Sensor based measurements of a single phase AC/DC converter to estimate lifetime
Master in Systems, Control & Robotics Date: December 18, 2019
Supervisor: Jonas Forssell Examiner: Bo Wahlberg
Swedish title: Sensorbaserade mätningar av en enfas AC/DC-omvandlare för att estimera livslängd
School of Electrical Engineering and Computer Science
Maintenance of power electronic systems is of interest for larger systems entirety. The reason is that they in turn could affect the whole system and cause failures if they are not functional. Maintenance of systems that are critical to be functional at all times is an area of research that is developing.
For power electronics, there is more research needed in the specific area of when failures will occur and the health of the system. In the following thesis, research in the field is done to examine what causes the failures and how to prevent them at most. Further, a sensor based measurement system is developed to collect data in forms that are considered to be useful for the lifetime of the converter and the degradation. The data is further processed and analyzed with estimation methods relevant for the research.
Underhåll av kraftelektronik är ett intressant område för ett större systems helhet. Orsaken är att det kraftelektroniska systemets funktionalitet kan påverka allt som är kopplat mot det och ge upphov till grövre problem för systemet i helhet. Generellt är underhåll av system, som är kritiska att vara funktionella, ett växande forskningsområde som utvecklas. Inom kraftelektroniken krävs det mer forskning gällande systemets hälsa och vad som orsakar att systemets funktionalitet misslyckas. Detta examensarbete syftar till att efterforska vad som orsakar att kraftelektroniska systemet misslyckas och hur dessa orsaker kan förhindras. Utöver detta är ett sensorbaserat system utvecklat för att samla data som anses vara relevanta för livslängden av systemet och dess degradering. Data är behandlad och analyserad med estimeringmetoder relevanta för forskningen.
I would like to thank my supervisor Jonas Forssell for his guidance and support throughout the project. Furthermore, I am also thankful to the staff at EK Power Solutions for all the support and valuable discussions.
I would also like to acknowledge gratitude to my examiner Bo Wahlberg for his support during the project.
Introduction ... 1
1.1 Purpose ... 1
1.2 Previous work ... 2
1.3 Outline ... 2
Background ... 3
2.1 Power electronic converters ... 3
2.2 Lifetime model of a power converter ... 4
2.2.1 Transistors in converters ... 6
2.2.2 Capacitors in converters ... 6
2.2.3 Diodes in converters ... 7
2.2.4 Metal oxide varistors ... 7
2.3 Solder joints ... 8
2.4 Bond wire lift off ... 9
2.5 Efficiency of a power converter ... 9
Estimation approaches ... 12
3.1 Coffin-Manson-Arrhenius estimation... 12
3.2 Capacitor lifetime estimation ... 13
3.3 Solder joint lifetime estimation ... 13
3.4 Bond wire lifetime estimation ... 13
3.5 Remaining useful lifetime ... 14
3.5.1 Run to failure data of AC to DC converter ... 15
3.5.2 Lifetime data of AC to DC converter ... 15
3.5.3 Threshold data of AC to DC converter ... 16
3.6 Evaluation and reliability of the models ... 16
Method ... 18
4.1 Measurement system ... 18
4.2 Measurement equipment ... 19
4.3 Safety precautions ... 21
4.4 Voltage divider design ... 21
4.5 Analog to Digital Converter ... 25
4.6 Aliasing ... 26
4.7 Experimental setup ... 27
4.8 Experiment procedure ... 29
4.9 RUL estimation through real time data ... 30
4.10 Regression analysis ... 31
4.11 MOV experiment ... 32
Results and discussion ... 33
5.1 Case 1: 100 W output power ... 33
5.2 Case 2: 200 W output power ... 36
5.3 Case 3: 400 W output power ... 39
5.4 Case 4: 800 W output power ... 42
5.5 RUL estimation ... 46
5.6 Capacitor lifetime ... 46
5.7 MOV results ... 49
5.8 Evaluation of the results ... 50
Conclusion ... 52
6.1 Future research ... 53
Power electronic devices are means to control the energy conversion.
However, the application depends on the system and the load. Generally, it is done in a manner so that the output fits the load of the system  . Some applications of where power electronics can be applied is in the automotive industry, for energy production in renewable energy sources and electricity transmissions. 
An issue regarding power electronics is that there has not been enough research in remote diagnostics. Like many other systems, the downtime can be costly and could result in further problems. It is therefore necessary to know more about the condition of the system to reduce hazardous influences. Research in the field of power electronics could put forward an estimation of when a failure will occur. The research would have to provide sufficient knowledge about components in the system to make such estimation. Therefore, the focus should be on the common failing components in the system and what the cause of its failing depended on.
The uncertainty also lies in what can be measured that is relevant for the research. Could voltage spikes in the resistors be a cause for the significant degradation in that component? The focus should therefore not be mainly on measuring the same quantities, but rather choosing appropriate quantities to measure.
When the most critical components are known, is it possible to make a prediction of the life time? Is there any possibility of implementing machine learning to predict the device degradation? By predicting the life time, the service could be optimized and scheduled. It is therefore interesting to research in this field of area for all sorts of systems which require systematic maintenance.
1.2 Previous work
In general, there have been approaches to estimate lifetime of products with machine learning algorithms. It is however done in different ways and depends on the product itself.
There has been an approach to estimate the lifetime of a turbofan engine with machine learning. Different algorithms are compared with each other in order to find a suitable algorithm. 
In the case of power electronics, it can differ a lot depending on the system itself. Therefore, there has been research done in what similar failures there are between the systems. In  , the research is literature based where failure rates are taken in consideration of different systems. There has also been research for lifetime estimations but none with a machine learning approach.
