# On the Reliability of Transformerless Photovoltaic DC/AC Converters Based on Mission Profile

Authors: Ignacio Villanueva; Nimrod Vazquez; Joaquín Vaquero; Claudia Hernández; Héctor López; Rene Osorio; Sergio Pinto
Journal: International Journal of Photoenergy
 (2021)

---

## Abstract

Photovoltaic systems are a technology for the generation of electrical energy that is constantly increasing thanks to current technological advances and that contributes to sustainable development. The main stages of photovoltaic systems are the conversion stage, using an inverter, and filtering. These systems may be considered as a mature and growing technology; however, regarding its reliability, there exists some uncertainties, and they are related to the operation, incidents, and its potential failures, due to the number of elements, the environment, and the operating nominal values. For this reason, this article presents a comparative analysis of the reliability of single-phase transformerless photovoltaic inverters used to inject active power into the grid. This evaluation is carried out under the same design specifications for all the inverters analyzed; the study is made using a mission profile considering the IEC TR 62380 standard, where the events and environmental operating conditions are defined, and numerical simulations. This work is aimed at providing suggestions to improve the quality of the photovoltaic system also considering reliability.


---

## Body

## 1. Introduction

Energy is an essential part of the technological and economic development of countries and regions worldwide. The constant increment in the demand and price of energy in industrialized countries has gradually led to the substitution of fossil fuels for the use of alternative energies. The higher use of those energies, mainly wind and solar photovoltaic, brings favorable effects on the environment, such as the reduction of greenhouse gases and other types of pollutants [1–4].The great number of advantages that this type of energy presents is remarkable. However, the way in which energy is produced has certain technical disadvantages, such as dependent on climatic conditions, which implies a deficiency in energy production [3–5].Nowadays, environmentally friendly energies have been developed but with some drawbacks such as high penetration, which causes certain problems within the electrical grid, such as voltage variations. The control of those systems is very complex; therefore, the useful life and reliability of photovoltaic systems are becoming important factors [5–7].Advances in power electronics have allowed the application of transformerless inverters, used in photovoltaic systems. They have good efficiency, low volume, and lightweight. These topologies are operated to not generate a common-mode voltage in order to avoid the generation of leakage currents between the photovoltaic module and the ground. The evolution of these systems brings with it the optimization and improvement of the semiconductors that make up the system, such as higher voltages and nominal powers, best efficiencies, higher thermal resistance, higher reliability, and lower cost [5–8].The reliability of semiconductors and capacitors is affected by operating temperature. Therefore, the system losses could lead to a failure in the semiconductor devices, such as MOSFETs and filter capacitors. The set of operating environmental conditions of a system during its useful life is called the mission profile. It is very important to design a real field mission profile, under which the system will be operating. In this way, its reliability and service life can be guaranteed; that is, the system should be designed for an environment with conditions similar to those that would be operating normally [9, 10].The most recent studies of reliability prediction are based on the design of the mission profile, where the phases, events, and operating environments define the mission [10, 11]. In [12], the authors calculate the converter reliability using different prototypes and semiconductors by using the IEC TR 62380 standard, taking into account an annual mission profile and the effect of extreme thermal cycles in a desert area. The authors of [13] present tools for the design of the safe operation mission profile for photovoltaic inverters connected to the grid with LCL filter, based on silicon carbide devices, including electrothermal models to predict junction temperature of the device case. In [14], it is evaluated the reliability of three transformerless inverters under an annual mission profile, taking into account the thermal load of the device, which is used for the prediction of the useful life, providing new ways for the design of photovoltaic systems.In this paper, the reliability analysis of different single-phase transformerless photovoltaic inverters is made, including an LCL filter. In each inverter, the reliability prediction is calculated using the model of French Telecommunications standard IEC TR 62380. The study considers simulations using the PSIM software for the different transformerless LCL inverter topologies. The objective is to determine what single-phase inverter topology presents the best reliability, based on the effects of the mission profile during a period. A discussion is presented on which topology is recommended based on its longevity, and comments are provided on the factors that influence failure rates, how to improve efficiency, reliability, and useful life of the photovoltaic system.The article is organized as follows: A background on transformerless photovoltaic inverters is presented, the IEC TR 62380 reliability standard is described, and the design and simulations are shown. Subsequently, a quantitative analysis of the reliability employing the standard is determined, the results are also analyzed, and finally, some conclusions are presented.


## 2. Photovoltaic Inverters and Reliability

In this section, the single-phase photovoltaic inverters, the mission profile, and the IEC TR 62380 standard are addressed to provide the basis for the employed PV converters and reliability analysis considering the mission profile.


### 2.1. Photovoltaic Inverters

The single-phase inverters used for active power injection may use a transformer, which allows to protect and avoid leakage currents between the photovoltaic system to the ground [15]. The advantage of connecting the inverter with a low-frequency transformer is galvanic isolation between the input and the output, but it has disadvantages such as its low efficiency and big size [5]. Another part of the system is the passive elements of the output filter. The most common configurations are L, LC, and LCL filters; the latter being the one that has the advantage of smallest size and highest efficiency.To increase the efficiency and reduce the volume, a transformerless topology may be employed; however, a high leakage current may appear [16, 17]. There are different strategies to reduce the leakage current in transformerless photovoltaic inverters connected to the electrical grid.One strategy is to use a modulation technique that does not generate common-mode voltage variations.The full-bridge inverter (Figure1) is one of the simplest inverters. Consists of four switches organized in two legs, the first formed by S1 and S2 and the second by S3 and S4. This configuration has four switching states and three different output voltage levels. Two PWM modulation schemes may be employed: bipolar and unipolar modulations [6, 15, 16, 18] and [19]. The unipolar modulation is not good to avoid common-mode voltage, and the bipolar modulation should be preferred. However, in this case, a disdvantage is the incresed size of the output filter.Figure 1
Full-bridge inverter.The dual buck inverter (Figure2), based on the full-bridge topology, combines two unidirectional buck converters during the positive half cycle, S1 switching at high frequency, while S4 is always on. During the negative half-cycle, S2 switches at high frequency, while S3 is always on. This produces a unipolar modulation. According to the literature, one of the advantages is the high reliability; due to the diodes connected in series to the inductor, there are no tripping problems and reverse recovery issues [4, 15], and [20].Figure 2
Dual buck inverter.Another technique used to reduce the leakage current is the disconnection of the photovoltaic module but keeping the unipolar modulation. In this case, switches are added on the DC or AC side of the inverter to disconnect the photovoltaic module from the grid and to create new routes to reduce the leakage current.H5 topology (Figure3) is based on the full-bridge topology; a switch is added on the DC side. The operation is similar to that of the full-bridge inverter, but adding switch S5, its main function is to decouple the DC side from the AC side. Switches S1 and S3 commute at grid frequency, switch S2 switches only in the negative half cycle, and switch S4 only switches in the positive half cycle. Unipolar modulation is obtained and allows to reduce the leakage current [15, 18], and [19].Figure 3
H5 inverter.The HERIC topology (Figure4) is derived from the full-bridge converter; however, a branch is added on the AC side in parallel to the bridge output, to isolate the PV panel from the grid. The switches S1, S2, S3, and S4 switch at high frequency; normally MOSFETs are used and S5 and S6 at grid frequency; regularly IGBT’s are used. It integrates the advantages of unipolar PWM modulation and reduces the leakage current of the solar panel [15, 18], and [19].Figure 4
HERIC inverter.The H6 configuration (Figure5) is based on the traditional full bridge as well, adding two switches and two diodes. For the operation, a unipolar modulation is considered, where the switches S1, S2, S5, and S6 are switched at high frequency and MOSFETs are regularly used. Switches S3 and S4 switch at grid frequency; IGBTs are generally used and provide a current path with diodes D1 and D2. During the free conduction time, during the positive half cycle, the current flows through S4 and the diode D1 allowing the disconnection between the photovoltaic module and the grid [4, 15], and [18].Figure 5
H6 inverter.Another alternative to reduce the leakage current is connecting the grid neutral point to the average input voltage, which eliminates variations in high frequency. The Neutral-Point Clamped (NPC) inverter fits in this category (Figure6). It is composed of four switches; since two switches are added to the half-bridge inverter, the DC terminals are connected to two capacitors in series, which divide the panel voltage, providing a common or neutral point. The topology has two diodes connected to the neutral point. A unipolar modulation is used, and the output voltage has three levels [4, 6, 18], and [19].Figure 6
NPC inverter.Instead of connecting the grid neutral point to the average input voltage, the connection to the negative terminal of the PV panel can be made. The virtual DC bus topology considers this strategy (Figure7); it is derived from the full-bridge topology and consists of five switches S1-S5. The photovoltaic panel and capacitor CDC1 form a real DC bus; the virtual DC bus is generated by CDC2. Capacitor CDC2 is charged through S1 and S3 to maintain a constant DC voltage. It can be controlled with a unipolar modulation [4, 15], and [21].Figure 7
Virtual DC bus inverter.


