Welcome to class 25 and topics in power electronics and distributed generation. We will start this class by summarizing what we have been discussing which is what we mean by the basic specification of a inverter. So, when we talk about basic specification you start off with something as elementary as a power rating, your AC voltage rating, what frequency you are operating, standard frequencies are 50 hertz, 60 hertz, your nominal range of voltage, what is the range around the nominal and which has implications on current rating, etc. The type of interface whether it is a single phase interface, three phase interface, three wire, four wire, we also discussed about the environmental specifications, temperature, ingress protection, etc. have actually a large impact on the design of the power converter. We also looked closely at the single phase, a simple single phase topology which is essentially consisting of a split capacitor bank and we saw the implication of the AC voltage on deciding what your DC voltage has to be. And the DC voltage we saw is related there are factors relating to the range around you might have 5 percent above the nominal grid voltage which you need to handle, you might have some percentage voltage which gets lost as dead time, on state drops of your devices, etc. You might also have some range of voltage that gets dropped across your filter inductor. And so, for a 230 volt system you might end up having to require a DC bus voltage which might be close to 800 volts and this immediately would imply that now you need a capacitor bank, if you are having 2 in series you are talking about 400 to 450 volts as a value of the voltage that you need for the capacitors. And for the IGBTs or transistors and diodes you need components which commonly would be available at 1200 volts. So, then you can actually look at what given this preliminary specification, what are the implications on your DC bus capacitors and we the starting value point is to discuss what the voltage rating is, then to look at what the current rating is. And we saw that there are a variety of current signals that can flow through the DC bus capacitor bank. And when you are talking about a typical DG application your actual capacitor bank, your voltage sources over here might consist of capacitor banks connected in series. And your actual voltage source is a prime source connected in parallel with the capacitor bank and the capacitor bank is effectively acting as the voltage source on a high frequency and intermediate frequency basis. And what you are trying to regulate is ensure that the voltage across this capacitor bank stays ideally as close to the DC value that you desire. And then we looked at what would be the currents that can flow through your positive bus and we saw that there is a DC current which is essentially what transfers power in a typical DG application. You have a 50 hertz component especially in this center tap topology which flows through your capacitor bank. You have a 100 hertz which would show up in again in a single phase topology or it can even show up in a three phase topology if you have unbalanced in your AC voltage or unbalanced in your AC system. You also have switching frequency components that can actually flow through your positive DC bus and we linked the current in your output eye out to your current in your DC bus. And we derived expressions for the DC current 50 hertz current the second harmonic 100 hertz current and your switching frequency component. And these are relatively simple expressions to actually obtain that can be obtained for your bus capacitor currents. And then the next question is how to actually make use of these currents that you have evaluated in the design of your capacitors. So, the first thing that you when we are looking at say the design of the capacitors are there are a variety of capacitors out there. So, capacitors are commonly classified based on the dielectric that is used in the capacitor. You might have ceramic mica paper, you might have tantalum electrolytic, polyester, plastic capacitors, polypropylene. So, depending on your application for example, mica capacitors etcetera are really good at very high frequencies, but the value of the capacitance that you get is really small. Electrolytic capacitors have a large value, but you may not get it in AC rated as in with AC rating. So, if you look at the common capacitor that is used in the DC bank of a voltage source inverter which is used in a DG type of application you are talking about commonly it is electrolytic capacitors. Once you have decided to say you want to make use of a electrolytic capacitor in your DC bank, then what are the advantages of using a electrolytic capacitor? One thing is you have electrolytic capacitors in hundreds, thousands of micro farads or millifarads range also depending on your voltage rating and a larger capacitance means for a given current ripple you are having smaller voltage ripple or better filtering ok. So, larger capacitance implies you have lesser voltage ripple, a larger capacitance half C v square is the energy stored in a capacitor and large value of capacitance means that you are emulating ideal voltage source more closely it can provide a large amount of energy without getting discharged or changing the value of the voltage ok. You also have now capacitors, electrolytic capacitors with low ESR, ESR is equivalent series resistance. So, low ESR again we will see has a advantage in terms of dissipation, life, temperature rise etcetera and today commonly you get electrolytic capacitors with low ESR capability which has implication in the amount of ripple current that can actually flow through these capacitors. Another negative point of a electrolytic capacitor is that it does not have AC voltage rating, but AC voltage rating is not required in the DC bus of a voltage source inverter. So, even though it is a drawback it is not a major drawback for a electrolytic capacitor in a VSI application. So, depending on the nature of the ESR you can also have different types of electrolytic capacitors, you might have electrolytic capacitors where the ESR might be minimum at lower frequencies and you might have electrolytic capacitors where your minimum of your ESR might be at this the switching frequencies tens of kilohertz or few kilohertz. So, if you are having a specific capacitor which is designed to have lower ESR at may be 100 hertz 150 hertz you might be having a rectifier grade electrolytic capacitor which is used in standard diode bridge rectifiers where you know most of the ripple is going to be at lower frequencies. Sometimes people refer to high frequency electrolytics as SMPS grade electrolytics which are optimized for the ripple now flowing at may be many kilohertz tens of kilohertz etcetera. You also have other parameters of the capacitor which is important if you look at a capacitor which is acting as a equivalent voltage source in bus of a inverter you also have a parasitic inductance which can actually come in series with the capacitance and this parasitic inductance actually can cause a significant problems because the switching speed of your transistor it can actually have very large d i d t d i d t's of the order of kilo amps per micro second to tens of kilo amps per micro second. So, even a few tens of nano Henry's of inductance can actually cause a fairly significant voltage spike of the order of 100 volts 200 volts etcetera depending on the inductance. So, it is very important to actually minimize the ESL of your capacitors. One thing that people might do is instead of just having a electrolytic capacitor you might actually