The thesis will initiate in the first chapter with an introduction of power electronics and the problem description. Chapter two will describe background details of power electronic systems on a more technical level and past research. The third chapter will be an analysis of failing causes and components and what models are available for evaluating. The fourth chapter presents the method used for evaluating the system and how measurements will be done. The fifth chapter will present the results of the thesis in more depth. Finally, the sixth chapter will conclude the work and include the impact of future work in this field.
2.1 Power electronic converters
There are four main kinds of power electronic converters that are of use in electronic products. Most are designed as such that the converter is a switching converter. The switching converter consists of input and output ports. Input ports contain power injections and other input ports process control inputs. The output ports consist of the output power which is the processed input power passed through the converter.
One type is the DC to DC type of converters which converts the input voltage to either a higher or a lower voltage at the output. Depending on the application, the design can be adjusted to fit the desired output voltage. For example, the boost converter ramps up the input voltage to a higher output voltage.
Another method of conversion is the DC to AC conversion. The converter is also known as an inverter. Its DC input voltage is converted in such a manner that there will be an AC voltage on the output of the converter.
The AC to DC converter is known as a rectifier and the purpose is to convert AC voltage into DC voltage. The usage of such converters could be in for example household electronics that are connected to the power outlets of the house.
The final conversion type is to convert AC voltage to AC voltage. It is used to convert the input AC voltage to either a higher or lower output AC voltage.
2.2 Lifetime model of a power converter
Power converters, like many other electronic systems, are dependent on its components to be functional. Failure in some parts of electronic systems might not yield direct failure but could have a negative impact on the system. In reliability engineering, a bathtub model can be used to describe components lifetimes. The model can be depicted as in figure 2.1 and shows how the lifetime can be viewed. Initially, the converter is in a stage called infant mortality where failures occur because of practical reasons such as soldering and welding issues. Subsequently, the converter reaches its steady state phase where the failure rate is constant and lower than the infant mortality phase. As the converter reaches the end of the steady state phase, it will reach the wear out phase and degrade exponentially.
Figure 2.1: The different lifetime stages expressed in failure rate as time passes. Copy from 
One interesting aspect that in the lifetime model is when a failure will occur. Therefore, the mean time to failure (MTTF) could be of good use in terms of reliability. The probability of failure, ( ), in a power electronic
system can be described by the equation (2.1) which is also known as Weibull distribution.
( ) (
(2.1) In equation (2.1) the t is time parameter and the , and are variables that must be decided through tests or previous data and fit to the measurements. The probability of failure can in turn be used for the calculation of the reliability function ( ). More closely, it is explained in equation (2.2) how they are related.
( ) ( ) (2.2)
Which further implies that the reliability function can be calculated as in equation (2.3).
( ) (
(2.3) With all the necessary information, it is possible to find the MTTF as in (2.4).
∫ ( ) ∫ (
(2.4) The bathtub model in figure 2.1 is expressed with the failure rate ( ) over time. This failure rate can be estimated as in [reliability metrics] from the known or calculated ( ) as in (2.5).
( )( )
( ) (2.5)
In  they estimate the in the bathtub model to be in the infant mortality stage and in the wear out stage. It is estimated that the in the steady state stage.
Individual components can have significant effect on the entire system.
Therefore, studies have focused not only on converter system failures but also on the component reliability.
2.2.1 Transistors in converters
Transistors are used in power converters as switches. The two types of transistors are the insulated gate bipolar transistor (IGBT) and the metal oxide semiconductor field effect transistor (MOSFET). Issues regarding transistors are that there are no general models for lifetime. Several research papers have tried to evaluate transistors during high stress conditions to enhance the knowledge around transistor failures. Important factors, like temperature, is a main interest regarding transistor lifetime modeling. Further, lifetime models express its lifetime in cycles to failure depending on the temperature. Therefore, how often the cycles occur is an important factor to estimate the lifetime for the transistor. 
Transistors in a converter act as switches for the control of the power conversion. However, the switching does come with power losses.
Switching time between the on and off state may result in large power losses even if the switching time is low. Therefore, the control is crucial for decreasing the time between the switching between on and off. With a proper duty cycle or an advanced controller, the switching can be better controlled and decrease the losses.
It is also estimated that a large portion of the failures in power electronic systems are of consequence to semiconductor failures. They are accounted for approximately of the failures which can be seen in  .
2.2.2 Capacitors in converters
Capacitors in power converters are used in several parts of the converter. It is the type of capacitor that is of most interest. In the power electronic system, capacitors are of various kinds and not specific to a certain model.
The entire system uses capacitors of different size and models which are used for different purposes. Therefore, all the capacitors in the converter are not critical to the lifetime of the converter.
One interesting capacitor model used in the field of power electronics is the electrolytic capacitor. The interest specifically for electrolytic capacitors is that it is one of the components in a converter that degrades the fastest.
Therefore, it is of interest to examine a power electronic system´s lifespan by considering the electrolytic capacitors. It is estimated that electrolytic capacitors are the largest contributing component that fails in power electronic systems. Approximately of the failures consist of electrolytic capacitors.
2.2.3 Diodes in converters
Diodes are essential components in power converters. They appear in different models and different parts of the design. It is a key component in the AC to DC converters, also known as rectifiers. For the specific case of AC to DC conversion, the diodes are used for the rectification of the ac current.
Studies show that diodes in power converters are a failing component which could have a broad impact on the system. It is, however, not as common for diodes to fail as much as other components. It is an interesting component to consider due to its importance for the power electronic converter. Approximately of the total failures are accounted for diodes failing, according to  .