### 2.2. Mission Profile

A mission profile refers to define or represent certain characteristics or conditions of an operating environment. The mission profile is defined to reproduce the operating conditions of an electronic component set that represents the system to evaluate. That is, the environment, events, or phases of operation are defined (solar irradiance, temperature, operating time, among others), to which the components are subject during their life cycle and allows to evaluate reliability [9, 10].Reliability is the probability that a component will function properly during the period for which it was designed, under the specific operating conditions. The mission profile must be clearly defined, to avoid inaccuracies in the reliability calculation, which will cause errors in the final development of the system [15].The cases that are commonly used to define a mission profile based on a one-year cycle use component normal operation, like:(a)
On/off working phases with average outside temperatures(b)
Storage mode or inactive phases(c)
Permanent working phases with fluctuations in the average outside temperatureThe mission profile parameters are defined as follows. The total annual relationship of times must be defined, in the printed circuit board (PCB) which will be in permanent operation mode (energized). This is represented byτon as:
(1)τon=∑i=1yτi,whereτi is the total annual relation of times for the PCB, in permanent operation mode, with supply and at the external ambient temperature (tac) that surrounds the equipment during the ith phase of the mission profile taci.It is also important to define the total annual relationship of times for the PCB in storage or inactive mode of operation. This is represented byτoff:
(2)τoff=1−τon.Addingτon in both terms of (2) is obtained:
(3)τon+τoff=1.The other parameter of the mission profile that is defined is the internal temperature increase in the components of the PCB compared to (tac) during the τon phase, and it is represented by Δτi:
(4)Δτi=ΔTj3+taci−taei,where taci is the average ambient temperature of the PCB, close to the components (it is considered the most critical temperature), ni represents the annual number of thermal cycles seen by the components of the PCB in phase ith of the mission profile with a temperature variation, and Δτi is defined as the average oscillations of the variation seen by the components of the PCB in the phase of the mission profile ith [11–14, 21].


### 2.3. Standard IEC TR 62380 and Reliability Design

There are different standards used for reliability prediction based on the mission profile. One of the best used is the IEC TR 62380 standard, which is a French standard (Union Technique de L’Électricité, UTEC C 80-810), which is used for the prediction of the reliability of electronic components, PCBs, and equipment.In this standard, environmental factors are defined in the mission profile; the data contained in the standard is obtained from field data in different operating environments.The reliability model used by the IEC TR 62380 standard is based on a failure rate model to be adjusted for each component defined asλcomponent:
(5)λcomponent=λdie+λpackage,(6)λdie=λthermaleffects+λEOSeffects,whereλdie is the failure rate related to the effects in operation, λthermaleffects is the failure rate related to thermal effects, λEOSffects is the failure rate related to the effects of electrical overstress, and λpackage is the failure rate related to thermo-mechanical effects.Then, the model of the IEC TR 62380 standard is centered on the elements. In photovoltaic inverters, the main devices are the diode, the MOSFET, the capacitor, and the inductor.The general mathematical model for the fit failure rate obtained by combining (5) and (6) is
(7)λcomponent=λthermaleffects+λEOSeffects+λpackage.The general model (7) is used to adjust the failure rate of the components. Table 1 shows the factors and failure rates of adjustments from the general model, corresponding to the diode. The adjustment of the failure rate and factors of the MOSFET are shown in Table 2. The inductor failure rates are shown in Table 3. Finally, the failure rates of thermal and mechanical adjustments for the capacitor are shown in Table 4.Table 1
Adjustment failure rates for the diode.
λdiodeλthermaleffectsπU.λ0.∑i=1yπti.τi/τon+τoffλEOSeffects2.75E−3.∑i=1zπni.ΔTi0.68.λBλpackageπ1.λBTable 2
Adjustment failure rates for the MOSFET.
λMOSFETλthermaleffectsπS.λ0.∑i=1yπti.τi/τon+τoffλEOSeffects2.75E−3.∑i=1zπni.ΔTi0.68.λBλpackageπ1.λBTable 3
Adjustment failure rates for the inductor.
λinductorλthermaleffectsλ0.∑i=1yπti.τi/τon+τoffλEOSeffects7E−3.∑i=1jπni.ΔTi0.68Table 4
Adjustment failure rates for the capacitor.
λcapacitorλthermaleffects0.1.∑i=1yπti.τi/τon+τoffλEOSeffects1.4E−3.∑i=1jπni.ΔTi0.68The parameters of Tables1–4 are defined as follows:λ0 is the base failure rate given in the standardλB is the base failure rate of the component packagingλEOS is the failure rate related to electrical overstress in the application consideredπU is the use factor for the diode (permanent or not); in switching conditions, it is considered permanent workπti=ith is the temperature factor related to the junction temperature Tjτi=ith is the component working time ratio to the junction temperature ith of the mission profileπni=ith is the influence factor related to the number of annual cycles of thermal variations observed in the packaging with amplitude ΔτiΔτi=ith is the variation of the temperature amplitude of the mission profileπ1 is the influence factor related to the use of the component (protection interface or not)πS is the load factor for transistors related to the influence of the applied voltageTheπS load factor described previously is used in the standard for power transistors (FET, MOS, and IGBT), which is given by:
(8)πS=πS1+πS2,where πS1=0.22e1.7S1 and πS2=0.22e3S2.S1 represents the quotient between the maximum applied repetitive voltage value and the specific nominal voltage in VDS. S2 is the quotient between the maximum applied repetitive voltage value and the specific nominal voltage in VGS. They are determined by:
(9)S1,2=MaximunrepetitivevoltageVDS,VGSSpecificnominalvoltageVDS,VGS.The influence factorπn depends on the number of annual cycles of thermal variations to which the component is subjected. There are two important relationships to define this parameter, which are shown below.
(a)
If the component is subjected ton≤8760 thermal cycles/year, then πni=ni0.76(b)
If the component is subjected ton≥8760 thermal cycles/year, then πni=1.7ni0.60The temperature acceleration factor is given by the Arrhenius equation, which shows that the rate of changeπt is a function of the increase in temperature. Each component depends on a specific adjustment value; Table 5 shows the models for each given component.Table 5
Arrhenius model.
ComponentπtDiodeπt=exp46401/313−1/Tj+273Transistorπt=exp34801/373−1/Tj+273Inductorπt=exp17401/303−1/Tj+273Capacitorπt=exp29001/303−1/Tj+273The reliability standard based on the mission profile is very sensitive to the temperature parameter; this can be seen in Table5 in the Arrhenius models. Therefore, it is very convenient to define the models to determine the amplitude of the thermal variation for an on/off phase; in the following Table 6, this parameter is defined for each component of the inverter [11, 12, 22].Table 6
Amplitude of thermal variation in on/off phases.
ComponentΔτiDiodeΔTj/3+taci−taeiTransistorΔTj/3+taci−taeiInductorΔTR/3+taci−taeiCapacitortaci−taeiIn the case of low current in the inductor in the on/off phase,Δτi is calculated in the same form as in the capacitor. As it has been observed, the thermal effects play a fundamental role in the reliability evaluation. It can be realized that the mission profile is based on the effect of temperature πt during the performance of photovoltaic systems, as shown by the Arrhenius equation shown in Table 5. It is dependent on the junction temperature in each one of the components that make up the system and the effects Δτi of the rate of temperature change during the phases.The junction temperatureTj for switches and diodes is calculated by (10):
(10)Tj=TC+θjc.ploss,where ϴjc is the junction-encapsulated thermal resistance, Ploss is the losses on the switch, and TC is the temperature of the package.The losses in the MOSFET are the sum of static and dynamic losses and are represented by [7, 12, 16, 22]:
(11)Plossstatic=RDSon.Irms2,(12)Plossdynamic=Vavg.Iavg.ton+toff.fSW,(13)Ploss=Plossstatic+Plossdynamic,where Ploss is the total power losses, RDSon is the internal resistance, Irms is the effective current, Iavg and Vavg are the average values, ton+toff represent the on and off time, and fsw is the switching frequency.The power loss of an inductor is defined by:(14)Ploss_inductor=Pcore+Pdcr+Pacr,where Pcore is the core loss that can be calculated or provided by the manufacturer, Pdcr represents the cable loss caused by the DC resistance, and Pacr is defined as the cable loss caused by AC resistance.For this calculation is used [17, 23]:
(15)PcoremW=K1fxByxVe,where K1 is the constant for core material, fx is the frequency in kHz, By represents the maximum flux density, x is the frequency exponential function, y is an exponential function of flux density, and Ve is the effective core volume.
(16)PdcrW=Irms2DCR,where Irms is the effective value of the peak current applied to the inductor and DCR is the DC resistance of the inductor.
(17)PacrW=Irms2ACR,where Irms represents the effective value of the peak-to-peak ripple current applied to the inductor and ACR is the AC resistance of the inductor.


