 Welcome to class 34 in topics in power electronics and distributed generation. We have been looking at the structure of an IGBT module and we have seen that it consists of multiple layers and each layer made up of different material and during operation of the power module these layers heat up and cool down and they expand and contract because of the thermal variations and they can expand and contract to different extents resulting in stress between adjacent layers and the stress can actually lead to strain or plastic deformations which can actually cause damage. And we also saw that different parts of the module will operate at different temperatures your junction temperature would be one your top surface temperature of the chip would be different bottom surface temperature of the chip would be different coming all the way to the case where which would be another value. So there is thermal gradients within the power module and because of these variety of reasons you have the buildup of stress occurring within the power module within when it is in operation. Good reference to look at for the thermal models and thermal evaluation of the power semiconductors is a application manual of manufacturers such as a Semicron, ABB, IPEC, Mitsubishi wide range of manufacturers they provide good information on how you could actually do accurate characterization of the power semiconductor. And because of the heating up and cooling down the temperature cycling the fatigue can cause cracks in the dielectric ceramic layers isolation layers it can cause the wire bonds to break form cracks eventually break and lift off from the chip surface it can cause fatigue in solder joints the chip can delaminate from the substrate and lift off again losing electrical connection impacting the power dissipation within the chip and the power handling capability of the power module eventually leading to failure. These mechanisms are actually described in the reference by JEDEC standards and publications so this is a good standard to take a look at. We have seen that the thermal the cyclic life to failure due to the thermal cycling can be modeled by the Coffin Manson equations and the version of that was used by this group early in the mid 90s to evaluate the life and the impact of thermal cycling on power modules and they came up with an expression showing that your junction temperature variation delta Tj and your mean junction temperature could be factors which can actually affect the number of cycles to failure. So, with that we then looked at what could be the impact of looking at different junction temperatures Tj max for your design. So, you could design with a Tj max of 125 degrees centigrade or 135, 115 what would be the impact of doing that on your number of cycles to failure and the service life of your power module and we saw that we could use that as a design guideline based on your application requirement. And in this particular case we are looking at a system where it was going to a full on full off condition. So, it was essentially between it cycling between two temperatures, but in a practical application we know that you will be operating at multiple temperatures and not just at two temperatures. So, you have different cycles to failures depending on between two temperatures your which temperature you are cycling. So, you are you might be operating under different stress levels sigma i and if you have n i be the number of cycles to failure for the stress condition sigma i and small n i be the actual number of cycles that are experienced in your actual application. Then we looked at how you could evaluate the overall life based on the concept of accumulation of damage and this is essentially the miners law palm grain miners rule for accumulation of damage and evaluating fatigue failure under conditions of varying stress. So, we will before we go to the example will we looked at how one could then consider conditions of varying stress essentially what you are doing is you are looking at longer periods of time over which your semiconductor would be exposed to similar conditions of loading. For example, you might have daily loadings routines in a industrial environment you might have weekly loading types and transportation or household environment in renewable energy systems wind turbines might see similar level of wind patterns weather patterns on may over many months or on an annual basis. So, you have periodic loading conditions and then you are splitting it up into smaller cycles over the period and you are identifying the cycles to failure for each small sub period and then you accumulate the damage over the entire period and see how many such longer periods would be required for the damage normalized damage to actually become one. So, now we will look at an example where we are looking at case where your maximum junction temperature is 125, but you are varying between multiple temperatures. So, over a hour you are first going from 125 degree centigrade to 65 then going back to 110 coming down to 50 then going back up to 125. So, to evaluate the number of cycles to failure you then look at this one hour duration and you have you could consider one cycle as going back and forth between a valley to a peak back to the valley or. So, if you are going from only in one direction you could consider that to be half a cycle. So, in the first transition from 1 to 2 you are having a delta T of 60 degree centigrade and the mean temperature is 125 plus 65 plus 273.15. So, the mean temperature is 368 degree centigrade and then using the expression for cycles to failure and the parameters that were given in the previous example that we considered last time we have the number of cycles to failure to be 9.61 into 10 to the power of 4 cycles to failure. And in the second case when you