Hello everyone, Masal Khayr with Ali Hamadi representing Tick Mill and the webinar series for futures and how they're used in the capital markets. I hope everybody is doing well and had a good week over the last week since we last discussed the last webinar last Tuesday and we have more interesting information to cover this evening. But before we start, we have the line, if you want, with us, Adnan Shwakie from Tick Mill. There were some last week, for me, where we found the webinars that we did last week on their YouTube channel. Adnan, if you can please provide the link where everybody can access the webinars that have been done in the past. That way everybody can have access to them at any time they need. Adnan, if you can find all the previous webinar recordings in one playlist on YouTube, the link is available. So if you don't have it, please feel free to access the link at any time. And just so you know, tonight is going to be, is our eighth webinar within the futures series. So you should be able to find the seven previous webinars. And this evening's webinar will be updated and to the platform within one to two business days. Come in. So Adnan Shukran, have a good evening. I'll catch up with you later and I'll get started now with the webinar itself. So, hello. What we're going to be discussing this evening are the futures curves. Now I promised everyone last time that I will be trying my best to incorporate Arabic, the conversation, the Hadith. So bear with me if it's inaccurate in some shape or form. But like I said, I will do the best I can. But tonight we're going to be discussing the futures curves and how to analyze and distinguish between the different curves and how to best use that in your decision making and to any type of positions that you may or may not be investing in and taking in. Without further ado, how to view and analyze futures curves on specific commodities or assets. I like to keep the Hadith very informal and conversational so that I'm actually having a conversation with you and try to explain a little more than just reading it off of the slides that are prepared. But you can read them obviously and I'll be discussing them in further detail. But the main thing that we're going to be discussing tonight are the two main types of futures curves that will help you distinguish where the specific asset or commodity is within the market in relation to its spot price and in relation to its future price, depending on what type of maturity that you end up choosing. So with that being said, the shape of the futures curve is important to commodity hedgers and speculators. So this works both ways. It's not necessarily bust the hedgers or the speculators. And the two main types of curves that they pay attention to are one, the contango curve and two, the backwardation curve. And in this Hadith, I will also share with you some examples later in the presentation. But both care about whether the commodity futures markets are contango markets or normal backwardation markets. Normal backwardation is the same as the backwardation curve. And the contango and backwardation refer to the pattern of prices over time, specifically if the price of the contract is rising or falling. So what are the curves? Contango refers to when the futures price is above the expected futures spot price. A contango market is often confused with a normal futures curve. Very simply, is that the spot price, Masalaam Hamsin, or the future price, Hamso Hamsin, this produces a contango curve. The spot price is lower than the expected futures price. What is backwardation? A normal backwardation or backwardation is when the futures price is below the expected spot price. And a normal backwardation market is often confused with an inverted futures curve. Using the example of the spot price Hamsin, or the futures price Hamso Hamsin, the backwardation is below. The spot price is Hamso Hamsin, and the futures strike price for expiry date price is Hamsin. So this is the difference between contango and backwardation curves. And what do those look like? Now here I will give you an example of rolling futures in contango and backwardation. When I'm going a portfolio of futures contracts and you're rolling in one and in and out of another and into another out of one and into another contract over the course of time based on the positions that you have within your portfolio. But if we were to take just one specific isolated futures contract and look at, okay, what scenario are we in? Are we in a contango curve situation? Oh, are we in a backwardation curve situation? So if you look at the green line here on the corn shoe is spot price of the actual commodity or asset that we are investing or trading in. And as time gets closer towards the expiry date, the price of the futures price is higher than the spot price. And as you can see here, the backwardation would come with the spot price. And as you can see here, the futures expiry date price. So the actual spot price and its curve is a down swinging curve. And this is why they think it's often confused with an inverted curve. And the other contango curve is often looked at as a normal type of futures curve. Okay. Now, to, okay. So to better understand the difference of the two to start with a static picture of a futures curve static. It's not dynamic. A static picture of the futures curve places futures prices against contract maturities. So with, if you look here, the head of this graph, it's very simple where the blue would let's say symbolize a normal futures curve, whereas the orange line would depict an inverted futures curve. Okay. And these are the price differences at different contract maturities. So as you can see any a normal curve of if the spot price here