## 2.1. Photovoltaic Inverters

The single-phase inverters used for active power injection may use a transformer, which allows to protect and avoid leakage currents between the photovoltaic system to the ground [15]. The advantage of connecting the inverter with a low-frequency transformer is galvanic isolation between the input and the output, but it has disadvantages such as its low efficiency and big size [5]. Another part of the system is the passive elements of the output filter. The most common configurations are L, LC, and LCL filters; the latter being the one that has the advantage of smallest size and highest efficiency.To increase the efficiency and reduce the volume, a transformerless topology may be employed; however, a high leakage current may appear [16, 17]. There are different strategies to reduce the leakage current in transformerless photovoltaic inverters connected to the electrical grid.One strategy is to use a modulation technique that does not generate common-mode voltage variations.The full-bridge inverter (Figure1) is one of the simplest inverters. Consists of four switches organized in two legs, the first formed by S1 and S2 and the second by S3 and S4. This configuration has four switching states and three different output voltage levels. Two PWM modulation schemes may be employed: bipolar and unipolar modulations [6, 15, 16, 18] and [19]. The unipolar modulation is not good to avoid common-mode voltage, and the bipolar modulation should be preferred. However, in this case, a disdvantage is the incresed size of the output filter.Figure 1
Full-bridge inverter.The dual buck inverter (Figure2), based on the full-bridge topology, combines two unidirectional buck converters during the positive half cycle, S1 switching at high frequency, while S4 is always on. During the negative half-cycle, S2 switches at high frequency, while S3 is always on. This produces a unipolar modulation. According to the literature, one of the advantages is the high reliability; due to the diodes connected in series to the inductor, there are no tripping problems and reverse recovery issues [4, 15], and [20].Figure 2
Dual buck inverter.Another technique used to reduce the leakage current is the disconnection of the photovoltaic module but keeping the unipolar modulation. In this case, switches are added on the DC or AC side of the inverter to disconnect the photovoltaic module from the grid and to create new routes to reduce the leakage current.H5 topology (Figure3) is based on the full-bridge topology; a switch is added on the DC side. The operation is similar to that of the full-bridge inverter, but adding switch S5, its main function is to decouple the DC side from the AC side. Switches S1 and S3 commute at grid frequency, switch S2 switches only in the negative half cycle, and switch S4 only switches in the positive half cycle. Unipolar modulation is obtained and allows to reduce the leakage current [15, 18], and [19].Figure 3
H5 inverter.The HERIC topology (Figure4) is derived from the full-bridge converter; however, a branch is added on the AC side in parallel to the bridge output, to isolate the PV panel from the grid. The switches S1, S2, S3, and S4 switch at high frequency; normally MOSFETs are used and S5 and S6 at grid frequency; regularly IGBT’s are used. It integrates the advantages of unipolar PWM modulation and reduces the leakage current of the solar panel [15, 18], and [19].Figure 4
HERIC inverter.The H6 configuration (Figure5) is based on the traditional full bridge as well, adding two switches and two diodes. For the operation, a unipolar modulation is considered, where the switches S1, S2, S5, and S6 are switched at high frequency and MOSFETs are regularly used. Switches S3 and S4 switch at grid frequency; IGBTs are generally used and provide a current path with diodes D1 and D2. During the free conduction time, during the positive half cycle, the current flows through S4 and the diode D1 allowing the disconnection between the photovoltaic module and the grid [4, 15], and [18].Figure 5
H6 inverter.Another alternative to reduce the leakage current is connecting the grid neutral point to the average input voltage, which eliminates variations in high frequency. The Neutral-Point Clamped (NPC) inverter fits in this category (Figure6). It is composed of four switches; since two switches are added to the half-bridge inverter, the DC terminals are connected to two capacitors in series, which divide the panel voltage, providing a common or neutral point. The topology has two diodes connected to the neutral point. A unipolar modulation is used, and the output voltage has three levels [4, 6, 18], and [19].Figure 6
NPC inverter.Instead of connecting the grid neutral point to the average input voltage, the connection to the negative terminal of the PV panel can be made. The virtual DC bus topology considers this strategy (Figure7); it is derived from the full-bridge topology and consists of five switches S1-S5. The photovoltaic panel and capacitor CDC1 form a real DC bus; the virtual DC bus is generated by CDC2. Capacitor CDC2 is charged through S1 and S3 to maintain a constant DC voltage. It can be controlled with a unipolar modulation [4, 15], and [21].Figure 7
Virtual DC bus inverter.


## 2.2. Mission Profile

A mission profile refers to define or represent certain characteristics or conditions of an operating environment. The mission profile is defined to reproduce the operating conditions of an electronic component set that represents the system to evaluate. That is, the environment, events, or phases of operation are defined (solar irradiance, temperature, operating time, among others), to which the components are subject during their life cycle and allows to evaluate reliability [9, 10].Reliability is the probability that a component will function properly during the period for which it was designed, under the specific operating conditions. The mission profile must be clearly defined, to avoid inaccuracies in the reliability calculation, which will cause errors in the final development of the system [15].The cases that are commonly used to define a mission profile based on a one-year cycle use component normal operation, like:(a)
On/off working phases with average outside temperatures(b)
Storage mode or inactive phases(c)
Permanent working phases with fluctuations in the average outside temperatureThe mission profile parameters are defined as follows. The total annual relationship of times must be defined, in the printed circuit board (PCB) which will be in permanent operation mode (energized). This is represented byτon as:
(1)τon=∑i=1yτi,whereτi is the total annual relation of times for the PCB, in permanent operation mode, with supply and at the external ambient temperature (tac) that surrounds the equipment during the ith phase of the mission profile taci.It is also important to define the total annual relationship of times for the PCB in storage or inactive mode of operation. This is represented byτoff:
(2)τoff=1−τon.Addingτon in both terms of (2) is obtained:
(3)τon+τoff=1.The other parameter of the mission profile that is defined is the internal temperature increase in the components of the PCB compared to (tac) during the τon phase, and it is represented by Δτi:
(4)Δτi=ΔTj3+taci−taei,where taci is the average ambient temperature of the PCB, close to the components (it is considered the most critical temperature), ni represents the annual number of thermal cycles seen by the components of the PCB in phase ith of the mission profile with a temperature variation, and Δτi is defined as the average oscillations of the variation seen by the components of the PCB in the phase of the mission profile ith [11–14, 21].