put snubber capacitors in parallel with the electrolytic capacitors. So, many times one might wonder why is there a 1000 micro farad capacitor and in parallel with that you are putting a one micro farad capacitor or a 4.7 micro farad capacitor it is from a ESL perspective where the ESL of your snubber grade capacitor would be much lower and for higher frequencies the ESL is also a significant factor in ensuring that you do not have voltage spikes that come across your capacitors. Also another aspect to keep in mind is when you just draw a power converter you might just connect source to a transistor often because your parasitic inductance is so critical you might actually decide to make special DC bus connections you might have parallel structures plate structures in your printed circuit boards or copper buses with a parallel structure to minimize these inductances. So, as to ensure that even though your DC bus might be sitting at 800 volts and your device is 1200 volt if you do not pay close attention to what these stray inductances are given the capability of modern day transistors you can end up causing voltage spikes that can damage these devices. So, once you actually have adequate margin between your voltage in your DC bus and you know a preliminary value of the voltage then you can ask what are the constraints that can happen on a capacitor bank and we saw that the DC the voltage rating is a basic constraint your DC voltage rating is something that we just discussed. In addition to the DC voltage rating we know that we are having low frequency currents 50 hertz 100 hertz also switching frequency currents those currents can actually induce and cause ripple voltage and you need to ensure that the ripple voltage is also adequately addressed. So, we also saw that the 100 hertz ripple might become so significant that you might actually want to add additional DC to DC converter etcetera to prevent this ripple voltage from flowing back into your prime source and cause losses in your overall dg system. Also you have current rating which is a important factor in any component many times your terminals that you connect a component is specified by what current that terminal connection can handle. If your current becomes too large then your terminals your screws your whether snap in connections or your PCB insertion points they can overheat and can melt. So, current rating is a important aspect of terminals and connection points and also components and when it come to components the current rating reflects itself in terms of the thermal effects which eventually leads to overheating ok. So, if you are having overheating in a component like say the DC bus capacitor one thing is you could directly say you are passing too much current through a component ok. If you are passing too much current one way to prevent say large current is to parallel components if you have a given amount of current and you want to actually you find that the current that is flowing is too large you could then connect components in parallel and then the currents take the parallel parts and ensure that the current per device comes down ok. The other aspect which can lead to higher thermal effects over overheating in components is the ESR itself is being is too large. If you select a capacitor where the ESR is large your I square R the R part of it is given a current the R part is too large which means that you are having higher power loss and which in turn results in too much temperature rise. So, you need to ensure that whatever capacitor or component that you are selecting has a ESR that ensures that the temperature does not go too high and which was one of the criteria in modern day electrolytic capacitors having low ESR capability. Low ESR which is actually advantage. Another thing your IRMS capability might be your RMS current might be small your ESR might be small, but given how a small a power dissipation is having is occurring within a component. If the component is not being cooled then it is an integration process where you are adding thermal energy into a component where the thermal energy does not flow out. So, if the cooling is not adequate then again you are going to get overheating which means that you need to consider say whether your capacitors how is it packaged. Is it packaged in such a manner where you allow say natural convection if your capacitors are too tightly placed there may not be possibility for air flow around it. If it is kept in a horizontal configuration rather than a vertical configuration it will determine whether you can have natural convection around a capacitor bank or you might be as simple as maybe you need to add a fan for the capacitors. You might have this capacitor sitting in a sealed cabinet and you might be having poor air exchange and you need to have some air circulation within whatever cabinet you have to ensure that your components does not get too hot. And these so there are multiple aspects when you consider the thermal effect it is not just a question of just the current being too large it can be ESR it can be cooling so all these factors have to be considered together. Also if you are looking at the constraint another constraint on a capacitor bank is how much energy is there in the capacitor bank. So, for example, if you have a short term outage your energy that is there as half CV square might be available to provide for a short term requirement within the power converter. So, this has implications on hold up time of your converter in many dg applications people are talking about low voltage right through or 0 voltage right through which means that you need some energy storage capability which is becoming more and more important in dg applications. And out of many of these constraints the hold up time thermal current voltage rating many times when you eventually come up with the design the thermal effect is actually a major factor which needs to be considered. And so close attention to thermal effect would also incorporate the current rating issues and the voltage rating issues because the current causes ripple the current causes overheating. So, many times when you get to the detail of the thermal design you are in fact, covering many of the other constraints in the design of your capacitor bank. So, then you could ask if you have say different temperatures what is the constraint that what is causing problems within your capacitors ok. So, if you look at a typical component say you are talking about a electrical electric capacitor and any chemical process if you are looking at temperature effects on a chemical reaction say you are having some A plus B reacting to form C. And we know that the rate of a reaction can be expressed at as some R is dependent on some rate constant K which is a function of temperature it is proportional to the concentration of your reactants A and B. And these are things that we have looked at studied in maybe a high school chemistry class and we know that these rate these rates of reaction is actually a function of temperature. So, if you think about the chemicals within components like the electrolytic material etcetera they degrade at a higher rate at higher temperature. And often your K of t there is people express it as a adrenous rate law some A exponential activation energy gas constant your Kelvin temperature. So, with factors such as this you can see that at a higher temperature you end up with a higher rate constant. And often when you look at many electrical systems further simplification that people might make is to say that when you are increasing your temperature by say a 10 degrees you might lose your lifetime by