in the home, that come up to $60 a year, and then back to $80 a year, but then back to $65 a year, or back to $90 a year, etc., etc. What's that is she on the inverted curve? And this is analogous or basically similar to a plot of the term structure based on the interest rates. We're looking at prices for many different maturities as they extend into the horizon. So home is a, we look at very simply they're increasing and hiking interest rates as we speak. The interest rates have increased three quarters of a point, 75 basis points. We'll see Haki Kamena and the next meeting that they're going to minimum hike another 50 basis points, which would take the interest rate window, the Fed window is about the between 75 basis points and 1% all the way up to one and a quarter percent to one and a half percent. All of this has an effect and let's say cascading effect and drawdown effect on futures pricings based on specific assets, namely commodities and more importantly so interest rates, futures assets and contracts. So now that we know what we're trying to identify within the futures market on a specific asset that you may be wanting to invest in or you already are invested in and looking for ways to either speculate further and or hedge your portfolio. Now we're going to learn how to identify where the spot prices of the asset that you're invested in and what type of curve or scenario that it lies in and what are the normal outcomes and it should be here under the normal circumstances. As we have to understand there is nothing that we would be able to forecast with 100% accuracy. It is important for both hedgers and speculators to know whether the commodity futures market are in contango or backwardation scenarios. So all of this means that the asset or commodity will always end up having a spot price and a forward futures price embedded in a futures contract depending on the maturity. So the maturity of each of these contracts will vary in the futures price of that contract. So literally from the beginning you'll be able to see okay it's spot and then the futures price based on the maturity that you're looking at is about 600 or 100 or 200 or whatever it is. They will be higher than the spot price or they will be bigger than the spot price. But then they will be able to know how to manage and how to analyze what the value of these curves is. Investors in general who are long, they are buyers, they end up not selling short, they're holders or buyers want a normal backwardation spot price meaning that the future spot price is below the current spot price and want the future spot price to increase over time as it gets closer to maturity. Okay and I'm going to give you some examples here but first of all I want to give a little bit of information on a historical chart on oil, crude oil, it's not up to date meaning it doesn't exist in the picture but it gives us up through 2015 the actual spot price when can it and it gives us the forecast up to 2021 and I want you guys to take a look and see how accurate or inaccurate or or how let's say relevant futures contracts are regarding specific assets and in this case it would be oil. Okay so Anna before we get started reading Schumannetta, Kilshihon Al Yameen, but they come here and get this into context. So now what we're looking at is Brent crude price and if you look at the dates at the bottom okay and each column represents Sydney. So I'm talking January 2008 January 2009 January 2010 etc etc all the way to January 2021 okay I'm going to take this out of the way so we can have a better idea. All right what we're looking at now everything in black is the actual spot price of the movement of Brent crude so you can see here it was at $60 a barrel and it creeped up to 140 plus or minus came back down to 40 plus or minus etc etc and then then it stops here at the time of this example that I'm providing you in 2015 the spot price in 2015. Okay now what are we looking at? We're looking at now everything from 2015 to 2021. I don't want you to get too confused with all these colors. I'm going to make it very simple and simplified. This blue line here represents the SEC. The SEC the Securities and Exchange Commission out of the United States the forecast based on their year end of 2014. Look at if it's basically a flat line forecast of plus or minus a hundred dollars a barrel over the course of what the following five years 17, 17, 18, 19, 20, even 16, 20. Okay if you look at the red line these are the futures forward curve the futures curve men January 2015 moving through 2021. Now where is what I want to get at today? Okay so what we're missing out of this is from February 2021 all the way up to year to date as we speak today but as of today Hala looking at my screen here crude oil is trading at 113 dollars a barrel plus or minus. Okay their forecast was plus or minus a hundred the futures contracts when the spot price was down here but look at the curve what that curve is this this is a shoe a can a shoe can taken curve. Okay now this type of curve indicates the spot price is lower than its future value at expiry. Okay so I'm going to get into in the discussion further what types of scenarios in theory and what to be looking for. Okay so that we can see the information that I have for you listed to the right of the graph. There we go. Okay so knowing the difference between the contango and the backwardation will help you avoid losses in futures markets. Now how do we value them what type of markets do we want to be involved in understanding to take when to take profits and when to cut losses how hedgers use them how speculators use them etc etc. So during contango as the future price is higher the profit is maximum when you sell it in the future that