## 2.3. Standard IEC TR 62380 and Reliability Design

There are different standards used for reliability prediction based on the mission profile. One of the best used is the IEC TR 62380 standard, which is a French standard (Union Technique de L’Électricité, UTEC C 80-810), which is used for the prediction of the reliability of electronic components, PCBs, and equipment.In this standard, environmental factors are defined in the mission profile; the data contained in the standard is obtained from field data in different operating environments.The reliability model used by the IEC TR 62380 standard is based on a failure rate model to be adjusted for each component defined asλcomponent:
(5)λcomponent=λdie+λpackage,(6)λdie=λthermaleffects+λEOSeffects,whereλdie is the failure rate related to the effects in operation, λthermaleffects is the failure rate related to thermal effects, λEOSffects is the failure rate related to the effects of electrical overstress, and λpackage is the failure rate related to thermo-mechanical effects.Then, the model of the IEC TR 62380 standard is centered on the elements. In photovoltaic inverters, the main devices are the diode, the MOSFET, the capacitor, and the inductor.The general mathematical model for the fit failure rate obtained by combining (5) and (6) is
(7)λcomponent=λthermaleffects+λEOSeffects+λpackage.The general model (7) is used to adjust the failure rate of the components. Table 1 shows the factors and failure rates of adjustments from the general model, corresponding to the diode. The adjustment of the failure rate and factors of the MOSFET are shown in Table 2. The inductor failure rates are shown in Table 3. Finally, the failure rates of thermal and mechanical adjustments for the capacitor are shown in Table 4.Table 1
Adjustment failure rates for the diode.
λdiodeλthermaleffectsπU.λ0.∑i=1yπti.τi/τon+τoffλEOSeffects2.75E−3.∑i=1zπni.ΔTi0.68.λBλpackageπ1.λBTable 2
Adjustment failure rates for the MOSFET.
λMOSFETλthermaleffectsπS.λ0.∑i=1yπti.τi/τon+τoffλEOSeffects2.75E−3.∑i=1zπni.ΔTi0.68.λBλpackageπ1.λBTable 3
Adjustment failure rates for the inductor.
λinductorλthermaleffectsλ0.∑i=1yπti.τi/τon+τoffλEOSeffects7E−3.∑i=1jπni.ΔTi0.68Table 4
Adjustment failure rates for the capacitor.
λcapacitorλthermaleffects0.1.∑i=1yπti.τi/τon+τoffλEOSeffects1.4E−3.∑i=1jπni.ΔTi0.68The parameters of Tables1–4 are defined as follows:λ0 is the base failure rate given in the standardλB is the base failure rate of the component packagingλEOS is the failure rate related to electrical overstress in the application consideredπU is the use factor for the diode (permanent or not); in switching conditions, it is considered permanent workπti=ith is the temperature factor related to the junction temperature Tjτi=ith is the component working time ratio to the junction temperature ith of the mission profileπni=ith is the influence factor related to the number of annual cycles of thermal variations observed in the packaging with amplitude ΔτiΔτi=ith is the variation of the temperature amplitude of the mission profileπ1 is the influence factor related to the use of the component (protection interface or not)πS is the load factor for transistors related to the influence of the applied voltageTheπS load factor described previously is used in the standard for power transistors (FET, MOS, and IGBT), which is given by:
(8)πS=πS1+πS2,where πS1=0.22e1.7S1 and πS2=0.22e3S2.S1 represents the quotient between the maximum applied repetitive voltage value and the specific nominal voltage in VDS. S2 is the quotient between the maximum applied repetitive voltage value and the specific nominal voltage in VGS. They are determined by:
(9)S1,2=MaximunrepetitivevoltageVDS,VGSSpecificnominalvoltageVDS,VGS.The influence factorπn depends on the number of annual cycles of thermal variations to which the component is subjected. There are two important relationships to define this parameter, which are shown below.
(a)
If the component is subjected ton≤8760 thermal cycles/year, then πni=ni0.76(b)
If the component is subjected ton≥8760 thermal cycles/year, then πni=1.7ni0.60The temperature acceleration factor is given by the Arrhenius equation, which shows that the rate of changeπt is a function of the increase in temperature. Each component depends on a specific adjustment value; Table 5 shows the models for each given component.Table 5
Arrhenius model.
ComponentπtDiodeπt=exp46401/313−1/Tj+273Transistorπt=exp34801/373−1/Tj+273Inductorπt=exp17401/303−1/Tj+273Capacitorπt=exp29001/303−1/Tj+273The reliability standard based on the mission profile is very sensitive to the temperature parameter; this can be seen in Table5 in the Arrhenius models. Therefore, it is very convenient to define the models to determine the amplitude of the thermal variation for an on/off phase; in the following Table 6, this parameter is defined for each component of the inverter [11, 12, 22].Table 6
Amplitude of thermal variation in on/off phases.
ComponentΔτiDiodeΔTj/3+taci−taeiTransistorΔTj/3+taci−taeiInductorΔTR/3+taci−taeiCapacitortaci−taeiIn the case of low current in the inductor in the on/off phase,Δτi is calculated in the same form as in the capacitor. As it has been observed, the thermal effects play a fundamental role in the reliability evaluation. It can be realized that the mission profile is based on the effect of temperature πt during the performance of photovoltaic systems, as shown by the Arrhenius equation shown in Table 5. It is dependent on the junction temperature in each one of the components that make up the system and the effects Δτi of the rate of temperature change during the phases.The junction temperatureTj for switches and diodes is calculated by (10):
(10)Tj=TC+θjc.ploss,where ϴjc is the junction-encapsulated thermal resistance, Ploss is the losses on the switch, and TC is the temperature of the package.The losses in the MOSFET are the sum of static and dynamic losses and are represented by [7, 12, 16, 22]:
(11)Plossstatic=RDSon.Irms2,(12)Plossdynamic=Vavg.Iavg.ton+toff.fSW,(13)Ploss=Plossstatic+Plossdynamic,where Ploss is the total power losses, RDSon is the internal resistance, Irms is the effective current, Iavg and Vavg are the average values, ton+toff represent the on and off time, and fsw is the switching frequency.The power loss of an inductor is defined by:(14)Ploss_inductor=Pcore+Pdcr+Pacr,where Pcore is the core loss that can be calculated or provided by the manufacturer, Pdcr represents the cable loss caused by the DC resistance, and Pacr is defined as the cable loss caused by AC resistance.For this calculation is used [17, 23]:
(15)PcoremW=K1fxByxVe,where K1 is the constant for core material, fx is the frequency in kHz, By represents the maximum flux density, x is the frequency exponential function, y is an exponential function of flux density, and Ve is the effective core volume.
(16)PdcrW=Irms2DCR,where Irms is the effective value of the peak current applied to the inductor and DCR is the DC resistance of the inductor.
(17)PacrW=Irms2ACR,where Irms represents the effective value of the peak-to-peak ripple current applied to the inductor and ACR is the AC resistance of the inductor.