2.2.4 Metal oxide varistors
The metal oxide varistors (MOV) is a component that is used in converters as protection from transients. Voltage spikes that could damage the system are avoided and will not affect the system. The interest in MOV´s is rather in the degradation of the component. MOV´s can protect the system to a certain point depending on the amount of transients it has tolerated. After that, the component will not be able to tolerate the stress it has endured as it used to. One type of transient that could be considered is lightning strikes which could have an impact on the MOV.
The MOV´s are typically degraded as transients occur. Mainly there are changes in the structure of the component which causes the component to
degrade. The leakage current yields losses in form of heat, which in turn affects the component structure that causes the degradation.
2.3 Solder joints
Soldering is an essential part of the manufacturing and necessary for putting components on the converter. However, soldering joints are prone to be fatigued. It is of interest especially for the transistors which makes up for a part of their failures. Whenever the joints are fatigued, the same phenomenon occurs as for the bond wires and the temperature will increase. The increase in temperature results with the component to increase in temperature as well. This temperature increase could in turn lead to the bond wire loosening and that it lifts off. In figure 2.2, all the layers of an IGBT transistor and their connections are shown, as well as the soldering and the bond wire.
Figure 2.2: The layers of an IGBT transistor and their connection to each other. Copy from 
2.4 Bond wire lift off
The bond wires can be found in the power module in power electronic converters. Its function is to provide a connection between two spots, basically a different form of a cable but is made of aluminum.
The challenges the bond wires faces is that they are prone to degradation whenever the bond wires starts cracking, which can be seen in figure 2.3.
Bond wire cracks occur whenever the bonding happens. Its form can shift from hard to soft and vice versa whenever the bonding takes place and causes these cracks. The cracks will cause increase in the resistance and thus increase losses which result in increased temperature. This implies that cracks might not be viewable with the eyes but can be understood from the temperature increase.
Figure 2.3: The cracks in bond wires from stressed conditions. Copy from 
2.5 Efficiency of a power converter
Power electronic systems deal with the issue of power loss like many other systems in practice. The fundamental importance of the losses in the following study is that they can be found as heat in the system  . A converter can in terms of power be viewed as in figure 2.4 where it is possible to note that there are losses in the system.
Figure 2.4: Power electronic system with input power, output power and the power losses in between.
The three powers that are depicted in figure 2.4 are described differently but relate to each other. Input power into the converter, which is an alternating current, is defined by first calculating the input current in root mean square form (RMS) as the following:
Further, the power calculations require the voltage to be in RMS form as well and can be described as the following:
The is the peak value of the voltage. With the known RMS current and the corresponding RMS voltage, it is possible to calculate the input power as:
(2.8) The output power on the other hand is a direct current and can thus be calculated differently. The current nor the voltage require any RMS calculations and the output power can therefore be expressed as:
(2.9) Where is the output voltage from the converter and the is the corresponding output current. 
With the known quantities, it is possible to calculate the efficiency of the power converter. The relation is defined as the output power over the input power and mathematically described as the following:
It is possible to acquire the relation of the powers in the system from figure 2.4 as:
(2.11) Which in turn imply that the losses are defined as:
(2.12) Losses in the system can theoretically be calculated by measuring input and output power of the system or deciding it from the loss percentage in the efficiency.
Degradation of the power electronic system and its components are of interest for the lifetime expectancy. The difficulty is to define a degradation feature that can at least be remotely surveyed. In this chapter, methods of lifetime estimation are analyzed and compared to choose a proper method to do such estimation.
3.1 Coffin-Manson-Arrhenius estimation
Estimation of some systems or components is sometimes done with the Coffin-Manson-Arrhenius estimation. It expresses the lifetime in life cycles, , rather than the usage of time. This type of model is commonly used in estimations for transistors and diodes. It is defined with aspects that are considered to be relevant for the lifetime. The model is denoted as the following:
(3.1) Where is the difference in the junction temperature and is the Boltzmann constant. Further, is the activation energy and is the average temperature. The rest, and are found through data fitting of measurements. However, activation energy can also be decided from data fitting.
3.2 Capacitor lifetime estimation
The capacitor lifetime is of interest for a converter when considering the lifetime. Several researches have included lifetime models of capacitor. The most common found lifetime model of capacitors is defined as:
(3.2) The expression provides the lifetime, , of a capacitor in hours. is the rated hour at the specific temperature given at . The final term, , corresponds to the temperature of the capacitor under operation. It is also the term that varies and the lifetime model is reliant on. Therefore, if the model of the capacitor can be found, then the lifetime can be predicted.
3.3 Solder joint lifetime estimation
Solder joints are estimated differently and depend on several aspects regarding lifetime. According to  , most of the lifetime models are based on energy. One model that is presented in the report is denoted as:
( ) (3.3)
The relation estimates cycles to failures like the Coffin-Manson-Arrhenius estimation. Other parameters are estimated to and from tests. The parameter that changes and is required for the estimation is the strain energy which is denoted as .
3.4 Bond wire lifetime estimation
Bond wires are, like the solder joints, estimated in terms of life cycles rather than time. Also in  , plastic strain is the key feature that is considered in the estimation and is based on the Coffin-Manson estimation. It is defined as the following:
(3.4) In the following relation, represent the plastic strain in the wire bonds. The constants and can found through experimental testing by applying stress to the wire bonds. It is also possible to use Finite Element Analysis to acquire the constants as well. Other models can also be found where the same relation is used, but use different features, such as the stress range rather than the plastic strain.