makes sense so if you if you buy something down here at the particular price that is being offered at and you sell it later well you can ride the curve up and you can sell it at any point in time along this curve and this will provide you the profit that we're discussing. During backwardation the futures price is going to decrease future further in the future purchasing it later for an investor would be a greater profit. So the longer you wait as it gets closer to maturity and he would be I'm tinsel as it gets closer to the expiry date so as I started here you're going to have a lot more risk involved. This is what they're talking about you're basically eliminating the risk and the loss for significant losses. And the price of the futures contracts would be $55 for the future depending on whatever the maturity is here the price is higher than the current spot price which means it's a in a contango curve scenario. The future price is lower than the current spot price hence a backwardation curve. Now this doesn't mean. Just because you're able to let's say isolate and locate a specific curve and opportunity within a particular asset or commodity this doesn't mean that you should go out and buy futures if it's below the physical price of a commodity or sell them if the futures price are trading higher. This is nothing more than an identifier this gives you information okay and when I get into the next slide I'll be able to get into further detail but it's based on supply and demand and it's telling you what the market is doing what the market is wanting or needing either supply is in more than the demand or there's more demand than the supply that the market is able to provide so the market is more sophisticated and these are why uh this is not plain vanilla type of securities where uh you think you can get it and make lots of money quickly and not know what's going on with the futures contracts the dynamics the mechanics and the sophistications sophistication involved in futures contracts they really really need to be understood thoroughly uh before you get involved in them so the market is more sophisticated and uh than that but this is one example of a strategy one could use and monitor constantly in some circumstances so to trade or invest in futures you need to have a starting point based on understanding the tick value and the risks involved uh well now you have a strategy starting point and bullish okay what type of curve scenario are we looking at is that a contango curve situation or is it a backwardation curve scenario and then based on history on that specific asset or commodity for example i'm in a similar type of situation uh can it contango and a rising interest rate environment which we're in interest rates have not been increased the amount that they've been increased this year that inflation from the US market is at its highest level in the last 40 years the official rate percent as the CPI indicator saying where core inflation is real inflation most likely is closer to 10 percent if not higher what does that mean you're talking about an increase in interest rates men basically zero the window can it zero to 25 basis points at the beginning of the year 75 basis points la 1 percent now and forecasted to be 2.75 to 3 by the end of the year so we are in an increased interest rate increasing interest rate environment so in order for us to use these curves let's say in a like for like situation we have to go back and find an interest rate increase environment based on the same commodity or asset that you wanting to get a position in whether you're hedging and or speculating and find similarities to say okay uh as about the interest rates per america and it but then they did what they started decreasing the interest rates because of the housing collapse in the bubble to the zero rate of interest rate environment that we've been in basically for the last six years plus or minus uh they increased rates one time under trump's administration and then they turned around and decreased them at the next fed meeting to bring it back down to where it was but now uh but at that time mutton so inflation under official data can it buy the ban name but me letting us be me hulla inflation started to many facilities to be me and it's still increasing so what does that tell us interest rates in the in the short term in the short term most likely they will not be decreasing anytime soon if anything they're going to continue to hike and increase until the fed feels that the economy should be let's say stable enough uh to accommodate where the inflation is and bring it down will this play out according to plan only time will tell there is no crystal ball but we can look back historically and see what what's taking place so uh knowing where your starting point can be here markets are fluid and constantly changing so decide if leverage derivatives fit your risk profile before you commence trading as the risk of loss is significant fee is a fee when you don't have an exit point or stop loss on your position the losses can be tremendous uh at the same time uh you've got to have your entry exit point your stop loss points and you've got to be consistent in your analyzation and the tools that i'm informing you with tonight uh are a very good starting point to identify possible scenarios for you to enter the market okay now getting back to regarding the supply and demand of of the of the markets in simple explanation of the dynamics in essence the term structure of commodity futures or the commodity curves are reflection underlying the supply and demand dynamics and what contango and backwardation curves signify what a contango in a usual context okay a usual feature of a normal market or if the contango