a factor of 2 ok. So, these are again simplifications given a given temperature activation energy, but this can be some simplifications which give you some insight into how to actually select a component for a given lifetime or what are the implications of temperature on the operation of a given component. So, with this we will look at say a design example of a capacitor bank and we will look at an example of say a 2 kilowatt power converter single phase center tap capacitor topology the topology that we have been looking at at 230 volts it is operating as a unity power factor converter. And the switching frequency is 10 kilohertz say it operates at a ambient temperature of 40 degrees and maybe there is a temperature rise between your ambient air temperature and the temperature of your cabinet this power converter might be sitting in a sealed cabinet and your ambient may be 40 your inside cabinet temperature might be 50 and say you are operating maybe it is a solar inverter it may be operating during the daytime 8 hours a day and around the year 365 days a year. And the question is how could you go about selecting a DC bus capacitor given a simple topology as what we have discussed ok. So, one thing that we can start off with is what would be the voltage and we know that the peak voltage that we are operating is 230 root 2 is 325 volts and based on the discussion that we had about the additional margin of due to dead band voltage variation 5 percent voltage variation in the grid again making assumptions relating to the filter design we might talk about VDC roughly about 800 volts. And then given that we need 800 volts we might select a capacitor which is maybe 450 volts and we go to manufacturers data sheet and take a look at what are the range of capacitors that are available and as a starting point we might say let us start off with maybe a 150 micro farad 450 volt capacitor and this I picked off from manufacturer Cornel Dublier CD.com you have many of manufacturers Chemette, Vishay, Sanu, Epcos many of these manufacturers provide data sheets of capacitors on their websites. And when I when you look at the capacitor they provide values of what years are is there a common frequency that people might specify might be at your second harmonic which might be a dominant frequency in such capacitor designs depending on whether it is 50 hertz, 60 hertz people might consider different second harmonic frequencies we will assume second harmonic frequency of 100 hertz. And there is a 0.8 ohms resistance at ESR resistance at 100 hertz. From the data sheet we also have current multipliers. So, the data sheet says that at 100 hertz you are able to carry one ampere of current, but at 50 hertz you can carry only 0.8 amps current at 10 kilo hertz you can actually carry 1.4 amps current. So, when you are talking about different current levels which can be carried at different frequencies you are consuming assuming that you get same dissipation now at with these different current levels in a given capacitor ok. So, you are talking about the fact that you are now your I square r effect because of the current at different frequencies are actually not the same for a given capacitor. Also in the data sheet it is provided that when the ambient temperature is increased for example, if it is 85 degree centigrade I can pass 1 amp of current and expect about 3000 hours of load life in the capacitor. But if I now reduce my ambient temperature to 55 I can actually carry 2 amps and get the same 3000 hours of life. If I reduce it to 45 degrees I can pass 2.25 amps and still get the same load life. So, you can see that you if you are able to reduce your temperature you can actually get improved life or on the other way looking at it in another way you can actually have higher current capability depending on how well you have cooling. So, the first question that you could ask is this capacitor appropriate for this application from both maybe current ripple and a voltage ripple perspective. And if it is not appropriate then what should it be maybe should it be 300 micro farads should it be 600 should I put many of them in parallel. How about how can I go about deciding on what would be a appropriate capacitor to choose. So, the first thing that you can look at is then your current rating. So, AC rating for this particular system your IAC is it is a 2 kilowatt system 210 power of 3 and 230 volts nominal. So, you have 8.7 amps RMS or 12.3 amps peak. So, the first thing that you could immediately calculate is your 50 hertz component because it is a center tapped DC bus topology. So, your I in your C DC at 50 hertz is 4.3 amps. We know your based on your DC bus voltage we have V DC times I P of T or I DC of T is 230 volts root 2 cos omega t and 12.3 amps peak cos omega t and we know your V DC is 800 volts nominal. So, we have your I DC of t to be equal to 2.5 amps 1 plus cos 2 pi 100 t. So, your so you know your DC current is 2.5 amps and your 100 hertz component of your current I C DC 100 is 2.5 amps peak or 2.5 amps by root 2 equals 1.8 amps RMS. So, then so another thing that we could maybe from the design you might start off with a switching frequency of maybe 10 kilohertz that is used in this particular application. So, we would like to calculate what is the 100 hertz component of your current flowing through the DC bus. So, to calculate I C DC 10 kilohertz you know your I out because if you are switching at 10 kilohertz will consider it as N switching instance. So, 200 switching instance in one fundamental cycle. So, you can think of it as your output volt current is 12.3 amps cos 2 pi 50 N T SW. So, depending on each switching instant you know what your output current is your output current is a sine wave which you are trying to control to be a sine wave. You also know your duty cycle duty cycle again depending on which instant you are operating is given by close to 0.5 plus 230 root 2 by 800 cos 2 pi 50 N T SW. Again this is assuming that your ideally ideal grid voltage is reflecting back to your pole voltage. You might have some small changes in the value because of the voltage drop across your filter, but it will not be majorly different. So, you could take this as an approximation and you also know that given FSW switching frequency is 10 kilohertz and F naught is 50 hertz so your there are 200 switchings per fundamental. And then you could calculate what your 100 10 kilohertz component is. So, your ICDC 10 kilohertz is 1 by 200 summation i from 1 to 200 i square of N T SW into D of N minus D square of N the whole thing under a root. So, you could evaluate what this quantity is you know what your D is what your I out is and you can calculate the current you end up in this case of around 3.1 amps. So, if you look at your total RMS current in that flows through your capacitor is now your 50 hertz 100 hertz and your 10 kilohertz component. So, I RMS in your capacitor. So, we see that there is 5.6 amps and this is much greater than the current rating of the capacitor which was roughly around 1 amp. So, definitely 150 micro farad capacitor that we started off with is not adequate so this is much greater than rating current rating of. So, we need multiple capacitors in parallel and we will also we will now take a look at what the what the ESR implication of having the different current level at the different frequencies mean. So, if you look at the capacitor data so, that it can carry 1 amp at 100 hertz 0.8 amps at 50 hertz and 10 at 1.4 amps at 10 kilohertz. So, if you look at what does that mean. So, at 50 hertz I rated equals 0.8 amps. So, if you look at your 0.8 is your ESR at is your current I square