3.5 Remaining useful lifetime
Remaining useful lifetime (RUL) is a method of estimating how much is left of the lifetime of a product based on data. Three main estimator models can be used to reach such estimation. The choosing of the method is dependent on the product itself. It is therefore important to understand the system whether one of the methods would work or even be beneficial.
Figure 3.1: The main RUL estimation methods and their subgroups dependent on the data type. Copy from 
3.5.1 Run to failure data of AC to DC converter
The accelerated aging method relies on collecting data of similar products that have been stressed enough to fail. Data on the following matter would be used in a way that the algorithm matches the degradation data of a previous failure. By this method, it is possible to identify and match the current system to a previously failed system and estimate the RUL from that.
The practical problems regarding the following method is that it does not fit all type of systems. Accelerated aging of the proposed AC to DC converter would require a substantial amount of resources. The necessary resources for that type of data might not prove to be beneficial in the end.
It would require time in terms of years and an amount of converters that would be costly. The data would also lack external validity since its failures are not naturally reached. 
3.5.2 Lifetime data of AC to DC converter
Data of previous products that have been used until they no longer are functional is the data used for the following RUL estimation. The method uses hazard models and probability distributions to reach the estimation.
The algorithm mainly uses the data to determine the RUL by comparing with the current data. The product yields data, in for example the form of temperature of a system or component and can decide the RUL based on previous lifetime data.
The method can estimate the RUL accurately since it is based on similar products that have naturally reached their end life. In terms of validity, data of past products would result in more reliability of the results as well.
The main issue with the method is that it does not fit with the case of the AC to DC converter. The reason is that none of the AC to DC converters have ever failed. Since the converter is critical to always be functional, they have always been maintained before reaching failure. Therefore, there is no data of previous failures and the method is not compatible with the converter. 
3.5.3 Threshold data of AC to DC converter
Real time data processing of key parts of the converter design are of interest in the following method. The method acts as a surveillance system for the product and includes RUL estimation. Its way of estimating is however dependent on significant knowledge of the system and its behavior. Components that are of importance are manually given a threshold of a feature. That feature could be the maximum temperature of the component which is taken in consideration when estimating the RUL.
Threshold data is suitable for the AC to DC converter in the sense that run to failure and lifetime data are difficult to gather. It is also based on real time data collection which makes it valid for the specific environment it is used in. Except for the convenience, the method is neither costly nor difficult to implement on the converter itself. Mainly, the difficulty lies in the fact that there is need of more research in the threshold of the used components. But the initiation of data collection of components and the system in total will provide a clearer view of the operation of the converter and its components. 
3.6 Evaluation and reliability of the models
Methods that include life cycles are not precise in the specific matter and lack the necessary accuracy. They are mainly based on old models and are difficult to apply with real time data. The models that are found for transistors and diodes are from accelerated aging tests which imply lower external validity of the estimation. Meaning, the estimations are not as accurate as they could be from natural failures occurring in the system.
However, the capacitor lifetime model is well established and reliable to use. The estimation is also a general estimation and possible to fit to specific capacitors for higher accuracy in the estimation. Therefore, the following lifetime model is used as a basis for the lifetime estimation.
The methods for lifetime estimation of the converter are limited from run to failure methods and previous lifetime data. The reason being is that there is no data available of older products or the possibility of run to
failure experiments. Also, run to failure experiments could take a long period to finish and are also costly.
The threshold data RUL estimation is suitable for the converter as it can act as a real time surveillance system. Data will be collected and the RUL estimation will update consequently. Additionally, applying a combination of the capacitor lifetime model with the threshold data RUL estimation will form a basis. In continuance, real time data collection of other components will establish a better lifetime estimation of the remaining components.
In order to estimate the lifetime of the converter, it is necessary to have real time data of the converter. It provides true values that are specific for the converter. The data is mostly important for the RUL estimation and provides basic data of the converter which do not exist. The following chapter demonstrates the design and construction of a sensor based system that collects data. That data is further processed in Matlab.
4.1 Measurement system
The sensor based system´s purpose is to have sensors connected to the converter and collect data from it as well as logging it. In the future cloud computing might be used for such purposes. But for the moment, the sensor based system can be depicted as in figure 4.1.
Figure 4.1: The measurement process of the sensor based system from the converter to the processor.
The processes are shown clearly in figure 4.1 and the order of the processes. Sensors which are connected to the converter are transmitted through the measurement circuit, which is a prototype that establishes the connection between sensors and the analog to digital converter (ADC). The data is then processed through the ADC and passed to the processor which in turn process the data and logs it. Future designs of the converter could have an integrated sensor based system for the following cause as well.
4.2 Measurement equipment
To make measurements on the AC to DC converter, an Arduino MKR GSM 1400 will be used. The Arduino´s model importance for temperature-, voltage- and current measurements is not of great importance. Arduino boards, in general, are compatible with the corresponding measurements.
The specific model was chosen with regards to its capability of wireless communication. Processes can be initiated wirelessly as well as cut off on demand.
The data logging is done on a micro SD connected to an MKR MEM shield.
Logging data to a micro SD is preferred since it enables large quantities of data to be stored. The MKR MEM shield provides protection to the Arduino board in the case of hazardous currents and voltages, thus ensuring a reliable method of data collection as well as providing protection.
For the voltage measurements, the voltage is measured directly from the converter. In between the Arduino and the converter there is a voltage divider that attenuates the voltage. Arduino boards have a maximum input voltage for proper operation. The voltage read by the Arduino needs to be at a maximum of in the case of the MKR GSM 1400 model. Voltage sensors are not used for the following case since the measured signal is processed properly.
The current measurements are done with an LEM HO 6-P/SP33 Hall Effect sensor. Currents up to can be measured with the sensor. The maximum output current from the converter is which proves the sensor covers the entire range. However, the input current varies from up to .