market is very steep spot prices meaning too low versus the future price it denotes a bearish market what's a bearish market a bearish market means there's more shoe there's more sellers than there are buyers a bullish market or uptrend means that there's more buyers than sellers so if you identify a contango curve and you see that there's a very steep disconnect between the spot price and the future price it usually denotes a bearish market why is this the case because no one wants the commodity today there's poor demand or there's too much supply at the spot rates so then it gets back to supply and demand where's the supply it could be too much and at the same time nobody wants to pay the price that the spot is trading at so if you have the supply and nobody is buying what does that mean well you have a contango curve situation backwardation is an unusual market when i say unusual which denotes the underlying bullish trend bullish commandment and a bullish market meaning there's more buyers than sellers a very deep backwardation curve signifies that the market is witnessing a serious boost or supply squeeze spot prices or near futures prices rise very fast because buyers want to ensure their supply so shuman at the home bitcoin you have your supply and if you have a very steep backwardation curve so it's going to look like like this in your case versus a relative usual backwardation curve it's going to be very steep that means you're going to have the spot prices here there could be a squeeze okay meaning what we could be seeing now in raw materials in raw materials like aluminum steel at the energy prices the the prices have spiked is part of the let's say scenario or part of the bigger picture here be considered one minimum two generations okay okay plus or minus panning living in between $30 per gallon okay now all of a sudden the some of the cheaper states or lower income state America and the more expensive states and they rely on their purchasing power on their money supply or cash flow so is a cash flow they're not getting raises or they're not getting bonuses and the consumer from a consumer driven market on their purchasing power is decreasing leish so now as you're going to see most likely the US market contract because they're going to start spending the American consumer is going to start spending on the necessities consumer staples benzene but they might start scaling back most likely on the non-consumables cyclicals or luxury items depending on what type of income bracket you're in so that now they're saying wallah allah benzene amtigla we're not going to go to the cinema for instead of going twice a month maybe we'll only go once every two months or they end up re-budgeting based on their cash flow from paycheck to paycheck because the meat of shawley ailey or show us what the fuck fear that we're not a sheen home in lebanon and a rampant inflation uh in the mission I know uh in the mission in lebanon I know uh home bus now sheen be what I mean the man is the worst economic uh disaster in human civilization since 1850 so uh to put it in relative terms they wouldn't understand how things are changing so fast on a daily basis but on a larger uh on the largest market in the most stable market when you have prices increasing and in clips at a time and they're feeling the pinch then it's going to have a water down effect on everything else that takes place uh within the market itself uh so this is what we mean when we're looking at identifying a contango curve versus a backwardation curve what type of environment are we in now being able to retrace find uh historically speaking within the markets uh and be able to find uh via research and analyzation okay where are some trends that we could identify that could be profitable trades and or profitable hedges to protect the portfolio that we are currently managing and involved in now at the moment and last but not least I always like to leave the webinar with a famous quote and I've said this before as part of doing your research understand what you get involved in know why uh know how to protect yourself uh etc etc and this quote comes from peter lynch uh an american a famous american investor mutual fund manager and philanthropist know what you own and know why you own it and he's a bit of a fear my feet on photo the futures contracts without understanding oh would she the sophistication involved in the futures contracts how they operate and what sector you're operating in the volatility the liquidity the look how deep is the liquidity in the particular asset that you're involved in how easy is it to get in and out to close positions at the same time what is the outlook based on the current market situation that we're involved in now and then getting back to before taking any type of position with a futures contract take a look at your own portfolio and or trading account look at what you own and answer the question to yourself why do you own x y z in your account can you answer this question can you answer why you own what you own in your portfolio okay if you can't then you need to reassess and i don't might be able to get into job but shaman and old woman square one but you need to reassess or unwind your portfolio and start building an educated research based account trading account and or portfolio knowing the information that you have now based on the webinar series of knowing how to use futures contracts to help benefit the the and compound your profitability you want to win more than you lose you're not going to win every single particular position it's impossible but if you're looking at the bottom line where you have more profitable trades and the profitable column than you do in the in the loss column then that's