R ESR at 50 would be similar to now your I square R at 100 hertz and we know at our ESR at 100 hertz is 0.8 amps which was there from your data sheet. So, you know that now your ESR at 150 hertz at 50 hertz is actually 1.25 ohms. So, similarly you can do a calculation at 10 kilohertz your you know your I rated is 1.4 amps. So, 1.4 square ESR at 10 kilohertz you can evaluate that into 1 square into ESR at 100. So, you get ESR at 10 K to be 0.41 ohms. So, in a way giving your current multiplier at different frequencies is a giving you the same information as ESR as a function of frequency. So, some manufacturers might actually give you a plot of ESR at different frequencies. So, in this case you might have a plot that looks like this where ESR is reducing with frequency. So, you had 50 hertz you have some value at 100 hertz and some value at 10 kilohertz. So, the other parameters that we can actually look at from the temperature multipliers that we have provided to us is that we were told that at for 3000 hours of life you at 85 you have 1 amp at 55 degree C ambient for the same life you can carry 2 amps etcetera. So, now with that information we can actually calculate what is the thermal impedance between the core of your capacitor and your ambient and also what is the actual core temperature at which this particular number is being specified ok. So, if you look at the number at 1 amp at 85 degree centigrade your life is 3000 hours and 2.25 amps at 45 degree centigrade you have the same life. So, your T core of the capacitor is similar under these 2 conditions because the degradation within the capacitor is happening at the same temperature because it results with similar lifetimes. So, if you look at your thermal impedance or thermal between your core of your capacitor and your ambient. So, you have T core minus 85 by your participation is 1 square into point 8 ohms which is your ESR is equal to T core minus 45. Now you can carry actually instead of 1 amp you have 2.25 amps into again the resistance is still point 8 ohms it implies that you can solve for what your T core is. So, the T core that is probably being used by this particular manufacturer is 94.8 degree centigrade and the thermal impedance under the measured measured condition your RTH from your core of your capacitor to your ambient is about now 12.3 degree centigrade per watt dissipation in the capacitor. Now you based on the current currents that we know is that are flowing through the capacitor you could then say what is a equivalent 100 hertz current that might be flowing in the application that we are considering. So, the currents in the capacitor is 4.3 amps at 50 hertz 1.8 amps at 100 hertz and 3.1 amps at 10 kilo hertz. So, equivalent 100 hertz current 100 hertz current in the capacitor from a thermal perspective. So, in terms of what gives the same temperature rise or in your capacitor is say some I prime square 100 into 0.8 is 4.3 square into 1.25 plus 1.8 square into 0.8 which is a ESR at 100 hertz plus 3.1 square into 0.41 which is the ESR at 10 kilo hertz. So, you are talking about I prime 100 we are talking of something like 5.4 amps and if you want to say target in your application 3000 hours roughly 3000 hours of life and we know that 2 amps of ripple can flow if your ambient temperature is 55 degrees which is the multiplier given to you at 55 degrees. So, targeting 3000 hours of life assuming 2 amps ripple at say 55 degrees because your cabinet temperature is 50 degrees not too far away from 55 ambient. So, one would need about 5.4 amps divided by 2 amps. So, you are talking of 2.7 capacitors rounded off to 3. So, you need roughly 3 capacitors in parallel. So, instead of 150 maybe you could selecting a 450 micro farad capacitor might be a good starting point ok. So, then you could ask now if you take 3 capacitors in parallel what would be the power dissipation in each of these 3 capacitors that you are going to put in parallel ok. So, the power dissipation per capacitor in this parallel combination of 3 banks is 4.3 divided by 3 square into 1.25 plus 1.8 divided by 3 square into 0.8 plus 3.1 by 3 square into 0.41. So, you have 2.63 watts plus 0.28 watts plus 0.43 watts. So, you have about 3.3 watts dissipation per capacitor in the parallel combination of 3 capacitors and then you could immediately say what your core temperature is given that your cabinet is sitting at 50 degrees centigrade. So, your core temperature in this particular case would be your 50 degrees which is your inside cabinet ambient temperatures given for your application plus 3.3 watts power dissipation per capacitor and we know at your thermal impedance from ambient to core which is 12.3 degree centigrade per watt. So, your actual core temperature if you use say 3 capacitors in parallel will be about 91.1 degree centigrade ok. Then you could actually calculate what would be the lifetime of this particular bank of 3 capacitors. We know life is approximately 3000 hours for your nominal core temperature. So, it is 3000 hours into we will again use a simplifying assumption of decrease in life by a factor of 2 for 10 degree temperature rise. So, it is 2 to the power of 94.8 which is your nominal specified temperature at which we made those specifications were being made. Your actual temperature is 91.05 divided by 10 to reflect the factor of 10 change having a multiplying factor of 2. So, you are talking about now 3900 hours of operation of this particular bank and then if you look at what it is in terms of 8 hours per day 365 days per year. So, this implies 3902 divided by 8 into 365. So, you are talking about 1.3 years is what you could roughly expect from this bank ok. Then you could ask what is the power dissipation in this bank you have 3 capacitors on top 3 capacitors at the bottom and the power dissipation in the capacitor bank is 3.3 watts per capacitor into 6 capacitors. So, there is about 19.8 watts of dissipation happening in this particular capacitor bank ok. So, you can see that you now have a way of linking the selection of the capacitor to your current ripple. I mean there are many other things that we need to calculate that the voltage ripple, but we could start off with some simple design tradeoffs. What say maybe a basic question could be instead of why did we select 3 capacitors in parallel we could have put 4 in parallel ok. So, what would be the implication of putting 4 capacitors in parallel rather than 3 ok. So, if you do your power calculation for 4 capacitors in parallel your power dissipation per capacitor is 1.25 into 4.3 by 4 square. So, instead of 3.3 watts per capacitor now you get 1.88 watts per capacitor. So, your power dissipation has come down because you have gone to a larger number of capacitors your core temperature now comes down from the 91 to about 73 and your life now comes goes up. So, it is 3000 hours into 2 to the power of 94.8 minus 73.1 by 10. So, you are talking about 13500 hours by 8 into 365. So, you are talking about 4.6 years rather than the 1.5 1.6 years that we previously looked at when you had 3 capacitors. So, you can see that your lifetime has increased because now you are able to bring down the temperature you could also now calculate your power loss in your capacitor bank when you use 4 in parallel is now 8 capacitors dissipating 1.88 watts. So, this is 15.04 watts. So, previously you had 19 watts when you had 3 capacitors it is come down to 15 watts when you are putting 4 capacitors. So, you can see that you have now a framework where you could address the what is the effective initial cost of selecting a single component just a capacitor because between 3 and 4 capacitors