are going from 65 to 110 your delta T j is 45 the mean temperature is 361 Kelvin 110 to 50 the delta T j is again 60, but now your mean temperature is lower 353 and the final transition 50 to 125 your delta T is 75 and your mean is 361. And for each of these conditions we are using this expression to obtain the cycles to failure. And then if you look at the number of the the number of actual operational cycles under each condition in a period period of one hour you are you are having half a cycle in condition one you are having another half in condition two. And so, each of this is actually each of the value of Ni is 0.5 and your Di by your normalized damage would be 0.5 divided by the NFI. So, your 5.2 into 10 to the power of minus 6 is 0.5 divided by 9.61 into 10 to the power of 4. So, you have the normalized damage for each of those sub durations and essentially what you do is you accumulate the total normalized damage. And on in one period which is essentially one hour your accumulated normalized damage is 1.7 into 10 to the power of 5. So, the question is how long would this particular semiconductor equipment last it would be your T rep divided by your total normalized damage during the T rep which is 1.7 into 10 to the power of and this is 5.87 into 10 to the power of 4 hours. So, converting from R to yours this is about 6.7 years. So, you can get an estimate for what the expected life would be in a more complex operating cycle of your equipment. You could also then consider you look at an actual loading situation for example, in a wind turbine you might not have a clean transitions which you could identify it could be much more complex nature of your waveform of your junction temperatures as a function of time. Also you would have large durations of time might be many months of data which you are actually trying to analyze. So, one need to find explicit methods to actually count the number of cycles and you are looking at multiple information. One is what is the delta T and also what is the average temperature or maybe the minimum temperature you are also looking at what would be the net result caused by such a variation and its impact on the expected life. And one way to do such counting of cycles is there are standards for us one is the ASTM standard practices for cycle counting for fatigue analysis. One way to do a cycle counting would be to actually maybe draw a line through the cycle and in fact, it will not be just one line you will have multiple lines because you are also interested in the range. And so, when you talk about the range it is essentially the difference from the peak to the valley and not just the level at which the number of cycles are being counted. So, if you could count the number of positive going and the negative going points in your level and you can see that you could for example, just count the positive going levels and for a sufficiently long sequence of data that would be just twice the number of counts if you are doing both positive and negative level crossing and you could use that information to actually look at how many cycles were there. Another way of looking at it would be to look at where you have points of inflection in the waveform where your d by dt is going through 0. So, identifying your peaks and the valleys often you may want to ignore extremely small cycles because we have seen that extremely small cycles very narrow cycles will not cause temperature change in that or the temperature change would be in the plastic range of deformation also we saw that because of the thermal capacitance it is not just the instantaneous loading it is a filter through the thermal time constants of your module and your heat sink. So, the waveforms would actually be much smoother than looking at it as a instantaneous participation times your thermal impedance thermal resistance of your thermal module of your system. So, you could calculate your peak and the valleys and use that to actually do the cycle counting another way is to look at the range counting. So, you look at the number of values where your delta t is going from one particular level to the next particular level and keep counting the number of such changes all along the waveform starting with the largest to the smallest. Rain flow counting is another range calculation where you are not just looking at say a positive range or also including the negative range. So, for example, you might look at the highest peak the next highest peak and the valley in between and you would count that as a cycle and then reduce the waveform and continue with the counts. So, there are a variety of ways of doing the counting your statistics that you get would be slightly different because depending on the number of the way in which you are counting, but the net result can be then used for your thermal evaluation of how many cycles to failure you could expect within such a module. So, the net results would be in the form of a table essentially your table would have the number of cycles your n i a small n i which is what you are trying to count and you are looking at delta t 1 delta t 2 up to delta t k. So, delta t 1 may be cycles which are 20 degrees from peak to valley delta t 2 might be cycles which are 40 degrees from peak to valley delta t k might be cycles which are 120 degrees from peak to valley. So, essentially you are looking at the range over which the cycle is occurring and the other column is your maybe the mean temperature this particular variation whether it is occurring at a mean temperature of 50 degrees or 40 degrees or whether it is at 60 70. So, if you might have t m 1 t m 2 t m 3. So, at the end of the cycle counting essentially you will have values that are populated all along this table and then you could evaluate the number of cycles to failure for each of those