Therefore the LEM HO 25-P/SP33 model was chosen to cover a larger range. The LEM HO 25-P/SP33 model can measure currents up to . The temperature measurements of the components are done with LM35DZ temperature sensors. The sensor can measure the temperature with a maximum deviation of at its maximum temperature. Its temperature range is between up to . The LM35DZ sensors are small in size and therefore do not require a large area for the measurement. It is also light and flexible sensors that can adapt to the measurement area. A multiplexer of model MAX4617 is also used in order to increase the number of input channels to the ADC.
The measurement circuit that contains all the connections from the sensors to the ADC can be seen in figure 4.2. All the measurements except the voltage are done with the circuit. The voltage will rather be measured from a voltage divider soldered onto a shield to protect from voltage spikes. Practically, it is easier to connect cables in that way.
Figure 4.2: The designed measurement circuit for temperature and current measurements
4.3 Safety precautions
Considering that the AC to DC converter chosen for this thesis can go up to up to , precautions have to be made. The Arduino MKR GSM 1400 can have an input maximum of which is less than of the incoming . Therefore, a voltage divider is designed for that specific purpose. For the same reason, an additional voltage divider is designed for the input voltage.
Preventive measures have also been taken to not harm computers or other hardware. Since the Arduino is dealing high voltage and high currents, an Arduino MKR Connector Carrier is used. The connector carrier will mainly work as shield and regulating the voltage supply. Therefore, no computer or other hardware is necessary to be connected. The carrier can be connected directly to a supply and control the voltage that is fed to the Arduino.
4.4 Voltage divider design
The accuracy of the voltage divider is crucial to the Arduino. Voltages over the maximum can be destructive to the Arduino board. Therefore, the voltage divider design considers a lower output voltage than . The reason is that the input could vary and go beyond the maximum . To ensure that it does not happen, the calculations consider an output voltage of . In the case of variations, the output voltage is ensured with a margin to be below .
According to the definition of a voltage divider, there is a relation between the input- and output voltage. The relation is in general defined as in (4.1)
It can also be viewed from the general definition as in figure 4.3 how the relation is represented.
Figure 4.3: The general voltage divider from input voltage to output voltage.
In figure 4.3, is the input voltage to the voltage divider and is the output voltage of the voltage divider. is the primary impedance of the voltage divider and is the second impedance.
For the specific case of the Arduino, the input- and the output voltage are
and . With the voltages known, the relation can be simplified as in (4.3).
The expression can be further simplified into a relation between the resistors. With simplification of the equation, the relation evolves such that
The relation implies that resistor should be approximately times larger than the resistor. A resistance of for gives a value of for the resistor. But in practice, the resistors are necessary to be measured to yield a close value as possible. Therefore, the chosen resistor for is which in turn implies that is closer to .
Resistors have a maximum tolerance of power to prevent them from over heating. In order to avoid the upper tolerance, the resistance is divided into four resistors. Therefore, can be expressed as four resistors. The resistors are defined in ascending order as , , and . Resistance can further be defined as . To reach a total resistance of , the resistors , and consist of resistances. For the resistor, a resistance of is designated to reach the calculated value of . The resistances are approximations and in practice the real values are denoted as the following equations.
Summing up the resistances, the total resistance of will be less than the calculated value. The calculations implied a higher resistance for the resistor . However, the total resistance with regards to practical correction is
The voltage divider for the attenuation can be seen in the figure 4.4.
Figure 4.4: The voltage divider split into several resistors to prevent over heating.
Similar to the output voltage, the input voltage needs to be attenuated as well. However, the input voltage is difficult to reach from a practical perspective. Therefore, another point that is close to the input is chosen as a measure point which only differs with an inbuilt voltage divider. The measure point already has a voltage divider that attenuates the voltage with a factor of . Maximum voltage for the voltage divider is which in turn is attenuated to . To measure the point, a voltage divider is designed to attenuate the voltage to . The same procedure is done for the design of the second voltage divider.
Setting the resistor to yields from (4.1) that should be . Since the values are difficult to match in practice, the closest values were chosen and taken in consideration. The value of the resistor which represents is and the resistor which represents becomes . The voltage divider for the input voltage into the converter is represented as in figure 4.5.
Figure 4.5: The voltage divider for the voltage coming into the converter.
The voltage dividers are soldered onto the shield and connected to the input of the microcontroller. Connections and the calculations to show the proper measured values are accounted for in the software. The construction can be seen in figure 4.6.
Figure 4.6: The soldered voltage dividers onto the shield and connected to the inputs.
4.5 Analog to Digital Converter
The Arduino board has an integrated ADC. ADC´s depend on the sampling frequency which the measurement is performed under. In the conducted measurements, the sampling frequency is not high enough to have significant consequences on the measurements. However, in order to prevent noise on the input of the ADC, a capacitor placed in between. The capacitor will smooth out and provide cleaner data. It can be viewed from a theoretical point of view in the figure 4.7 how the circuit will look like.
Figure 4.7: The voltage divider with a capacitor to decrease noise into the ADC.
The input current into the converter is an AC sinusoidal current with a frequency of 50 Hz. Therefore, in order to measure the current, the measurements are used to calculate the root mean square (RMS) value of the AC current. The RMS value of the current can be calculated from (4.9) which is the discrete form of (2.6)
Where is the period of the AC sinusoidal current. Since the current is of 50 Hz implies that it takes 20 milliseconds for one cycle. According to the well-established Nyquist criterion it is stated as in equation (4.10).