you know what the cost difference is. You have a way of evaluating your operation and maintenance life and you have a way of looking at your net present value of power loss which is going to be happening in your capacitor bank. So, a framework where you can actually do a such an evaluation on a per component basis of each component that goes into a power converter can actually then be rolled together to do a overall design of your bigger system or your overall power converters power conversion system. So, if you look at again the factors that we looked at in the life calculation of this capacitor we had essentially your life at a given temperature is related to some nominal operating life given by a manufacturers and using a simplistic assumption of 2 degrees per different I mean factor of 2 in life for 10 degrees change. So, you have a TCO minus T actual by 10 degrees into you also have a multiplying factor based on your voltage suppose you have a DC bus capacitor bank rated at 450 volts and you are using it very close to 250 volts then your you have a factor which imply effects on your life because you are operating very close to the rated voltage as you bring down your voltage of your capacitor you can have some small improvement in your life. So, you could incorporate factors that address different issues like temperature, a margin your thermal margins etcetera as we have just calculated and just for simplicity maybe you could take your voltage factor to be roughly 1 as long as you are ensuring that your voltage does not exceed your rated voltage during operation of your power converter ok. So, you can see that with this you could also ask a question what does it mean by having a capacitor which is going to last 4 years or 4.6 years or whatever number you have evaluated and that typically is reflected in terms of what is the failure rate of a typical component and people talk about mean time between failure of a component failure rate or when you look at a typical component essentially at the point at which it is initially built you might have large failure rates you might do some initial tests within your factory to ensure that some initial tolerance which is not being met in the component does not get shipped out of your factory. So, you might do some initial tests to ensure that you do not see what people talk about early mortality or infant mortality of your components in your power conversion systems. So, once you pass your qualification test within your factory whatever gets shipped out has fairly low roughly constant failure rate it is not that the failure goes to 0 it might be you might have a random failure depending on what the parameters the complexity of your component etcetera is, but you would have a low roughly constant failure rate. But after a while so, after a while it start the failure rate starts picking up it no longer stays that the low value what it was because of your operation because of the usage of your component you might end a reach a end of life value at which point your failure rate starts increasing. So, in the case of a capacitor what would one consider to be a end of life. So, your physical capacitance value might actually change with time your leakage current in your capacitor might change with time after a long time your leakage current through the capacitor might suddenly start increasing. Or if you look at your ESR of your capacitor initially you might have a ESR of 0.8 ohms, but after some 5 or 6 years you again measure the ESR of the component it may not stay the same 0.8 ohms it might increase to a different value. So, manufacturers have different specifications of what it means for a component to be reaching its end of life in case of say a capacitor a common specification might be the ESR goes up by a factor of 2 at the end of life ok. So, if a ESR goes up by a factor of 2 given the same RMS current that is flowing through the capacitor it means that now your participation has doubled which means that again your temperature is going to accelerate up. So, your degradation is going to now become more and more rapid at the end of the life you are quite quickly going to reach a point where you might end up with a failure of the device. So, you can see that it is possible to actually link the operation of the components to the operational life and try to incorporate these factors in the design. We have still to consider what is the impact of looking at the voltage ripple because we have looked at the current ripple. So, we also have to look at the voltage ripple to see whether the capacitor selection would be adequate for a for the design. Thank you.


I would like to, first of all, welcome everyone in the room and online to this session. I would also like to add that the World Economic Forum and this meeting is going to be bilingual. I will be talking English, but panelists will be speaking Spanish. With me, we have Alberto Velo, the editorial director of news and business news of Grupo Expansión. We also have Daniel Gomez, who is the head of competitive research at the World Economic Forum. Alejandro Cardoso, who is the chief executive officer and president of publicist communication based in Mexico and manages Latin America. Last but definitely not least, Ivan Sanchez, who is director of regional strategy at Denso Aegis Network. Today's conversation will have a backdrop of the launch of the digital media readiness framework produced by the World Economic Forum Global Agenda Council on the future of media entertainment and information. So, I now pass on to Alberto to speak on this framework. Well, thank you. Thank you very much for being here. So, let me now start by, you know, discussing what we're talking about. Hola soy German, a Chilean blogger came to Mexico. It was very welcomed and massively received and the daughters of several people at the newsroom were surprised the fact that a Chilean blogger was being so successful in Mexico speaks of a radical change in the way we communicate. Blogger's production costs are very low, but we're also seeing Mexican-Brazilian producers producing for Netflix. We are seeing a phenomenon like Mercado Livre or Amazon that become regional platforms. We're seeing Spanish media like El País or the New York Times launching Spanish online versions to compete with local dailies and also advertising campaigns on the social media, particularly Facebook, are unbelievable. And we're seeing other campaigns that the social media is changing and they all have something in common and that is being called the World Economic Forum by media information and entertainment. And the framework we are going to present tries to measure or rather to compare the levels of readiness in digital media of different communities, be they countries, cities or regions. I mean the readiness to adopt the content, product services and the apps of these digital media information and how ready is everyone to profit or make the best of the economic phenomena resulting from these goods and services. This initiative comes to life in November 2012 in the GAC Summit, the Global Agenda of WEF in November of 2014 in Dubai. And it also has the participation and collaboration of the Akeo University of Japan and the University of Southern California in the U.S. The methodology we'll be talking about, whose consequences we'll be discussing in greater length, has four major components, has 23 indicators, are existing, others are new indicators that try to measure these skills I was talking about. It also assesses and evaluates gaps between indicators and other indicators in the global competitiveness index. And in short, this is a