conditions then use the miners law to accumulate damage to look at what would be your actual expected lifetime of the equipment given that particular design. So, we have looked at how to look at the concept of accumulation of damage for power semiconductor device like a IGBT module. We could also use a concept of accumulation of damage to other components say for example, you could think of how it could be applied to the case of in case you are making use of a capacitor because we are not operating the converter always at its maximum power level you might be operating under a mixed condition where your core temperature might be going over different cycles depending on the loading the ambient etcetera. So, here we have an example where you have converter where you are making use of capacitors where you expect a lifetime of 5000 hours at a core temperature of 95 degrees centigrade and your power converter essentially operates in say an industrial environment and say your ambient temperature which is increasing from 40 degrees centigrade to 50 at 9 o'clock in the morning and it is reducing to a lower level at 9 p.m. and your converter is operating from 5 a.m. to 7 p.m. So, you might have a more complex operation like this and you want to see what could be the expected lifetime when you are having conditions of varying temperature then you could use the same concept of accumulation of damage to see how you could look at the life of the capacitor in such a more varying operating condition. So, you could then look at each duration. So, look at the duration when it is operating at night at maybe at no load at when the ambient temperature is low at 40 degrees at the core would be the same as the ambient temperature. So, when it starts operating the temperature gets hotter by the core gets hotter by 30 degrees and at once the ambient temperature also starts getting heated up around 9 then it goes from 70 to 80 when the power converter is shut down it comes back to say 50 and then at night it goes back to 40. So, you might have operation such as this. So, you could then look at the number of hours a day it would be operating under each of these conditions and what would be the corresponding core temperature under these different conditions. So, you are then looking at what is the life of the particular device the capacitor in this case in ours. So, we saw how you could make use of the expression that you have the linking the core temperature to life of the capacitor. So, based on such an expression you could evaluate the number of hours at 40 degrees the minimum life would be at the hottest temperature. So, it is going to just 1.41 into 10 to the power of 4 at 80 degrees whereas, when it at 40 degrees it is 3.54 into 10 to the power of 5. Then you could look at then what is the damage under each of these durations. So, for your duration di is essentially 8 hours, 3 hours, 11 and 2 hours under these different conditions. So, your D by D F which is the life of under each of this condition would be your normalized damage corresponding to one day overall period. So, you have 2.26 into 10 to the power of 5 which is essentially 8 divided by 3.54 into 10 to the power of 5. Similarly, the other entries in this particular last column. Then you could accumulate the damage occurring over the entire duration and that is 9.34 into 10 to the power of minus 4. Then you could look at what is the normalized this is the normalized damage that is happening on a daily basis and then you could look at what would be the number of days for this normalized damage to reach a value of 1. So, this would be 1 day divided by 9.34 into 10 to the power of minus 4. So, this is 1067 days this is 2.9 years. So, if you look at the table if you look at the number of hours at 80 degree centigrade that corresponds to 1.4 into 10 to the power of 4 hours. So, if you look at 1.4 into 10 to the power of 4 hours this corresponds to 1.6 years and that is just 11 hours a day. So, if you multiply that by the percentage of time that is getting operated you can see that most of the lifetime is getting consumed at the hottest temperature which is what one would expect in such a operation of the equipment. So, we can see that what we have seen so far is that between say for example, you have in a power converter between your device and your cost there is actually a trade-off say for example, if you want to reduce the power loss in semiconductor device you could use higher current rated say a device which would typically have a lower R on the on state resistance would actually be lower. So, as to reduce your power loss in the device, but then you would have to pay more money for essentially the higher cost of the higher current rated device. The other thing we saw in our examples of capacitor selection we could actually reduce your power loss in the capacitor bank at least initially by adding more capacitors in parallel when you are looking at the loss in the ESR, but adding more capacitors would involve more cost. So, there is actually a trade-off between the cost and the power loss and we also have now seen that there is actually a trade-off between the thermal analysis for reliability and essentially the power loss which is actually a function of the cost of the component. So, the reliability power loss and cost is actually a trade-off that you can actually apply in the design of the power converter and we have seen in our analysis of effective initial cost that we could actually now include factors of cost efficiency and reliability in a fairly straightforward manner to come up with something which balances between the cost of the component, the power loss over its operation and what is the reliability that you could actually expect for the component. It is also possible to incorporate factors such as