Where is the frequency of the AC current and sampling frequency that is necessary to avoid aliasing. Therefore, a sampling frequency is chosen so that a sample is taken every 1 millisecond. The sampling frequency will be 1000 Hz which is well over the criterion for aliasing. 
4.7 Experimental setup
The measurement setup initiates with the placement of all the sensors.
Depending on the sensor, it is placed on a specific area of interest to measure. The measurements can be divided in to three main categories consisting of temperature, voltage and current. Figure 4.1 can be evolved further as in figure 4.8.
Figure 4.8: The in depth process of the measurement done on the converter.
For the temperature measurements, temperature sensors are placed on components which are critical. The research is important for the placement of the temperature sensors. Components which are prone to fail and temperature sensitive are under consideration when the sensors are placed. These components are the capacitors, transistors and the diodes.
The MOV is also a component which is necessary for the system protection and is therefore of interest to examine as well. These are further connected to the multiplexer in the circuit to obtain more input slots for the ADC. The upper heatsink contains four Schottky diodes, three N- MOSFET transistors and one IC driver MOSFET which will be known as the
“upper heatsink” in the results. The same goes for the lower heatsink which consists of two Schottky diodes, two N-MOSFET transistors and one Diode-bridge.
The voltage measured on the input side of the converter is obtained with a voltage divider. Voltage divider that is used for the input side attenuates down to . The AC to DC converter has a specific point on the input were the voltage is attenuated to . It is a reachable point on the
converter where the noise is at minimum. The measured point attenuates the voltage by a factor of . That factor is accounted for in the measurements to get accurate data. Arduino boards have the capacity to read the voltage directly. Therefore, there is no sensor used for the specific purpose of measuring the voltage. The same procedure is done for the voltage measurement on the output side. In the case of the output, a different voltage divider is designed to meet the specifications. The used voltage divider attenuates the voltage down from to .
Current measurements are done with the Hall Effect sensors. To measure the current with the Hall Effect sensors, cables are run through the sensors.
The magnetic field generated from the cables is measured by the Hall Effect sensor and logged. Because of noise, the collected data will have large variations. To prevent large variations, averaging methods are used to smooth out the data on the output and RMS calculation for the input.
The voltage supply to the converter is connected directly to the grid.
Regular operation of the converter is when it is connected directly to the grid. Therefore, it is preferred to have it connected to the grid from a validity perspective. The voltage on the output of the AC to DC converter is controlled by a control box. To set the output voltage coming out, the control box is used. However, it cannot set nor control the output current of the converter. The way to control the current coming out is to connect a load on the output.
The ability to set the voltage and the current coming out from converter provides the possibility of controlling the output power. One main interest is to set different output powers with different voltages and currents.
The converter is placed inside the temperature chamber in order to expose it to different temperatures during operation. A circuit board is placed right beside it with the sensors being connected to the converter. The board is mainly used as a means to implement the multiplexer and minimize the use of cables. Therefore, the Arduino is placed outside the chamber and connected with minimal amount of cables to the board. It is also preferred to have the Arduino outside since it performs better in room temperature.
A test case with a simple circuit board is done before the measurement circuit is used. The test case is also done in the temperature chamber with all sensors connected and can be seen in figure 4.9.
Figure 4.9: The converter in the temperature chamber with all sensors connected.
4.8 Experiment procedure
The same procedure is done for three different temperatures.
Temperatures of interest to examine the converter under are , and . The high and low temperatures are chosen to examine the system performance during extreme environment temperatures. Room temperature is also of interest to examine.
Under each temperature, there are four output power cases to stress the converter with. According to the power law, the output power can be calculated from equation (4.11). 
Where is the output load and is the output current of the converter.
The test cases are stated as the following:
100 W ( output load and output current) 200 W ( output load and output current) 400 W ( output load and output current) 800 W ( output load and output current)
In total, the measurements will consist of four test cases for each temperature which sums up to 12 cases. What is interesting about the exact output power cases is that there are two loads used and each is examined for two output currents. Specifically, and then twice as much current which is . The interest is to examine whether there are any specific changes with twice as much current and the same load.
4.9 RUL estimation through real time data
The RUL estimation will be based on the collected real time data that has been logged. One limitation that this method will face is the fact that there is no previous data. Therefore, even though the method is based on real time data, it will not indicate an accurate estimation. However, in practice whenever the sensor system collects more data it will be possible to make more accurate estimations. More specifically, the equation found in  is depicted as in (4.12).
( ) ( )( ( ) ( ) )
(4.12) in the equation is the resulting value in exponential model and is a constant that defines the bound of the model. is a lognormal distributed value and is a Gaussian distributed value. Further, is the additive noise and is the noise variance. 
The reason that it is an exponential model is that according to the research, the damage is in cumulative form for most components. Meaning it increases over time and is not constant until the end life is reached. If it
however would be relatively linear, the model could be fit to the data. In fact, the model is fitted to the real time data and from that it is compared with the defined threshold. Through these measures, the RUL is estimated.
4.10 Regression analysis
The regression analysis will be a useful tool to predict the lifetime.
Regression could be used in the case of lifetime estimation in the parts where temperature is of interest for determining lifetime. The least square regression can be estimated from the following method.
̂ ( ) (4.13)
Where the and are expressed as
( ( ) ( )
) and ( ( ) ( )
The and the are the real time measurements in the research that will be done. Further, the is dependent on and expressed as in (4.15).
( ) ( ) (4.15)
In the following equation, the is the parameter vector of the expression and constant. 
Temperature measurements of components will most certainly increase in temperature in the early stages and then reach a steady state. By understanding the behavior, the temperature can be defined from the exponential function in (4.16).