the outcome that we're looking for and it all goes back to knowing what you're doing knowing what you own why you're in it and then how to better position yourself to protect yourself for the downside while not being greedy on the upside now with that being said i will leave it here i'll open up the floor for any questions that anybody may have please go ahead and show them in the chat and see if i can find where the chat room went first of all do we have any any questions going once going twice perfect but the shaker but the shaker gone for your time for all of you saying thank you i hope but you find this helpful and insightful i'll have we'll have another webinar inshallah espoir jair in harita leta come in i'm getting into the more more semantics and details so that i can provide you with the informational tools needed to better inform you so that you can make informed decisions and please go back adnan on the chat room had the link for the previous webinars elisarum and abili and there are seven previous ones that you own candidate daemon so you can go back and start from the first one up until now i've tried to lay it out each webinar in the most simplistic way uh to get you up to speed of understanding shohan the key key from req bean and how to use them and now we're getting into a little more of the sophistication part of identifying possible patterns or entry or exit points and and within the specific markets whether they're commodities indices or otherwise and help you make you some money inshallah that's the whole point so thank you all have a good evening and i will look forward to seeing you again next week have a good week good luck with the markets careful it's choppy the markets today are in an upswing the dow is up 300 points s and p is up 60 points oil is about flat at 113 gold is about flat at 1819 and but for the most part we're seeing a rebound in the u.s markets so we'll see if that's able to continue for the rest of the week considering that we had six bloody days in a row prior uh we'll see what happens but uh keep uh your mind in the game stay focused stay sharp and see you next week have a good evening to spot a good


U.S. soldiers and members of Japan's Ground Self-Defense Force partnered for a community cleanup project in Chitose City, Hokkaido, Japan. During bilateral training exercise Yamasakura, members from both armies took time to help clean up at a local park. Any military person can come to a Japanese post and say, I've been to Japan, but not anyone can come to an actual post and say yes, I've actually helped the civilians by cleaning up. The all-volunteer project attracted nearly 200 Japanese and American service members eager to participate. And what I got out of it was a lot of fellowship, a lot of friendship and the opportunity to get out and experience the Japanese culture. Along the banks of the Chitose River, everyone pitched in to leave their portion of the park a little better than they found it. From Hokkaido, Japan, I'm Army Sergeant Nate Boat.


So, welcome to this 29th lecture wherein we will see more about you know applications of non-homogeneous Neumann conditions which we actually analyzed in lecture 28. And then we will also then further see in this lecture how do we you know find out eddy current losses happening in a winding of a power transformer biasing FE analysis. So, now let us first you know see you know application of Neumann conditions. So, let us you know take a case of conducting material plate which is excited on its both surfaces by same magnetic field intensity H. Now this configuration is quite common for example any conducting plate in a rotating machine or a transformer for example a cold lamination or a winding conductor excited on its both sides by the same value of magnetic field intensity H. Now here B is equal to del cross A and then you know then it is H will be 1 over mu 0 del cross A and noting that A will be only in z direction because we are doing two-dimensional approximation right. So, then you get this and this in fact was derived in slide 7 of L28. Now in this case since H is only in x direction. So, only this component exists. So, you know you have H as this this component is not there on this surface. So, H is this. So, this is what we are imposing on this you know boundary and inside also H is going to be in x direction only and because of that what is going to happen H is going to reduce as you go from the surface to you know inside and that is the reason that daba Az by daba y also is going to change as you can see here. Now remember these are equi A or equi flux contours right. So, as I mentioned in one of the previous lectures lines and contours are used interchangeably in you know electromagnetic and particularly FE analysis. So, now here also you can see A is varying with respect to y because these colors are changing that you can easily understand from this. So, Hx is some Hx is imposed and then you have by the we are solving diffusion equation. So, the Hx is going to reduce as you go inside and then corresponding daba Az by daba y is also going to change as you go inside from both these surfaces when you go towards center daba Az by daba y is not going to be 0 or in other words Az is going to vary with respect to y as can be seen here. Now what is the application of what we just saw? Now let us take a conductor, a flat conductor which is excited by H on both sides and suppose let us take a very thick conductor. When we say thick conductor it is electrically thick I explained you in L10 then when you say electrically thick that means the thickness is much greater than the skin depth right. So, effectively suppose this thickness is much higher then what is going to happen?  