weight, size, power density in such a effective initial cost calculation and do a overall analysis such that your design is actually a cost-effective design. So, at this point we have seen that in a power converter we have taken a look at two of the components. One is essentially your DC bus capacitor and the power semiconductor device, the switch, the transistor and the diode. The next major component in the power converter is essentially the output filter and we will take a closer look at how one could go about the design of the output filter and if you look at the filter it is typically inductive filter and we have seen in our analysis that in a power converter you would like to switch between a voltage source and a current source. In the power converter the DC bus capacitor bank is actually emulating a voltage source. So, it is trying to keep the voltage constant and stiff on the DC side. On the other side you would expect a current source and essentially the inductor plays the role of the current source. We know that the inductor does not want to change the current level, current flowing through it on an instantaneous basis. So, essentially inductor can actually be used to emulate a current source. If you are also looking at the analysis that we have done for the current that is flowing through the DC bus capacitors etc., we assume that the current flowing out of the I out is actually a pure sinusoidal current. But we know practically it is not exactly going to be sinusoidal, it is going to have ripple on it, there will be some variation above the nominal sinusoidal shape. Ideally if you want to have an ideal current source the inductance would end up being very large, practical designs would need finite values of the inductance which is actually quite small and that would now add constraints on how large you can make the inductor or how small you would like to keep it in terms of the design. So, the first thing that one need to keep in mind is why have a filter at all. One thing that you have is your grid is actually a sinusoidal voltage coming at the input and we know that the output of the power converter essentially has pulsed waveforms. If you just directly connected essentially the current would not resemble anything close to a sinusoid it might have very large pulsed spikes which would not even work your inverter would not be functional. So, you would definitely need a filter in a practical power converter and to see why one needs a filter and what is the level of filtering that is required we have to look at what are the relevant regulations on connecting a dg to the grid and the standards that are associated with it. If you look at the previous case if you are having a dg system say a solar system solar panel and the inverter the panel and the inverter would essentially be within something that is being provided by the equipment manufacturer the point at which it gets connected to the external world is at the AC terminal. So, what happens within the box is up to the designer but what comes out of the box can actually be regulated because that affects the customer that affects all the people. So, you have regulations on how you can actually connect dg equipment out into the grid and two of the relevant standards are IEEE 519 and IEEE 1547 IEEE 519 is about harmonics and power power systems and 1547 is about connecting distributed resources with the electric power systems and the objective of these standards is to ensure high power quality. So, when you are talking about high power quality there are couple of ways of looking at it. So, you can have power quality in terms of the grid is when you are talking of the grid we are looking at no outage we want voltage amplitude and frequency is close to nominal and you can have small ranges around it and you want it to be sinusoidal which means that you do not have distortions you do not have harmonics you can also have power quality. So, these are grid factors you can also have load side factors for the power quality. So, one thing you might want is to ensure that you are not drawing very high reactive watts ok. So, you might not want very large surges to be consumed by the load and you do not want to have inrushes. So, those may be some concerns that you have you have another factor you do not want your load to be drawing harmonic currents and of course, another factor which would be overall requirement would be that you are not causing EMI problems because of your load that is being connected. And if you look at your the IEEE 519 and 1547 and the filtering requirement you are actually addressing the harmonic issues from the point of view actually both the load and the grid. Because if a load is drawing distorted power and we know that the grid has finite impedances it has finite x by r ratios. So, the harmonic current drawn by a particular load would interact with the impedance to cause harmonic voltages which would be exposed to other customers which are connected to the same line. So, you need to ensure that your currents are are within a range such that one particular user will not be able to cause power quality problems to the neighbor. And the level of the harmonic currents that are drawn depends on how stiff the grid is. For example, if the grid is extremely stiff you can draw a lot of harmonic currents and not distort the voltage. So, your allowance for harmonic currents can actually be quite high. Whereas, if you have grid width which is quite weak which means that its short circuit ratio is quite small then you want a small amount of harmonic current can actually cause a large grid voltage distortion. And when you are designing a power converter equipment you do not know whether it is going on a stiff grid or on a weak grid. So, you have to design it for the worst case condition which is the