methodology mapping the relationship and interdependence of each indicator and fourth case studies, revealing the importance of this assessment framework because this can include the use of digital books in schools in Japan and how that is going to change education. And in Chattanooga, we see how a society changes its economy once it's become digital. We also have the Mexican national digital system transforming the way government relates to customers in Pesa and African Kenya that has turned cell phones into a method of payment outside of the banking system or Shikan in China, which is a distant healthcare platform. And these are just a few examples. So let's delve into this. Why is this relevant in Latin America? And what is the importance of being prepared? Did you lead to measure this? Well, thank you, Gilberto. Thank you, everyone, for being here. I feel that this work comes at a very important time for Latin America, particularly because at this juncture, we are looking for new economic or engines for economic growth. Given the falling prices of commodities, coal, oil, other commodities, the region is seeing a significant economic meltdown, and the time has come to transition economies once based in extraction of resources to a knowledge-based economy. What this conceptual framework does is provide a tool for policymakers, yes, and industry to better understand the factors and institutions that will allow countries to develop these new sectors for job creation, new sectors for driving growth, and new sectors for reinventing our economies and implementing this productive transformation. One of these sectors that has been most affected and will continue to be affected is that of government communications, brand communications, individual communications. At Publicis Alejandro, you have your own view of this aspect. So how do you see this framework? Earlier today, I had the chance to lead a working group discussion on Latin America's tourism and business position, and we said that this fourth revolution, the connectivity revolution, will have a far more reaching effect than the previous revolutions, first because of the pace at which this change has taken place and will continue to take place, and its overall scope, how it's affected the lives of people and government agencies as well as private organizations. We are all connected with everyone at all times, and this fourth revolution has meant that the entire ecosystem and organization change radically and get on this monumental change. Another thing is that this change in the communication industry and marketing has forced companies to understand several phenomena. One is the multi-screen phenomena. Today it's a reality that consumers aren't just exposed to information and entertainment on one screen. There's a Garner study that reveals that today all the millennials in 16 countries are performing for activities simultaneously while they consume information content, and by the year 2020 there will be 20.8 million electronic devices connected simultaneously in the world, and the scope is unbelievable, and that forces organizations to understand this as well as the journey and the consumers' behavioral patterns. Another very important factor is the merger of technology and creativity in the world of communication for many decades. We were always based on a strategy and creativity model, and now, just like advertisers and media, have found ourselves forced to introduce other criteria different from our own industry, science technology, and that alchemy of science technology and information entails a fantastic challenge to us all and for brands. And I would like to close by saying that precision marketing, that ability to understand one-on-one the behavioral pattern of a consumer, not just in clusters as it's been done traditionally, men and women in the 2030 age group with ex-income is something of the past, it died years ago. The ability of media, private organizations and institutions to map the behavior of every consumer, not clusters of consumers and establish one-on-one relationships thanks to technology with great supporting ideas behind it is the future. Very well, I mean, this obviously is a triumph thing in Latin America and other parts of the world, but that obviously requires a series of public policy decisions and attitudes by private enterprise that facilitate access to and accessibility as well. One of the things that President Santos and President Marquis have just mentioned. So, Ivan, how do you see this? The truth be said, regulatory bodies, by definition, must know the object of their regulation. That's the starting point of the problem because the internet and digital world is a form in constant expansion. Internet and digital cannot be encompassed and that's why regulatory bodies find it so difficult to pinpoint what to regulate. And this has positive and negative aspects and implications, mind you, because it creates a certain chaos when there is no regulation. Then creativity is stimulated as is entrepreneurship. Disruptive technologies like Uber are the result of this. And if we look at it, Uber, when they come in, they're not looking for technology talent. What they need is PAP people who know public affairs who know how to relate to governments who can devise a normative framework to be legally viable. So, yes, regulation could encourage and stimulate lots of creative people and entrepreneurs. The negative side is that in the absence of regulation, there is no standardization. So if I have a company that has a strong digital component to it, I go to customers and customers may not know how to measure my results and they don't know whether what I do in digital media solutions is good or bad and there we start having problems in business terms. A way out to that negative aspect is to be perfectly honest and simply say that technology is moving at a faster space than politics and to engage more technical people who know how to deal with that constant development in the digital world. A wonderful example is for the former minister of technology in Colombia, Diego Molano. He was minister until last year. He had one of the most important administrations in infrastructure terms. He had his technical background. It was very easy for him to understand the importance of assisting people who have digital businesses. Okay, I'd like to clarify that those 23 indicators I mentioned and make up this methodology or framework are divided into three main areas. One is the environment capability, which is infrastructure and the other is use. And that's how the indicators have been distributed so you understand the makeup of this indicator. If you allow me, could I make an additional comment? Yes, of course. Talking about Uber is a wonderful example because there are others, Airbnb and Netflix have created a new business model, a new business model based on platforms that are no longer on goods and services. And to the extent we understand that phenomenon, the brands, the media, and we can better connect with consumers restructuring and redefining the company's business model based on this concept of platforms where technology is key. It's not simply a matter of adding on the business strategy to the digital component. No, it's the core. And second, the user experience is fundamental as well. This concept of having historically based companies on the strength of a brand as the core pillar, as the axis. Today, the key factor determining the strength of a brand is in just its communication position, but the brand ability to relate constantly and consistently with consumers. Keep talking about this, and it's a fascinating