losses and grid-side filtering requirements. Unipolar modulation exhibits very strong variations in vCM. Hybrid modulation seems to be most promising because of the lowest switching losses. However, the 50 Hz square waveform vCM induces large oscillations both in line and leakage current. To minimize large spikes generated every half of a line voltage period, a modification has been introduced into a hybrid modulation switching pattern. Unlike in the conventional technique, only one zero-voltage state is used during the converter operation (Fig. 9). In practical implementation, the operation interchanges the switching patterns between fast- and slow-switching legs in the converter depending on the line voltage sign. In other words, every half-cycle of the line voltage, high-frequency switching is assigned from one converter leg to another. Thus, only transitions from 0 to VDC/2 are present in the vCM voltage waveform.

Fig. 9.Switching states and common-mode voltage vCM waveform for the proposed hybrid modulation (switching states SA2 and SB2 are negations of SA1 and SB1, respectively).

No square-shaped waveform is generated; thus, high current spikes and oscillations are avoided and stable operation is assured. The switching pattern for a positive line voltage is exactly the same, i.e., DA2+SB2, SA1+SB2, and DA2+SB2. Total power losses in the semiconductor devices remain unchanged. Nevertheless, the overall efficiency of the converter is increased because of the absence of unwanted oscillations.

 

V. EXPERIMENTAL STUDY

To verify the behavior of the proposed system, experimental results were obtained with the prototype model of the converter system, as shown in Fig. 10. Instead of the PV array, the DC power supply with both voltage and current control capability was utilized. Parasitic capacitance was modeled by a branch of 15 nF/kW capacitors connected between the DC power supply negative terminal and neutral leg of the converter. The prototype contains the following: integrated DC-DC and DC-AC converters, common-mode filters, leakage current monitoring sensor, and control board based on Texas Instruments DSP TMS320F28069. The switches in both converters are Fairchild IGBTs FGH75T65UPD (650 V, 75 A). The most important parameters of the system are listed in Table II. The entire setup was developed and tested in ZE TWERD power electronics company and is now commercially available in the power range of 2–5.5 kW. Aside from leakage current measurement, converter efficiency and THD of line current were obtained. Total converter efficiency was measured with a Yokogawa WT1806 High-Performance Power Analyzer at nominal power of 5.5 kW. Every modulation scheme described in the previous section was tested using the same filtering elements. Sampling frequency was set to 16 kHz, which, in case of unipolar modulation, implies that the effective switching frequency was 32 kHz. Figures 11-14 show grid-connected operation of the converter with leakage current iCM and voltage measured on a parasitic capacitance vc. Detailed values obtained for every modulation scheme are shown in Table III. The leakage current has the lowest value for bipolar modulation because of nearly constant common-mode voltage vCM (Fig. 11).

Fig. 10.System prototype: boost converter (2 strings)+ H-bridge converter: 1- TMS320F28069 board with control panel; 2- input filter; 3- boost converter inductors; 4- output filter; and 5- RFI filter.

TABLE IISYSTEM PARAMETERS

TABLE III.Icm,RMS: RMS value of leakage current iCM,, converter efficiency η, and THD of line current iline. * Value obtained with resonance occurring (Fig. 11)

Fig. 11.Grid-connected operation with bipolar modulation: line voltage vline, line current iline, leakage current iCM, and voltage across parasitic capacitance vc.

Unipolar modulation generates vCM variations, thereby resulting in the highest iCM value (Fig. 12). However, because common-mode filters are employed, both PWM techniques result in iCM values that are below the limit set in VDE0126-1-1. In conventional hybrid modulation (Fig. 13), 50 Hz changes superimposed on vCM result in large iCM current spikes and oscillations every half cycle of the line. Therefore, its RMS value is much higher compared with the other techniques. For the same reason, efficiency and THD measurements were considered unreliable.

Fig. 12.Converter operation with unipolar modulation: line voltage vline, line current iline, leakage current iCM, and voltage across parasitic capacitance vc.

Fig. 13.Converter operation with conventional hybrid modulation: line voltage vline, line current iline, leakage current iCM, and voltage across parasitic capacitance vc.

As shown in Fig. 14, the leakage current of the proposed modulation technique is smaller than that of the unipolar and conventional hybrid modulations. Parasitic capacitance voltage vc for the proposed modulation techniques exhibit a half-wave shape that corresponds to only one zero-voltage state utilized for operation. The proposed hybrid PWM has two major advantages over other PWM schemes. First, it eliminates the oscillation problem. Therefore, it is applicable to the system while maintaining its most important feature: its high efficiency. Second, it allows for approximately 30% reduction of iCM compared with the unipolar PWM. Finally, the THD of the line current for the proposed modulation was less than 5%, and efficiency was above 97%, which served as the main criteria for the system design.

Fig. 14.Converter operation with the proposed hybrid modulation: line voltage vline, line current iline, leakage current iCM, and voltage across parasitic capacitance vc.

 

VI. CONCLUSION

A simple technique that reduces leakage current in a highly efficient converter for PV generation has been described in this paper. Both goals of this study are achieved by employing an appropriate hybrid modulation that reduces switching losses and by adding common-mode filters at the DC and AC sides of the system, which reduces the leakage current value well below limits set by the VDE0126-1-1 standard. For conventional hybrid PWM, these filters create a resonant tank with other system components, thus practically eliminating the errors from such application. Simple modification in the hybrid PWM technique solves the aforementioned problem and results in additional decrease in leakage current. Most importantly, without modifying the converter topology and violating existing patents, low leakage current and THD of the line current are obtained, which is a significant advantage of the proposed system.