So, this in other words will represent two semi-infinite cases. We also know from the literature that for semi-infinite case the edulars per unit area is given by s square upon 2 sigma delta. Sigma is conductivity and delta is skin depth right. Since the considered plate can be analyzed in terms of two semi-infinite house spaces. So, that is the reason that you can see here as your thickness 2B this is the total thickness 2B as thickness 2B exceeds and becomes much greater than skin depth this normalized eddy current loss which is p upon s square upon 2 sigma delta which is for semi-infinite case it will approach the value of 2.  How do we model transformer co-rejoins particularly for you know frequency response analysis when we want to actually you know want to find out transformer impedance as a function of frequency. Then we have to do time harmonic analysis with you know conductivity of the core considered and corresponding losses considered and hence the permeability will be complex permeability this also I have explained earlier that complex permeability will represent lossy magnetic material where in imaginary part of the complex permeability represents losses right. So, here again what we do we want to find out effective complex permeability of this core structure. Now, what is this cross section? This is a typical joint region of a leg or limb and yolk. So, vertical portion of the core and horizontal portion of the core of a transformer and if you take a cross section like this AA then you will get this kind of you know problem domain and these are the air gaps here. Here this is the air gap is in this region which basically in this cross section those air gaps will appear staggered like this. So, that mechanically hold this structure becomes stable air gap is never allowed to be along the same you know along the same line vertical line here. So, now here what we do is we again you know impose Hx here on both this you know horizontal boundaries top and bottom, but we do not actually you know have any you know information about HY because as you can see here because of this air gaps and all that you have these you know flux counters you know hitting this top and bottom you know surfaces or you know lines in 2D approximation at some angle. So, HY is varying all along these 2 you know lines. So, HY is unknown what you have imposed is only Hx, x component. So, again you know as we have seen this earlier these Hx and HY expressions we have seen in L28. So, those were this. So, Hx is this and we are imposing this HY is this and it is not 0 and it is unknown. So, now this corresponding to this boundary condition Hx the matrix the right hand side matrix Bb of the final linear system of equation. So, this will contribute to the B matrix overall B matrix on the right hand side of our final linear system of equations. So, this Bbe of I this I stands for you know node number B is the right hand side matrix small b is the contribution of boundary condition to this right hand side B matrix and this is related to element E under consideration and the corresponding node I. So, there are 3 nodes. So, one of the nodes is being considered and now this comes out of you know when we write weighted residual statement in Galerkin's method for you know each node then for ith node we will get Bbe as this again for this you refer slides 8 and 9 of this L28. And now here An hat will be simply Ay hat because for this line and the corresponding surface in 3D the unit normal will be in y direction we are considering these as xy plane. So, this is x and this is y direction vertical is y direction. So, now actually if you substitute this here instead of this we substitute Ay hat dx then this dot product will be 0 only this dot product will be non-zero and now in place of this we substitute hx 1 over mu 0 into this is hx which is the imposed boundary condition. So, that is hx and integral n i will remain because here it is 1 over mu 0 dabaiz by daba y. So, 1 over mu 0 dabaiz by daba y is equal to hx. So, that hx comes here and then n i e dx and over the edge. Now again as we saw in this L28 this the contribution to this for any node will come from the corresponding you know contour integral over the considered element. So, remember for each node of the element under consideration we will get this kind of statement corresponding to the you know boundary condition. And now here the contributions of this inner segments will get cancelled as explained in L28 and contribution will remain only for this edge 1, 2 and this edge is this edge 1, 2 for element 1 refer L28 for more details. So, now this and we also saw in this lecture L28 how to evaluate this. So, then you know we can calculate contributions of all such boundary edges by using this procedure for the imposed boundary condition. Because here there will be number of elements here triangular elements is it not and for each of those you know nodes of individual elements the corresponding edges will contribute to this b capital B small b matrix. And all those contributions can be calculated by this procedure and then the overall finally global matrix can be calculated accordingly. And then further calculations can be made you can you know get the value of you know b you can first you will get the value of a from this analysis from a magnetic vector potential you can calculate b. And then from b you can find out the average value of b for this whole you know domain under consideration. And then that average value of b divided by this imposed Hx will give you complex permeability for more details you can see this reference. Now let us go to the next topic which is very important how do we calculate eddy current losses in a coil. Again here as an example we are taking a high