## 3. Power Stage and Converter Design

The photovoltaic system is comprised of a photovoltaic panel, a conversion stage, that is the inverter, and the filtering stage.The stage responsible to inject active power into the grid is the inverter. Main transformerless inverter topologies were described in Section2, which are full-bridge, double buck, H5, HERIC, H6, NPC, and virtual DC bus.


### 3.1. Power Stage Design

The inverters were designed for a power of 1 kW, and an LCL filter was used in each of the inverters, since it is intended that all the inverters are under the same operating and design conditions to determine the reliability of each one using the IEC TR 62380 standard for the mission profile.The selection of the LCL filter was based on its advantages such as smaller size, higher efficiency, lower THD percentage, and better reliability than the L and LC filters [16].The LCL filter design considers the following aspects. In a photovoltaic system, we have the following relationship:(18)Vg=Vpvm,where Vg is the voltage of the electrical grid, Vpv is the voltage of the photovoltaic panel, and m is the modulation index.The resonant frequency must be in a range of values between the network frequency and the switching frequency, satisfying:(19)10fo≤fres≤fsw,where f0 is the frequency of the electrical grid, fres is the resonant frequency, and fsw is the switching frequency.The LCL filter is the combination of a capacitorCf in parallel with two coils Lf1 and Lf2; the calculation of Lf1 is obtained with:
(20)Lf1=Vpv1−mmΔiLf1fsw,where ΔiLf1 is the inductor current ripple.The inductor ratio is determined byα. The relation should be between αϵ [3, 7]. The relationship of the individual inductances is
(21)Lf1=αLf2.The filter capacitor is selected according to (22), and it is a function of ωres the resonant frequency (19) [4, 5, 16], [17]:
(22)Cf=Lf1+Lf2Lf1Lf2ωres.The design parameters of the inverter and the LCL filter were calculated using equations (18)–(22). The results are shown in Table 7.Table 7
Design parameters.
LCL filterP0=1kWVg=127VrmsVpv=200VLf1=425μHLf2=141μHCf=6.6μF


### 3.2. Reliability Design

It is important to define the concept of reliability and the average time between failures, used to evaluate the useful life of the inverters. Reliability was defined previously and is represented asRt:
(23)Rt=1−Ft=∫0tftdt,where ft is a function of failure density, t is the time when the component will fail, and Ft is the cumulative distribution function.In electronic systems, the exponential distribution is used, giving that represents the useful life of electronic systems with a constant failure rateλt assuming that they have survived the initial time. The exponential distribution function is represented by:
(24)ft=λe−λt.Substituting (24) in (23) and integrating, the exponential reliability function is obtained:
(25)Rt=e−λt.The average value of the useful life cycle before a failure occurs in the same equipment or component is known as the Mean Time Between Failures (MTBF) and is represented by:(26)MTBF=∫0∞tftdt=∫0∞λe−λt=1λ=1nλi.It is worth mentioning that the reliability with this standard is evaluated in terms of MTBF or FIT (Failures in Time). One FIT equals a one failure in 10E9 hours [12, 16, 24].A high number for the MTBF represent good reliability. Once these two concepts have been defined, a reliability analysis is made for each inverter using a serial model. It is known that a system is a grouping of interconnected components. In this way, the reliability of the system will depend on the individual reliability of the components. The serial model is used since in this model if there is a failure in any of the elements or components, the failure of the entire system would be assumed. The serial system is defined as the product of all the individual reliabilities that make up the system. The analysis ofλt and the MTBF allows determining which component is the weakest. Thus, improving the reliability of this component, the complete system reliability improves.As an example of calculation, the dual buck inverter (Figure8) is analyzed using the serial system to determine its reliability.Figure 8
Serial analysis of the double buck inverter.The following considerations are taken into account for this analysis: the reliability of the switches is equalRS1t=RS2t=RS3t=RS4t=R1t and that they present a constant failure rate λS1=λS2=λS3=λS4=λ1.For the diodes, the reliability is considered in a similar manner since they have the same characteristics. Therefore, diodes have a reliabilityRD1t=RD2t=RD3t=RD4t=R2t and a constant failure rate λD1=λD2=λD3=λD4=λ2.In the case of the inductors and the filter capacitor, the reliability is as follows. For the inductorLf1, there is a reliability RLf1t=R3t and a failure rate λLf1=λ3. The capacitor Cf has a reliability RCft=R4t and a failure rate λCf=λ4. Finally, the inductor Lf2 presents a reliability RLf2t=R5t and a failure rate λLf2=λ5.Solving the serial system would be as follows:(27)RSt=R1t.R2t.R3t.R4t.R5t.Substituting the exponential reliability function (25) in (27), the reliability of the series system is
(28)RSt=e−4λ1+4λ2+λ3+λ4+λ5t.The MTBF is calculated by substituting (28) in (26), where the following relationship is obtained:
(29)MTBF=14λ1+4λ2+λ3+λ4+λ5.The process described above is made for each of the inverters described.


## 3.1. Power Stage Design

The inverters were designed for a power of 1 kW, and an LCL filter was used in each of the inverters, since it is intended that all the inverters are under the same operating and design conditions to determine the reliability of each one using the IEC TR 62380 standard for the mission profile.The selection of the LCL filter was based on its advantages such as smaller size, higher efficiency, lower THD percentage, and better reliability than the L and LC filters [16].The LCL filter design considers the following aspects. In a photovoltaic system, we have the following relationship:(18)Vg=Vpvm,where Vg is the voltage of the electrical grid, Vpv is the voltage of the photovoltaic panel, and m is the modulation index.The resonant frequency must be in a range of values between the network frequency and the switching frequency, satisfying:(19)10fo≤fres≤fsw,where f0 is the frequency of the electrical grid, fres is the resonant frequency, and fsw is the switching frequency.The LCL filter is the combination of a capacitorCf in parallel with two coils Lf1 and Lf2; the calculation of Lf1 is obtained with:
(20)Lf1=Vpv1−mmΔiLf1fsw,where ΔiLf1 is the inductor current ripple.The inductor ratio is determined byα. The relation should be between αϵ [3, 7]. The relationship of the individual inductances is
(21)Lf1=αLf2.The filter capacitor is selected according to (22), and it is a function of ωres the resonant frequency (19) [4, 5, 16], [17]:
(22)Cf=Lf1+Lf2Lf1Lf2ωres.The design parameters of the inverter and the LCL filter were calculated using equations (18)–(22). The results are shown in Table 7.Table 7
Design parameters.
LCL filterP0=1kWVg=127VrmsVpv=200VLf1=425μHLf2=141μHCf=6.6μF