weak grid. And what is shown over here is the regulations for the harmonics. The objective of the overall system is to ensure that the voltage harmonic distortion at the point of common coupling PCC stands for point of common coupling. And the voltage total harmonic distortion is less than 5 percent and your individual harmonic amplitudes do not exceed 3 percent in the voltage. And the corresponding harmonic currents that can be drawn by the load would then depend on what is a harmonic number. And the overall objective is actually to keep your total demand distortion will look at the definition of what PCC is, THD, TDD etcetera is. You want to keep your total demand distortion to be less than 5 percent. And depending on what is a harmonic number you have different levels of allowed currents that can actually be able to injected by your DG system. So, if you look at the highest harmonic which is given in the standard which correspond to the 35th harmonic this would correspond to about 150 hertz for a 50 hertz system. So, what is being asked is when you are having harmonics at this particular frequency or higher you can inject less than 0.3 percent of your current demand at the PCC as harmonic currents. Often in a power converter your switching frequencies would be 2 kilo hertz or higher which means that you need to attenuate your harmonic distortion to less than 3 percent by your filtering action. So, this is actually an important number which comes up when you are looking at filter designs for DG systems. Another thing to keep in mind is when you are looking at the demand distortion you are looking at what is the demand over some time frame. Another thing is that if your harmonic is a even harmonic it is one fourth of what is given in this particular table even harmonics cause loss of halfway symmetry. So, you would like to actually keep it to a smaller extent. So, the first thing is to look at what the concept of a point of common coupling is. If you look at your typical household scenario the point of common coupling is the place where the public service stops and where your private consumption starts this would be in a house. The power meter might be considered as a equipment belonging to the distribution company whereas, the circuit breaker which is downstream of the power meter is equipment that belongs to the owner of the particular enterprise. So, you are not allowed to tamper with the power meter and the distribution company would expect you to ensure that whatever is connected downstream of that to be protected by the owner at the owner's expense. So, the point of PCC you can think of analogy between the electrical system and say your physical say home and the roads that come to your home. So, an interface between your home and the road would be your gate. So, beyond the gate is the public road inside the gate is your private home and essentially the objective is in that particular case might be you might have you might be coming in and out of your house, but you might also be generating some garbage in your house which you have to dispose of. So, you can think of harmonics as pollution which you do not want ideally it should be 0, but you know that if you want to have a complete garbage disposal facility in each and every house it might be too expensive. So, you are allowed to dispose of some amount of garbage, but if it is too large instead of maybe a bucket full of garbage you are disposing a truck full of garbage that is not acceptable. But whether the garbage is being generated by your elder brother or whether it is someone else in your family it does not matter the total should not be too large. So, that is essentially what is being seen at the PCC and the concern is if you have too much garbage your neighbors would not like it you might cause health problems in the neighborhood. So, you want to ensure that the your quality of life overall is good. So, essentially you can think about harmonics and power systems as a societal requirement is important that you meet the standards that ensure that the power system operates in a clean manner. So, we the other concept that we had mentioned is about THD. THD is essentially the ratio of your RMS of your harmonic components from the second to the largest value that you would have or would consider in your particular application divided by the RMS of your fundamental and commonly in the in the IEEE finance in context we look at the voltage specification of the PCC in terms of VTHD because the VTHD at the PCC is going to be similar same as the VTHD at all the loads within that particular facility because your IR drops in the conductors within your particular establishment is not going to be very large. So, irrespective of whether it is a load or at the PCC you would see similar levels of THD in your system. Whereas, that is not the case of your current say for example, you might have a current which is highly distorted from one equipment, but your current drawn by the other equipment might be clean and sinusoidal. So, when you are looking at the PCC overall you might not have much distortion just because you have other loads within the particular facility. So, what is being asked is that the overall demand based on the demand seen at the PCC your value of the distortion the ratio of your current harmonics from the second to the highest that is being considered divided by the RMS value of your demand is not exceeding a value and the demand might be considered over a 15 minute or half an hour duration and you want to ensure that it meets the particular standard. In a DGA application it may not just be your actual demand might actually go up and down depending on what other loads are there in the system. A worst case might be to consider your DG source as the only source in which case you are looking at