voltage winding of a power transformer. Now here just a three-dimensional view is shown here not everything is shown only the core leg is shown that is the vertical part of the core. And surrounding it we have LB and HV windings. Now the leakage field at an instant of time is vertically will be vertically upwards and here we are not showing the fringing field at the end we are just showing the axial field but of course there will be radial flux at the ends. So now our objective is to calculate eddy current loss of high voltage winding which is subjected to this alternating magnetic field B which is leakage field. And then we have already you know seen in lecture 10 the eddy loss formulae we will use those here. So before that let us understand this geometry little bit more. So now this high voltage winding is you know given here now of course this is not to the scale. So this point is this and this point is this. So this is the total radial depth of this HV winding. Now high voltage winding will have number of conductors placed like this this is called as one disk this is one disk this is second disk and this is say nth disk. Now individual conductor as shown here is a rectangular conductor and dimension chosen are this. Now this is the actual leakage field plot for a transformer and now you can see here there is a axial flux in the middle portion of the winding and at the ends you have fringing and predominant radial flux. And then we have seen in lecture 10 eddy loss formula for a thin conductor of thickness T which is less than or equal to skin depth and excited by B0 on both sides the thickness T and B0 is there like this. Then P eddy is given by this formula rho is the resistivity B0 is the peak value of flux density here T is the thickness of the conductor which is perpendicular to the direction of flux. Now here the flux is in this vertical direction. So T will be this perpendicular direction to this. So that is T and that is what is written here P eddy axial and remember this is loss per unit volume. So P eddy axial will be omega square omega is 2 pi f square then thickness square by vertical component vertical component of B upon 24 times resistivity. For the radial flux now at the ends particularly you have the radial flux component. So for the radial flux component the perpendicular dimension because flux is now like this the perpendicular dimension will be this W the width. So that is why here it is omega square W square Bx square upon 24 times rho. So we can individually calculate losses due to axial and radial fields and then basically sum them up for a winding under consideration. So if we have understood this let us go further. Now let us go again go back to the problem domain this is the whole HEA winding and now what is the title written here eddy current loss using magnetostatic FEM simulation. Now this is you know something it looks odd that we are finding eddy current losses. So that means it is a time varying case but we are you know using magnetostatic FEM solution for that. Now this is allowed because seeing the thickness of the conductor and dimensions overall dimensions of the conductors are such that no those dimensions this dimension and this dimension they are comparable or less than the skin depth you can consider them as you know electrically thin conductors and then the eddy currents induced in this individual conductors are not significant and it can be assumed that those eddy currents do not influence the leakage field much. So then in that case if eddy current reaction effect can be you know neglected then we can effectively use magnetostatic FEM simulation and then calculate you know values of Bx and By at the conductor centers and then you use this to formulate for calculating eddy current loss due to axial and radial fields for each conductor. So effectively what we are doing we are actually calculating field values using static simulation and then we are using eddy current theory because this is a classical eddy current theory this you know these expressions are derived starting from Maxwell's equations and solving diffusion equation. So we are using static FEM simulation and then using classical eddy current theory to calculate the eddy current losses of each conductor analytically and then we will sum of sum up all the losses for the entire winding. So now how do we do that? So we need to find out each this conductor and the corresponding representative point so what we will assume for the entire conductor we will assume that the flux density is that at the centroid. So then we have to first find out in which element this center point lies and then using that information of element we get the corresponding Bx and By of that element and then use it further in the eddy current loss calculation. How do we find out the you know element corresponding to this you know point or where in which element this point lies we have seen it earlier in one of the lectures.  