## 3.2. Reliability Design

It is important to define the concept of reliability and the average time between failures, used to evaluate the useful life of the inverters. Reliability was defined previously and is represented asRt:
(23)Rt=1−Ft=∫0tftdt,where ft is a function of failure density, t is the time when the component will fail, and Ft is the cumulative distribution function.In electronic systems, the exponential distribution is used, giving that represents the useful life of electronic systems with a constant failure rateλt assuming that they have survived the initial time. The exponential distribution function is represented by:
(24)ft=λe−λt.Substituting (24) in (23) and integrating, the exponential reliability function is obtained:
(25)Rt=e−λt.The average value of the useful life cycle before a failure occurs in the same equipment or component is known as the Mean Time Between Failures (MTBF) and is represented by:(26)MTBF=∫0∞tftdt=∫0∞λe−λt=1λ=1nλi.It is worth mentioning that the reliability with this standard is evaluated in terms of MTBF or FIT (Failures in Time). One FIT equals a one failure in 10E9 hours [12, 16, 24].A high number for the MTBF represent good reliability. Once these two concepts have been defined, a reliability analysis is made for each inverter using a serial model. It is known that a system is a grouping of interconnected components. In this way, the reliability of the system will depend on the individual reliability of the components. The serial model is used since in this model if there is a failure in any of the elements or components, the failure of the entire system would be assumed. The serial system is defined as the product of all the individual reliabilities that make up the system. The analysis ofλt and the MTBF allows determining which component is the weakest. Thus, improving the reliability of this component, the complete system reliability improves.As an example of calculation, the dual buck inverter (Figure8) is analyzed using the serial system to determine its reliability.Figure 8
Serial analysis of the double buck inverter.The following considerations are taken into account for this analysis: the reliability of the switches is equalRS1t=RS2t=RS3t=RS4t=R1t and that they present a constant failure rate λS1=λS2=λS3=λS4=λ1.For the diodes, the reliability is considered in a similar manner since they have the same characteristics. Therefore, diodes have a reliabilityRD1t=RD2t=RD3t=RD4t=R2t and a constant failure rate λD1=λD2=λD3=λD4=λ2.In the case of the inductors and the filter capacitor, the reliability is as follows. For the inductorLf1, there is a reliability RLf1t=R3t and a failure rate λLf1=λ3. The capacitor Cf has a reliability RCft=R4t and a failure rate λCf=λ4. Finally, the inductor Lf2 presents a reliability RLf2t=R5t and a failure rate λLf2=λ5.Solving the serial system would be as follows:(27)RSt=R1t.R2t.R3t.R4t.R5t.Substituting the exponential reliability function (25) in (27), the reliability of the series system is
(28)RSt=e−4λ1+4λ2+λ3+λ4+λ5t.The MTBF is calculated by substituting (28) in (26), where the following relationship is obtained:
(29)MTBF=14λ1+4λ2+λ3+λ4+λ5.The process described above is made for each of the inverters described.


## 4. Simulation and Reliability Results

The simulation of the inverters was carried out using the PSIM® software, as it is a very versatile software that allows fast simulation, thanks to the wide variety of device models it handles.The simulation of each of the inverters was carried out using a unipolar open-loop modulation, since it is the type of modulation that the branches switch at high frequency, allowing the output filter to be small and having high efficiency, in addition to generating three voltage levels at the output.In the filtering and coupling stage, the LCL filter will be used for all cases. SiC MOSFETs are used in the simulation, C3M0065090D (CREE Manufacturer). Considering the parameters according to the manufacturer’s data sheet and a behavior similar to the real environment as required by the standard, the simulations were made. For this analysis, a test ambient temperature provided by the mission profile was used, which is at which the device operates during the mission profile [16].The simulation is performed to obtain operating parameters required for the calculation of reliability, such as voltages and currents. The failure rate adjustment models require nominal, average, or effective values for each device. In the case of the load factor, it requires maximum operating values. In the case of the temperature factor, it depends on the junction temperature of the device; therefore, average and effective values are used.


### 4.1. Simulation Results

The simulation results in PSIM® are shown in Figures9–11. The control signals obtained are consistent for a unipolar modulation; for illustrating purposes in Figure 9, a switching frequency lower than the used was graphed to make it visible. Unipolar modulation signals can be observed from top to bottom on a 0.5 V/div scale and the control signals S1, S2, S3, and S4 on a 0.5 V/div scale.Figure 9
Unipolar modulation and control signals. (a–e) Modulation signals (0.5 V/div) and control signals (1 V/div).Figure 10
Inverter output voltage before filter. (a, b) Output voltage (100 V/div) and output current (10 A/div).Figure 11
Active power injection to the grid. (a, b) Filter output voltage (100 V/div) and filter output current (10 A/div).In Figure10, it can be seen from top to bottom the output voltage of the inverter before the output filter on a scale of 100 V/div and the current of 8.3 A at a scale of 10 A/div.In Figure11, it is observed from top to bottom the output voltage of the inverter after the filter, where a power of 1 kW would be injected into the grid. A voltage of 180 V is observed on a scale of 100 V/div and a current of 8.3 A at a scale of 10 A/div.In Table8, an inverter comparative analysis of the semiconductor elements is shown, as well as their efficiency, which is a parameter on which reliability depends. The efficiency of the inverters was obtained based on the simulation with a unipolar modulation for each case.Table 8
Comparison of number of elements and inverter efficiency.
TopologySwitchesDiodesCapacitorsEfficiencyFull bridge4XX99.05%Double buck44X98.93%H55XX98.67%HERIC6XX98.53%H662X98.55%NPC42X98.86%Virtual DC bus5X199.00%X indicates that it is not applied for the system.Another important parameter by which reliability is also measured is THD percentage. These parameters are directly related since they are attributes that allow evaluating the quality of the system. THD directly affects inverter reliability; it is related to the quality and safety of the system. The term quality refers mainly to the quality of the signal wave and safety; it is related to the system complying with the THD limits allowed by regulations. Table9 shows the THD percentage of the analyzed inverters, as well as the switches that switch at high or low frequency.Table 9
Inverter THD comparison.
TopologyHigh frequencyLow frequency%THDFull bridgeS1,S2,S3,S4X0.08200899Double buckS1,S2,S3,S4X0.08270188H5S2,S4,S5S1,S30.22131262HERICS1,S2,S3,S2S5,S60.22176104H6S1,S2,S5,S6S3,S40.22176183NPCS1,S4S2,S30.17539819Virtual DC busS1,S2,S3,S4,S5X0.01021878X indicates that it is not applied for the system.Tables8 and 9 show that comparing single-phase inverters, the one with the best characteristics in both efficiency and THD is the full-bridge inverter, with an efficiency of 99.05% and a THD of 0.08200899%, followed by the virtual DC bus with 99.00% efficiency and a THD of 0.01021878%, and double buck with 98.93% efficiency and THD of 0.08270188%.