what is the distortion divided by what is the fundamental being output from your DG source and because one might be interested in what is the maximum operating point of this particular equipment you might also be looking at what is the rating rated conditions under which such a system might operate and that is where you have your TRD your total rated distortion rather than looking at the demand distortion over 15 minute or 13 minute intervals. So, what we have done is so far we have looked at the AC side current to be a smooth sinusoid. So, the next thing that we could do is maybe look at what would be the ripple that would be coming out of say a power converter connected to the grid with a DC bus voltage and the grid side voltage in case of a simple topology such as the single phase center tapped topology. So, for that what we look at is look at the modulating waveforms and look at what is a ripple current depending on what the duty cycle is. So, if you look at your actual current your modulation signal that is being provided to the switch that that is shown as D over here and your you have your triangle triangles which is your carrier and you compare your D modulation do your duty cycle command with your carrier to actually look at what your modulation signals to the gates are. So, when S plus is on the top switches is on you are applying plus V DC by 2 across at the output of your converter leg and on the grid side you have V grid. One thing that we will assume is that grid voltage is close to your output voltage of your leg. So, we will assume. So, if you are another thing that we would assume is that your duty cycle is not changing by much. So, it is whatever your commanding is close to being constant over a duty cycle. So, you are assuming that your switching frequency is high you are also assuming if your grid voltage is close to the voltage that you are commanding it means that the voltage drop across the filter inductor is quite small ok. So, this would be the fundamental voltage drop in the inductor would be small. If L is small if the filter inductor itself is small or if your loading condition of your power converter is slight or it could be a condition of both. So, we could write an expression then for what is the current that is flowing through the filter inductor during your on duration and off duration. So, during T on essentially your S plus is on we have V dc by 2 minus your grid voltage which is taken as V dc into d minus 0.5 is L into delta I out change in the value of your output current divided by T on. Similarly, during the off duration we have minus V dc by 2 being applied at the output and your grid voltage is and the ripple is now going down. So, you have L minus delta I out by T off also we know that T on plus T off is your switching duration which is essentially the reciprocal of your switching frequency. So, you can write an expression for T on plus T off in terms of these two expressions over here you have 1 by FSW to be equal to L delta I out by V dc. So, you could then write an expression for what your current ripple is you have delta I out is V dc into d into 1 minus d. So, one can see from this expression that you have if you have a higher V dc one is if V dc is high then essentially your delta I out would be high. So, you do not want to keep your dc bus voltage to be too high for multiple reasons one is you do not want to stress out your confidence the other thing is you want to keep your ripple to be not too large. If your FSW is high then your ripple would come down, but with a higher switching frequency will end up with higher switching losses in your semiconductor components. The third thing would be if your value of inductance is high then your delta I out would be low which is natural to expect. The other thing to see is that if you look at this particular expression it is d into 1 minus d you can look at when you have minimum or maximum conditions of your ripple you will get maximum ripple for this single phase inverter it occurs when d is equal to 0.5. So, essentially this is when your output voltage is 0 you will end up with higher ripple you are going to have a minimum ripple when d is equal to 0 or 1. So, when d is equal to 0 or 1 this turns out to be 0 so you will not have ripple. So, under the close to the peak or value of your voltage reference you will end up with smaller ripple in the single phase part inverter. We will look at some of the constraints when you look at the selection of the inverter the selection of the inverter selection of the L. So, one thing you would like to do is you want to attenuate a selection of L to satisfy one is ripple attenuation for which you need L to be large you would also like to keep your fundamental voltage drop across a filter low for which you would like to keep your inductance low to keep your DC bus voltage low you would like your inductance again to be low if you look at it from a dynamic response perspective you would like larger inductor has more you can think of it as having more inertia. So, you would like to keep your value of your inductance low from your dynamic response perspective whereas, if you are looking at it from surge transients. So, you turn on the converter and you want to limit your surge current you would like to then have a higher impedance. So, you would like your inductance to be high if you look at the power loss it has to be if it is too low then the ripple current would cause lot of losses if it is too high your fundamental current loss would be too high you are looking at some optimum value of L which is lying in between. So, you have multiple constraints that come up when you are looking at selection of a inductor. So, we will look at a starting point of how you could start with the design of a simple inductive filter in the next class.