( ) (4.16)
Where and are variables of the parameter vector that are determined from the least square estimate. In the equation, t is the time of the taken measurement.
The expression can be translated into a line so that the expression is possible to use the linear least square relation. In the form of a line, the expression can be written by taking the logarithm as in (4.17).
( ( )) ( ) (4.17) In the following case, the equation of a line can be identified from the relation. The well-known equation of a line is denoted as in (4.18).
Where the factor is the slope of the line and is the value on the y-axis where the line cuts whenever . Matching the following, it is possible to identify that and that ( ).
If the equations (4.15) and (4.18) are considered, the parameter vector becomes as in (4.19).
( ) (4.19) With the following, it is possible to use the linear least square estimation to obtain the unknown values.
4.11 MOV experiment
The MOV used in the converter does not have any degradation model nor has there been an experimental measurement whether temperature increases as the degradation occurs. In following manner, a test is advised in order to validate the theory that leakage current increases the temperature of the MOV. Therefore, the MOV will be shot with electric pulses as high as possible to imitate a lightning. The pulses will contain 2000 ampere and 2000 volts which implies a power of 4000000 watt (4 MW). Since it will be difficult to measure temperature at a specific pulse, the experiment will just validate the theory that leakage increases temperature. Future research, could use the fact that temperature increases as the leakage current increases and create a degradation model.
Results and discussion
The converter was tested in four different power cases where each case was tested during different environment temperatures. In total, there were 12 measurement scenarios and the results included temperature evolvement, efficiency and capacitor degradation. Each case is presented in the following chapter with measurement results and a discussion of the case.
5.1 Case 1: 100 W output power
The case was the lowest power the converter was tested by. Its temperature evolvement in all three environment temperatures is depicted in figure 5.1 and the efficiency of the three environment temperatures in figure 5.2. In table 5.1, all steady state values are presented in comparison to the environment temperatures. Table 5.2 contains the efficiency in comparison to the environment temperature.
Figure 5.1: The temperature behavior of the converter with 108.8 and at , and respectively.
Figure 5.2: The efficiency of the converter with 108.8 and at , and respectively.
Deviation from room temperature
Deviation from room temperature
Deviation from room temperature
Table 5.1: Temperature of each component in comparison to the reference temperature for the case of 100 W.
Input Power in W Output Power in W Efficiency in %
Table 5.2: The efficiency of case 1 with respect to the environment temperature.
5.2 Case 2: 200 W output power
The case was achieved with a 195.6 load and current. Its temperature evolvement in all three environment temperatures is depicted in figure 5.3 and the efficiency of the three environment temperatures in figure 5.4. In table 5.3, all steady state values are presented in comparison to the environment temperatures. Table 5.4 contains the efficiency in comparison to the environment temperature.
Figure 5.3: The temperature behavior of the converter with 195.6 and at , and respectively.
Figure 5.4: The efficiency of the converter with 195.6 and at , and respectively.
Deviation from room temperature
Deviation from room temperature
Deviation from room temperature
Table 5.3: Temperature of each component in comparison to the reference temperature for the case of 200 W.
Input Power in W Output Power in W Efficiency in %
Table 5.4: The efficiency of case 2 with respect to the environment temperature.
5.3 Case 3: 400 W output power
The case was achieved with a 108.8 load and current.
Since , the input power reaches approximately . Its temperature evolvement in all three environment temperatures is depicted in figure 5.5 and the efficiency of the three environment temperatures in figure 5.6. In table 5.5, all steady state values are presented in comparison to the environment temperatures. Table 5.6 contains the efficiency in comparison to the environment temperature.
Figure 5.5: The temperature behavior of the converter with 108.8 and at , and respectively.
Figure 5.6: The efficiency of the converter with 108.8 and at , and respectively.
Deviation from room temperature
Deviation from room temperature
Deviation from room temperature
Table 5.5: Temperature of each component in comparison to the reference temperature for the case of 400 W.
Input Power in W Output Power in W Efficiency in %
Table 5.6: The efficiency of case 3 with respect to the environment temperature.
5.4 Case 4: 800 W output power
The case was the highest output power the converter was tested with. Its temperature evolvement in all three environment temperatures is depicted in figure 5.7 and the efficiency of the three environment temperatures in figure 5.8. In table 5.7, all steady state values are presented in comparison to the environment temperatures. Table 5.8 contains the efficiency in comparison to the environment temperature.
Figure 5.7: The temperature behavior of the converter with 195.6 and at , and respectively.
Figure 5.8: The efficiency of the converter with 195.6 and at , and respectively.
Deviation from room temperature
Deviation from room temperature
Deviation from room temperature
Table 5.7: Temperature of each component in comparison to the reference temperature for the case of 800 W.
Input Power in W Output Power in W Efficiency in %
Table 5.8: The efficiency of case 4 with respect to the environment temperature.
5.5 RUL estimation
The RUL estimation with a pre decided threshold provided a result of 1.5 years. 1.5 years is not an accurate result since the products have been in use more than 1.5 years. However, the inaccuracy can be a result which indicates that the slope of the degradation model is difficult to estimate.
The slope requires more information to be calculated more accurately.
Lack of data proved in the calculations of the degradation model that the method is inefficient with the collected data. This is however not a significant issue in practice as data flows in and is logged.
5.6 Capacitor lifetime
The electrolytic capacitor lifetime is estimated with the formula derived from the Arrhenius Law. In figure 5.9 the lifetime can be viewed as the temperature increases. The electrolytic capacitor´s specific rating was used in the estimation model to increase the validity of the experiment.