subject, but I just want to make sure that we have the time for questions. Does anyone have questions in the room? Yes. Marta Ortiz, the editor of El Colombiano newspaper, I have a question for you. Three weeks ago, we had the pre-launched preview of a book where he said that behavior has changed in respect of technology and the need for capital has also dropped. I asked him, you know, and where is the regulation? Where's the law? And he said, regretfully, the law will never come because it will never have the ability to come. As you said, when I look at a business like Uber, which is the one you've chosen as an example, I don't think that's such a big problem because the Uber business model is simply giving a different use to existing tools. The thing is no one was prepared for it, but when we look at copyright, and former minister Milano didn't do anything in respect of that part of the regulation, he may have done a lot of things in dissemination and people understanding technology and disseminating it, but he didn't do much in the area of regulation when we speak of copyright, things that are pure common sense. That's where I'd love to see whether the study can help us because that's what worries me, you know. In the dark social, nobody speaks of the dark social, it's there, and this is something we will have to discuss eventually. Yes, and this is one of the points, Daniel, I was going to ask you what the role it plays in the framework is. Let me give you some detail. The work emphasizes the demand side and content generation, which is where intellectual property is going to be very important. The framework identifies a series of specific indicators that are not in the global technology report of the forum that has to do with the quality of the regulation. It's not the quantity of the regulation, but rather far more agile, dynamic, regulatory framework, less industry specific, but a framework that is more flexible and allows us to incorporate these new platform-based business models. The framework gives emphasis to platforms. It also attaches great emphasis to the existence and the ability and the ease of creating those platforms. Another very interesting aspect in the framework is called fair involvement, which has to do with intellectual property or copyright and the respect for intellectual property. The framework does present a structured view of this, and I agree with Ivan. The regulation will tend to always lag behind technological development, hence the need to have quality regulation that will be far more flexible and can adapt easier to all these new realities of the market. We organized a meeting with several industry players, both phone carriers, media editors, Facebook, and this is key. You can ask me how do you measure it, and I am a journalist, I have a question. When are we going to see an indicator ranking countries in terms of who is more or less ready? That's a very clear challenge. What the indicator does is to take existing indicators, and that's on the supply side, which is the availability of infrastructure, the supply of infrastructure, the use of coverage. All that has been very well measured, but the demand-signed content generation, how easily accessible, I mean, can the population engage in the development of this product is something that isn't as well measured. So the challenge is to implement the framework. So there are a series of indicators that are very well measured, while there are others that we are going to have to go out and look for and incorporate. However, the conceptual framework is there. The theory is there, the rationale is there. The indicator framework is there, and now it's a matter of finding no ideas to measure it. I mean, some ideas go along the lines of ideas that are from culture to digital media, or how easy is it to censor content. That's another key aspect. Because what we've seen with the network readiness indicator is that you can have all the infrastructure in the world, but we don't see the development of sectors because maybe you don't have content in local language or there's no relevant content. So how do you go about matching the demand for content with the supply or physical and institutional supply for sustaining all that content? Available? That's a tough question. That's a very good question. Evidently, yes, I do believe that the forum, we just launched the logo information technology report. The new one will be launched in two weeks. We've been publishing it since 2001. You can do benchmarking. You can do follow-up and track the progress of countries in terms of coverage, readiness, and usage. Those are the three areas we measure. We are currently in the process of reviewing and revising the frameworks, and I believe that this work urges us all to work on the other side of demand and to try to incorporate it into the new version of the report. And we will most likely have it ready by next year. I won't commit to a date, but we will hopefully have it ready by next year. That is our project and that is the overall direction, which is equally important. Good afternoon, Adriana Molano, director of colombiadigital.net, and I have specialized in technology for development. What is the perspective, how you are understanding the digital divide, because we know connectivity and infrastructure is one thing, but another very different thing is when actually people are using and making the best of this, these are two different measurements, very complex, even more so when countries like colombia and specifically Medellin, we have video gaming, three-day gaming, but there are other sectors in the city and the country are disconnected and have no digital knowledge. What happens there?  You need culture, education, access, accessibility as well. A wonderful question, and we are very much in line. The World Bank produced its annual report called the digital divide. So we must, or it looks at the importance of understanding what leads to the proper development of new entertainment in the industries, digital industries, to develop the industry, the sector, and there is a very important human capital aspect there. These are the human ability to interact with new technologies and the existence of content, so we have to think about how to generate more appealing and attractive content because you may have connectivity and you don't know what to use it or if you don't have relevant apps for your day-to-day. That's an issue, but there are some very interesting examples in the developing world. In Africa, there are agricultural apps that give you in real time the price of the gold, what is the price there of at this or that market, and with the refugee crisis from the Middle East to Europe, it's unbelievable to see that they are using mobile phones and for web access and social media to connect to their physical networks in the host countries. One of the refugees explained at this meeting that the height of his fear was the moment between Turkey and Greece where there is no coverage in either place. That is the peak point of fear. I mean, they're in a barge, they can, you know, capsize it, but that doesn't scare them. They're scared that they don't have web access. And I think then that there are challenges to generate content, content with the relevant tools for the people. Supplementing what Daniel has said, I think it's equally important to make room for the data discussion and for it to mature because maybe right now we are focused too much on, you know, the theory of numbers and my being tracked in, what have you. And there's a fear that can be actually unfounded because this will translate into benefits for users. Naturally, there