### 4.2. Reliability Calculation Results

The numerical reliability calculation is performed using the IEC TR 62380 standard. Table10 shows the base factors taken from the standard for each of the components that make up the inverters. The λB corresponds to the TO-220 package. The λEOS factor corresponds to the type of telecommunication mission profile.Table 10
Adjustment factors for power components.
Componentλ0λBλEOSπUπ1Diode0.7 FIT5.74011Transistor2 FIT5.7401Inductor0.6 FITTable11 shows the mission profile, which complies with the total annual relationship of times given in equation (3). There is only one annual working phase to consider for a permanent working.Table 11
Mission profile.
Application typeEnvironment typeEquipment typetaei °Ctaci °Cτ1τonΤoffn1 cycles/yearΔT1 °C/cycleTelecomGround fixed (GF)Transmitting and access11310.50.250.253658The mission profile of Table11 is given for a permanent working; inverters operate with conditions, and values for “ground; stationary; non weather protected”(ground; fixed for Mil-HDBK-217F) can be calculated for various climates.The mission profile is related to the failure rate adjustment equations shown in Tables1–4. The time parameters and operating cycles shown in Table 11 are applied to the adjustment equations. The temperature factor is determined by the temperature of Table 11, and the junction temperature is obtained with values from simulation, using the Arrhenius model.Table12 shows the results of the reliability calculations for each of the single-phase inverters analyzed in this study. It can be observed that the full-bridge inverter and virtual DC bus present better reliability compared to the other inverters, with a lower failure rate and a higher MTBF.Table 12
Total reliability of inverters.
TopologyλSystemFITMTBF (FIT)Full bridge193.4150.005171Double buck377.5550.002649H5332.6910.003006HERIC379.9370.002632H6379.9970.002632NPC285.4850.003503Virtual DC bus240.6710.004155The full-bridge being the best of these, with a 193.415FIT failure rate and an MTBF of 0.005171FIT, followed by the virtual DC bus with a 240.671FIT failure rate and 0.004155FIT MTBF. The virtual DC bus inverter and the HERIC present a very similar failure rate and MTBF, only differentiated by the contribution of some element’s failure rate in the NPC inverter. The inverters with the worst reliability are the HERIC with a failure rate of 379.937FIT and a 0.002632FIT MTBF and the H6 with a 379.997FIT failure rate and a 0.002632FIT MTBF.In Figure12, a comparative graph of the reliability of the different single-phase inverters analyzed is observed, represented in FIT. Analyzing the best case of the full-bridge inverter, it has an MTBF of 0.005171FIT, equivalent to an annual failure probability of 0.16% and reliability of 98.40%. Now the worst case, the H6 inverter has an MTBF of 0.002632FIT, equivalent to an annual failure probability of 0.33% and reliability of 96.70%. The number of years also indicates that the inverter that would present a probability of failure in the first instance is the H6. It can be seen that the curve of the complete bridge has a longer lifetime compared to the other inverters. The full-bridge turned out to be the most reliable inverter; it is convenient to represent the reliability cumulative distribution function (24). The cumulative distribution function can be interpreted as the probability of failure presented by the system in FIT. In Figure 13, a relationship between the reliability function and the failure probability function of the full-bridge inverter is observed, through an equilibrium point at the intersection of the curves.Figure 12
Comparative graph of the reliability of single-phase inverters.Figure 13
Representation of the probability of failure of the full-bridge inverter.It is important to highlight, although the full-bridge inverter has better reliability and efficiency, its use is not recommended; since it presents a leakage current between the PV and ground, and it is higher than that allowed by the European standard VDE 0126-1-1 [25], which should not be higher than 300 mA.Table13 shows the percentage of contribution of each component to the total failure rate of the system, concerning the number of components in Table 8. It is observed that the failure rate depends directly on the number of components that make up the system. Therefore, the reliability is directly related to the number of elements that the system has. In addition, it is visible that in each one of the inverters that were analyzed, which are the components that have the most contribution to the failure rate of the system, that is, the components that may have the most failures and that may have a shorter lifetime. To reduce the power losses and increase reliability, the C3M0065090D SiC MOSFET (CREE Manufacturer) is used. Since the turn-on resistance is too low, a synchronous rectification occurs when the current becomes negative in the device; therefore, the free-wheeling diode does not conduct during this time, as traditionally occurs in the inverters. Since the MOSFET’s voltage drop is smaller than the diode forward voltage, the MOSFET conducts for positive and negative currents, Certainly, there are some topologies where diodes conduct and synchronous rectification does not occur.Table 13
Percentage of contribution to the failure rate of the photovoltaic system.
Inverter failure rateLCL filter failure rateTopologySwitchesDiodesCapacitorsInductorsCapacitorsMOSFETParasitic diodeFull bridge97.73%XXX2.21%0.06%Double buck50.06%X48.77%X1.13%0.04%H571.00%27.67%XX1.30%0.03%HERIC74.61%24.23%XX1.13%0.03%H674.61%X24.22%X1.13%0.04%NPC66.21%X32.25%X1.51%0.03%Virtual DC bus98.14%XX0.04%1.78%0.04%X indicates that it is not applied for the system.In general, in inverters, the highest percentage of failure contribution is made by the switches, followed by the diodes, then the inductors, and with the lowest percentage the capacitors. The characteristics of an MKP capacitor were used; it has advantages such as thermal and electrical stability, reliability, and a long useful life.It is also observed that the switching frequency is a parameter that greatly affects the reliability. If the switching frequency is reduced, the reduction of losses is considerable. When determining reliability, the parameter that is related to the standard, through the Arrhenius model, is the junction temperature and thermal resistance of the component encapsulation. Therefore, the failure rate depends on the bonding temperature and the temperature in the casing; this is on the mission temperature profile. Reducing the switching frequency reduces the component failure rate by 0.10%. Then, it is obtained aλsystem=193.214FIT and an increment of the MTBF to 0.005176FIT.Other simulations were carried out to verify the impact of the device on the reliability; a 3rd Generation SiC MOSFET (C3M0025065D) was used since the internal resistance is smaller, as mentioned previously. Then, better results were obtained; the losses were reduced, and there is a positive, but small, effect on reliability.Following the analysis that has been made is recommended to the designer to increase the MTBF of the systems, since it is the parameter that measures the useful life of the system. This may be achieved by using component heat dissipation and cooling systems to reduce thermal stress and at the same time reduce the component failure rate as well as using devices made of better materials such as silicon carbide, which have lower (better) thermal resistance.Also, from the analysis, the converter with fewer components will be the best option for reliability but not forgetting the leakage current of the PV system. Then, of all the inverters studied, the best alternative is the virtual DC bus inverter with SiC devices. This is because it offers a low THD, high efficiency, best reliability, and useful life while satisfying the leakage currents for PV system standards. The following alternative is the NPC inverter. Certainly, the final selection of the inverter is left to the designer, since the difference is relatively small between them.


## 4.1. Simulation Results

The simulation results in PSIM® are shown in Figures9–11. The control signals obtained are consistent for a unipolar modulation; for illustrating purposes in Figure 9, a switching frequency lower than the used was graphed to make it visible. Unipolar modulation signals can be observed from top to bottom on a 0.5 V/div scale and the control signals S1, S2, S3, and S4 on a 0.5 V/div scale.Figure 9
Unipolar modulation and control signals. (a–e) Modulation signals (0.5 V/div) and control signals (1 V/div).Figure 10
Inverter output voltage before filter. (a, b) Output voltage (100 V/div) and output current (10 A/div).Figure 11
Active power injection to the grid. (a, b) Filter output voltage (100 V/div) and filter output current (10 A/div).In Figure10, it can be seen from top to bottom the output voltage of the inverter before the output filter on a scale of 100 V/div and the current of 8.3 A at a scale of 10 A/div.In Figure11, it is observed from top to bottom the output voltage of the inverter after the filter, where a power of 1 kW would be injected into the grid. A voltage of 180 V is observed on a scale of 100 V/div and a current of 8.3 A at a scale of 10 A/div.In Table8, an inverter comparative analysis of the semiconductor elements is shown, as well as their efficiency, which is a parameter on which reliability depends. The efficiency of the inverters was obtained based on the simulation with a unipolar modulation for each case.Table 8
Comparison of number of elements and inverter efficiency.
TopologySwitchesDiodesCapacitorsEfficiencyFull bridge4XX99.05%Double buck44X98.93%H55XX98.67%HERIC6XX98.53%H662X98.55%NPC42X98.86%Virtual DC bus5X199.00%X indicates that it is not applied for the system.Another important parameter by which reliability is also measured is THD percentage. These parameters are directly related since they are attributes that allow evaluating the quality of the system. THD directly affects inverter reliability; it is related to the quality and safety of the system. The term quality refers mainly to the quality of the signal wave and safety; it is related to the system complying with the THD limits allowed by regulations. Table9 shows the THD percentage of the analyzed inverters, as well as the switches that switch at high or low frequency.Table 9
Inverter THD comparison.
TopologyHigh frequencyLow frequency%THDFull bridgeS1,S2,S3,S4X0.08200899Double buckS1,S2,S3,S4X0.08270188H5S2,S4,S5S1,S30.22131262HERICS1,S2,S3,S2S5,S60.22176104H6S1,S2,S5,S6S3,S40.22176183NPCS1,S4S2,S30.17539819Virtual DC busS1,S2,S3,S4,S5X0.01021878X indicates that it is not applied for the system.Tables8 and 9 show that comparing single-phase inverters, the one with the best characteristics in both efficiency and THD is the full-bridge inverter, with an efficiency of 99.05% and a THD of 0.08200899%, followed by the virtual DC bus with 99.00% efficiency and a THD of 0.01021878%, and double buck with 98.93% efficiency and THD of 0.08270188%.