Therefore, figure 5.9 depicts the lifetime in years in reference to the temperature. It can as well be understood that every increase in temperature halves the lifetime of the capacitor.
Figure 5.9: Capacitor lifetime model depicted in years in reference to the temperature.
As it is viewed in figure 5.9, the capacitor´s lifetime is dependent on the temperature it is exposed to. The specific temperatures that were exposed to the capacitor can be found in table 5.9 with the lifetime estimation.
Temperature Lifetime at 100 W
Lifetime at 200 W
Lifetime at 400 W
Lifetime at 800 W 5 413 years 399 years 360 years 343 years
23 103 years 96 years 90 years 80 years
55 11 years 10 years 9 years 8.5 years
Table 5.9: The lifetime of the capacitor in terms of years with respect to the exposed temperature.
As stated earlier, temperature is a key factor for capacitor lifetime. The regression analysis proves that there is a strong correlation between used time and the temperature as well. These regression models can be used for machine learning purposes for predicting upcoming temperatures and calculating lifetime. The regression models compared to the raw data can be viewed in figures 5.10, 5.11, 5.12. Regression models are matched with the same load and current since it varies significantly depending on the current.
Figure 5.10: The regression models, colored in black, of the acquired data at 5 .
Figure 5.11: The regression models, colored in black, of the acquired data at 23 .
Figure 5.12: The regression models, colored in black, of the acquired data at 55 .
Regressive models for the temperature prove that there is a strong correlation between the temperature and the used time. In the beginning, the temperature rises until it reaches its steady state. The steady state however does increase in temperature as time passes and the regressive models can be used for such purposes. A logarithmic function would be the opposite of what is obtained. It would rather be a better fit for shorter times but would in the end have a high slope when the temperature reaches steady state.
5.7 MOV results
The results from the pulses that were shot into the MOV proved that it increases in temperature as the degradation occurs. In total, there were 200 pulses shot at the MOV with 4 MW in each pulse. The MOV was measured for temperature and leakage after every 50 pulses to investigate its degradation. In the final pulse, the MOV resulted in a small but intriguing explosion in which the remains can be seen in figure 5.10.
Figure 5.10: The destroyed MOV after 4 MW pulses consisting of 200 pulses in total.
5.8 Evaluation of the results
From the temperature measurements of the components, it is found that they reach approximately the same temperature with different input power. The interesting aspect is that at 100 W input power, the efficiency is rated 65-67%. Meanwhile the efficiency is rated at 89-92% at 800 W input power into the converter. The efficiency rating can give a hint to how much of the power that has fulfilled its duty and how much that has gone lost. At the 800 W input there are losses from 8% to 11% from the input to the output. The 100 W input case has 33% to 35% loss, which is 22-27%
difference in losses compared to the 800 W input case. Losses in efficiency implicate that parts of the electrical energy has been transformed to another form, heat. Low efficiency is therefore not desirable since components in the system are exposed to higher temperatures.
In the following case there was actually no excessive heat in the specific components for the low efficiency cases. It means losses occur not only in the specified components but also in the less important ones for lifetime importance. However, it is possible to see that the upper heatsink and lower heatsink yield higher temperatures in the cases where there is 2 A output current. This is because of the power losses in the transistors and the Schottky diodes are highly dependent on the current flowing through.
Therefore, lower current is desirable for the transistors and Schottky diodes in terms of degradation.
The resulting measurements indicate that the environment temperature have an effect on the converter´s performance. In tables 5.2, 5.4, 5.6 and 5.6 it is clearly seen that the higher the environment temperature is the more efficient the converter will be. The reason is that some components perform better at higher temperatures rather than lower temperatures.
However, the difference between the efficiency at and is around 2-5% on the same load and current. The importance of the matter is that environment temperature can definitely affect the efficiency.
By examining figure 5.9, it is understood that lower temperatures yield very long lifetime for the capacitor. Every will halve the lifetime expectancy of the capacitor. However, it is difficult to give an estimation of lifetime for components such as transistors and diodes. If the capacitor is
improved in the sense of lifetime expectancy, it will bring forth other problems. From a reliability perspective, it is better to be dependent on the capacitor in terms of lifetime and not any other component. The issue with the capacitor having prolonged lifetime will cause the converter to be vulnerable to system failure from other components. It is therefore desirable to not have a too long lifetime expectancy of the capacitor as for example 100 years or more. There should be a balance, aiming for the same life expectancy on all components to minimize cost.
The metal oxide varistor also proved that the more pulses that it takes the more it will degrade it. 200 pulses of which consisted of 2000 A and 2200 V in each pulse resulted in the MOV to have a small explosion. The idea was that it will degrade over time and not be able to provide protection to the converter. Leaking current was checked for in between and measured directly and it proved that it was increasing as the pulses degraded the MOV. The leaking also proves that temperature will increase as the MOV is degraded. Therefore, real time measurements of the temperature can be sufficient enough to indicate if there has been degradation of the component.
In general the power electronic system would benefit of being used in a slightly warmer environment, not per say. It would enjoy the benefits of higher efficiency which leads to fewer losses. Rather than keeping the converter at lower temperatures, the system would be more dependent on the capacitor lifetime. The reason being that the converter is crucial to always be functional. Downtime of the converter would be costly and risk damage to the system it is connected to. Prolonging of the capacitors lifetime would mean that the lifetime of the system is not dependent on the capacitors lifetime expectancy. Components such as transistors and diodes are difficult to estimate properly in terms of lifetime expectancy. It would therefore bring forth random failures that cannot be predicted and would cause system failures which in turn is what is sought to prevent. A stable temperature is also good to avoid bond wire wear and solder joint fatigue.