are laws like the habeas data that will assure and secure the identity of consumers, but for these platforms that we evolve, we need to migrate this discourse of I am being surveilled to I am being, they are getting to know me to serve me better. Yes, and obviously they can provide a better service like Amazon, you know. It's been a fascinating conversation. I just want to take one last statement from Alejandro and Alberto and then we will be closing the conversation. In this new revolution, a new market reality, I think we will be in a much better position beyond the infrastructure of the technology of the wide range. It's a step forward in which many of the organizations that I interact with, I mean the world level, have understood it and done it, but many others that would surprise us are very late. I think it's the central step, understanding this new reality in different cities that we are used to in recent years. Well, I would like to conclude that we are all waiting, Daniel, for this report to come out and that we can see the countries and in each indicator, how they compare to each other, there is a lot of work here, I invite you to do it. I think you can see this paper if it's available. This paper will be published, right? I think it's already available. It's fascinating how a group of people and different intrusions sat down to think about a way to measure what it's possible that in a country there is a Uder or there is a Netflix or there is a... Well, I'm seeing many in the United States. There is a Waze, from Israel, or there is a free market in Argentina. What makes it possible that this happens? From the point of view of the offer and the demand, it's a fascinating framework. I invite you to see it and I invite the community forum to read the following that we soon have a way to measure all these indicators. Thank you very much.


The chain rule is important as a method of finding derivatives, but what makes it a power tool of differentiation is the use of what's called implicit differentiation. The reason this is useful is that it's often easier to write down some relationship between x and y than it is to write down a formula that gives you the value of y in terms of x. Now in some cases if we have this equation that relates x and y we might be able to solve for y. But this is not one of those cases where we can easily solve for y and fortunately, we don't have to. Rather than solving for y, we can differentiate in place using the chain rule assuming that y is a function of x. Now in order to do this most efficiently, it helps to introduce something called operator notation. And this goes back to one of the ways we have of indicating the derivative. And again, dy dx should not be read as a fraction, but it's convenient to read it as d over dx applied to y, where d over dx means take the derivative of what follows with respect to x. So for example, d over dx of x squared is take the derivative of x squared with respect to x and you get 2x. The advantage of operating notation is that we can write down an expression without knowing what it actually is equal to. So we can write d over dx of y and we know this is take the derivative of y with respect to x, which we can write as dy dx. We can combine this operator notation with the use of the chain rule. So d over dx of y cubed. So if I want to take the derivative of y cubed, I look at the last thing that we do, which is we cube something and I'll ignore everything except for this last operation. So this derivative of y cubed becomes the derivative of cubed. And our chain rule says find the derivative normally and then multiply by the derivative of the inside function. So the derivative of cubed is 3 squared times the derivative of we'll invoke the kindergarten rule and put things back where you found them and in this case what was in the was a y, so we put the y back into every set of parentheses. And we still have this unresolved derivative. So now we find the derivative of y with respect to x and while we don't know what that is, we can at least write it down, dy over dx. An interesting thing happens if we try to do this with a function that we can differentiate already, such as x cubed. Let's look at the derivative of x cubed this way. So again, we'll ignore everything except for the last function. This is a cubed function. So I'll drop that out and say that I want to find the derivative of cubed. And the chain rule says if you want to find the derivative of cubed, it's 3 squared times the derivative of putting everything back where we found it, we have an unresolved derivative, which we can write as dx over dx. Again, this differential notation does not represent a fraction. It represents an operation. In this case, find the derivative of x with respect to x. However, differential notation is a useful form of notation because it suggests a much simpler way to get this result. If we take dx over dx to be 1, which it is, and we get the following useful result. You can never go wrong by applying the chain rule. In particular, the worst thing that happens when you apply the chain rule, when you don't need to apply the chain rule, is you'll end up with a couple of factors of dx over dx. But if dx over dx is replaced with 1, we still get the correct derivative. How about x cubed plus y cubed equals 8xy? So we'll differentiate with respect to x. Over on the left-hand side, we have a sum, so we can differentiate that as a sum. So that gives us the derivative of x cubed plus the derivative of y cubed. And again, this is the derivative of something cubed. So we'll differentiate. We'll get 3 something squared times the derivative of our something and put things back where you found them and likewise for our other derivative. Now we have the derivative with respect to x of x and the derivative with respect to x of y. dx over dx is just 1 and dy over dx is dy over dx. And so this gives us our left-hand side. On the right-hand side, we have the derivative of a product, so we can use the product rule. So that'll be x times the derivative with respect to x of y, otherwise known as dy dx, plus y times the derivative with respect to x of x and simplifying. And so there's our right-hand side. Now remember, we want to solve for dy dx, so here's a couple of places where dy dx appears, so we'll try and solve our equation. So the first thing we'll do is we'll get all of our dy dx terms onto one side and if in doubt factor out. And now I can find dy dx by dividing through by 3 y squared minus x and I get my final expression for dy dx. We can also use implicit differentiation to simplify some ordinary differentiation problems. This is especially useful when we have a function like cube root that corresponds to a simpler inverse function. In this case, if I have y equals the cube root of something, then I can eliminate the cube root through a simple algebraic manipulation. And then I can differentiate both sides. Over on the left-hand side, I need the derivative of y cubed. So I need the derivative of something cubed, which will be 3 y squared dy dx. And I'll also need the derivative of x squared plus 5 x plus 4, which will be 2 x plus 5. And since I want to find dy dx, I'll solve by dividing by 3 y squared. And while we could leave the derivative in the form 2 x plus 5 over 3 y squared, a good rule is to answer the question in the same dialect it was asked in. And what that means in this particular case is that since we're given the function as a function of x only, our derivative should also be expressed as a function of x only. And so we know what y is equal to, so we'll substitute that in to get our final expression.