## 4.2. Reliability Calculation Results

The numerical reliability calculation is performed using the IEC TR 62380 standard. Table10 shows the base factors taken from the standard for each of the components that make up the inverters. The λB corresponds to the TO-220 package. The λEOS factor corresponds to the type of telecommunication mission profile.Table 10
Adjustment factors for power components.
Componentλ0λBλEOSπUπ1Diode0.7 FIT5.74011Transistor2 FIT5.7401Inductor0.6 FITTable11 shows the mission profile, which complies with the total annual relationship of times given in equation (3). There is only one annual working phase to consider for a permanent working.Table 11
Mission profile.
Application typeEnvironment typeEquipment typetaei °Ctaci °Cτ1τonΤoffn1 cycles/yearΔT1 °C/cycleTelecomGround fixed (GF)Transmitting and access11310.50.250.253658The mission profile of Table11 is given for a permanent working; inverters operate with conditions, and values for “ground; stationary; non weather protected”(ground; fixed for Mil-HDBK-217F) can be calculated for various climates.The mission profile is related to the failure rate adjustment equations shown in Tables1–4. The time parameters and operating cycles shown in Table 11 are applied to the adjustment equations. The temperature factor is determined by the temperature of Table 11, and the junction temperature is obtained with values from simulation, using the Arrhenius model.Table12 shows the results of the reliability calculations for each of the single-phase inverters analyzed in this study. It can be observed that the full-bridge inverter and virtual DC bus present better reliability compared to the other inverters, with a lower failure rate and a higher MTBF.Table 12
Total reliability of inverters.
TopologyλSystemFITMTBF (FIT)Full bridge193.4150.005171Double buck377.5550.002649H5332.6910.003006HERIC379.9370.002632H6379.9970.002632NPC285.4850.003503Virtual DC bus240.6710.004155The full-bridge being the best of these, with a 193.415FIT failure rate and an MTBF of 0.005171FIT, followed by the virtual DC bus with a 240.671FIT failure rate and 0.004155FIT MTBF. The virtual DC bus inverter and the HERIC present a very similar failure rate and MTBF, only differentiated by the contribution of some element’s failure rate in the NPC inverter. The inverters with the worst reliability are the HERIC with a failure rate of 379.937FIT and a 0.002632FIT MTBF and the H6 with a 379.997FIT failure rate and a 0.002632FIT MTBF.In Figure12, a comparative graph of the reliability of the different single-phase inverters analyzed is observed, represented in FIT. Analyzing the best case of the full-bridge inverter, it has an MTBF of 0.005171FIT, equivalent to an annual failure probability of 0.16% and reliability of 98.40%. Now the worst case, the H6 inverter has an MTBF of 0.002632FIT, equivalent to an annual failure probability of 0.33% and reliability of 96.70%. The number of years also indicates that the inverter that would present a probability of failure in the first instance is the H6. It can be seen that the curve of the complete bridge has a longer lifetime compared to the other inverters. The full-bridge turned out to be the most reliable inverter; it is convenient to represent the reliability cumulative distribution function (24). The cumulative distribution function can be interpreted as the probability of failure presented by the system in FIT. In Figure 13, a relationship between the reliability function and the failure probability function of the full-bridge inverter is observed, through an equilibrium point at the intersection of the curves.Figure 12
Comparative graph of the reliability of single-phase inverters.Figure 13
Representation of the probability of failure of the full-bridge inverter.It is important to highlight, although the full-bridge inverter has better reliability and efficiency, its use is not recommended; since it presents a leakage current between the PV and ground, and it is higher than that allowed by the European standard VDE 0126-1-1 [25], which should not be higher than 300 mA.Table13 shows the percentage of contribution of each component to the total failure rate of the system, concerning the number of components in Table 8. It is observed that the failure rate depends directly on the number of components that make up the system. Therefore, the reliability is directly related to the number of elements that the system has. In addition, it is visible that in each one of the inverters that were analyzed, which are the components that have the most contribution to the failure rate of the system, that is, the components that may have the most failures and that may have a shorter lifetime. To reduce the power losses and increase reliability, the C3M0065090D SiC MOSFET (CREE Manufacturer) is used. Since the turn-on resistance is too low, a synchronous rectification occurs when the current becomes negative in the device; therefore, the free-wheeling diode does not conduct during this time, as traditionally occurs in the inverters. Since the MOSFET’s voltage drop is smaller than the diode forward voltage, the MOSFET conducts for positive and negative currents, Certainly, there are some topologies where diodes conduct and synchronous rectification does not occur.Table 13
Percentage of contribution to the failure rate of the photovoltaic system.
Inverter failure rateLCL filter failure rateTopologySwitchesDiodesCapacitorsInductorsCapacitorsMOSFETParasitic diodeFull bridge97.73%XXX2.21%0.06%Double buck50.06%X48.77%X1.13%0.04%H571.00%27.67%XX1.30%0.03%HERIC74.61%24.23%XX1.13%0.03%H674.61%X24.22%X1.13%0.04%NPC66.21%X32.25%X1.51%0.03%Virtual DC bus98.14%XX0.04%1.78%0.04%X indicates that it is not applied for the system.In general, in inverters, the highest percentage of failure contribution is made by the switches, followed by the diodes, then the inductors, and with the lowest percentage the capacitors. The characteristics of an MKP capacitor were used; it has advantages such as thermal and electrical stability, reliability, and a long useful life.It is also observed that the switching frequency is a parameter that greatly affects the reliability. If the switching frequency is reduced, the reduction of losses is considerable. When determining reliability, the parameter that is related to the standard, through the Arrhenius model, is the junction temperature and thermal resistance of the component encapsulation. Therefore, the failure rate depends on the bonding temperature and the temperature in the casing; this is on the mission temperature profile. Reducing the switching frequency reduces the component failure rate by 0.10%. Then, it is obtained aλsystem=193.214FIT and an increment of the MTBF to 0.005176FIT.Other simulations were carried out to verify the impact of the device on the reliability; a 3rd Generation SiC MOSFET (C3M0025065D) was used since the internal resistance is smaller, as mentioned previously. Then, better results were obtained; the losses were reduced, and there is a positive, but small, effect on reliability.Following the analysis that has been made is recommended to the designer to increase the MTBF of the systems, since it is the parameter that measures the useful life of the system. This may be achieved by using component heat dissipation and cooling systems to reduce thermal stress and at the same time reduce the component failure rate as well as using devices made of better materials such as silicon carbide, which have lower (better) thermal resistance.Also, from the analysis, the converter with fewer components will be the best option for reliability but not forgetting the leakage current of the PV system. Then, of all the inverters studied, the best alternative is the virtual DC bus inverter with SiC devices. This is because it offers a low THD, high efficiency, best reliability, and useful life while satisfying the leakage currents for PV system standards. The following alternative is the NPC inverter. Certainly, the final selection of the inverter is left to the designer, since the difference is relatively small between them.


## 5. Conclusion

This article presents the prediction of the reliability of different single-phase inverters using an LCL filter in the filtering stage. For the calculation and approximation of the prediction of the reliability, the standard IEC TR 62380 is used.In this study, they were compared the full-bridge, double buck, H5, HERIC, H6, NPC, and virtual DC bus converters. The full-bridge inverter presents better reliability and better useful life. In addition, it features a higher THD percentage, at better efficiency. The virtual DC bus and NPC inverters have the following best realiability, there is a small difference in reliability and efficiency. The use of a virtual DC bus inverter with SiC devices is recommended since the full-bridge presents higher leakage current than allowed by the standards.The study shows that the devices present a failure rate percentage in the following order: switches, diodes, inductors, and to a lesser extent, capacitors. It was observed that the switching frequency affects the reliability of the component to a lesser extent.The parameter that directly affects reliability is the number of elements that make up the system. The reliability and average useful life of the systems can be increased, using cooling systems to reduce thermal stress, which is the parameter that directly relates to the failure rate and therefore the reliability of the system. It is also recommended to use silicon carbide devices, which are components with smaller internal resistance and thermal resistance that allows to have few losses, high efficiency, and reliability.



---

*Source: 9926316-2021-11-11.xml*