See it is always you know in any kind of FE analysis always you know you should have some verification either you should verify it with approximated analytical solution or if you have some you know verification problem in the literature and all the geometrical and electrical parameters are given then you can first solve that problem get confidence and then you know you do analysis for your problem. So here in this case I am using analytical formula to verify my FE analysis. So now in analytical formulation obviously we have to do some approximation. So what is the approximation we are doing? We are actually you know analytically integrating you know the effect what this entire you know radial depth of the high voltage winding. Now we have seen this in one of the earlier lecture. This is the ampere turn diagram associated with the leakage field in a transformer with this LV and HUE windings and this is the gap between the LV and HUE windings. So in the gap region the flux is uniform and in LV and HUE windings as you go away from the you know gap towards you know the other ends then the leakage field reduces. So if we analytically integrate this flux then what we will get? We will get integral b0 square mean as b gap gp stands for gap b gap square by 3. Now this you know derivation is given here in this reference. So basically what we are doing? We are analytically integrating because why we are doing this? Because we need to integrate over the entire winding analytically. So in our formula for ideal loss we have omega square t square b square. So when we want to integrate over the whole winding you basically find out the mean value of you know b0 square and use that mean value which is representative to you for whole this winding. So then the integration becomes you know straightforward. In fact the integration does not really remain integration because we have already taken into account you know that integration by using you know the mean value of b0 square. And remember bgp b gap is given by root 2 mu 0 ni by hw. hw is the height of the winding and this because there is a root 2 factor here i is the rms current. So always remember in this formula always these are the peak values. So that is why root 2 into the rms value. So we are considered peak value and s is the cross section area of each term. So let us understand this formula now. Again what we are doing? In analytical formulation we are considering only axial field. So axial field when we consider in this way and this is the corresponding thickness which is perpendicular dimension to this field and that is why this t appears here. So t square this we had you know seen it earlier omega square t square b square upon 24 rho. But here since we are taking b0 square mean as this. So that is why b square gets replaced by this bgp square by 3 here. And now this is you know for you know if there are n turns then we have to multiply it by n obviously because this we are calculating for each turn multiply it with number of turns multiply it with 3 for 3 phases. So then this will give you ad law square unit volume for all turns for the 3 phases. So now we have to multiply then by the volume. So volume is nothing but cross section area of each turn into pi into mean diameter. Now again we are taking mean diameter as the diameter as mean diameter. So that again simplifies the calculation.  That ad loss for 1 turn is multiplied by n turns to give you for n turns and then it is multiplied by 3 to give you you know losses for all 3 phases of the high voltage winding. So now the final verification. Now see in the axial formulation we have considered only axial field right in the analytical formulation. In the analytical formulation we have considered only axial field. So in the FEM also we should have axial field only so that then the comparison is you know valid. So then what we do in case of FEM simulation this is we basically you know take the horizontal boundaries at top and bottom very close to these low voltage and high voltage windings and impose homogeneous Neumann condition right. So the derivative of you know potential with respect to the normal is 0. So effectively you know you will have you know all the flux lines you know almost going straight and impinging on both the horizontal boundaries normally. So now the since we are we have constrained axial the flux to remain axial throughout the this geometry in high voltage winding also the flux is axial. So then the ad loss calculated by FE analysis we can compare with the analytical formulation value. So before doing that let us understand this formula for EAD in FE analysis. Now here we are not analytically integrating or you know calculating the average value and you know doing what we did for approximate analytical formulation. We are going each conductor wise at every conductor as I explained earlier we are finding BX and BY and then correspondingly here we are you know taking that. Now here you know we need to worry about only BY because BX B horizontal or X direction is almost 0. So B is entirely in Y direction vertical direction. So only BY will come here and corresponding thickness because thickness of the conductor will be the perpendicular dimension to BY. So omega square T square B square upon 24 times rho is the ad loss per unit volume of that conductor into the conductor area because S is the cross sectional area of each conductor. Some these over all conductors and then so this is ad loss per unit length because area is now already considered. So now this becomes ad loss per unit length and now that you multiply here by point to mean diameter of the entire winding. So now this becomes ad loss for ad loss for the entire winding and that is for one phase of the HV winding and then multiply by 3 for all the three phases of the high voltage winding. So this is how you calculate the PAD. For more details of all these you know theory and corresponding you know explanation you can refer this reference and get more insight into the whole thing. So then now here and of course here I already explained you B is the peak magnetic flux density at the center of each conductor and then we calculate ad loss per unit volume for each conductor, sum it then multiply by area, sum it over all conductors, multiply by pi into mean diameter. So this gives you total ad loss for the entire one phase of the HV winding and then for three phases. Now here you can now see analytical and FEM results are compared and now you can see they are quite close. So this gives us confidence that finite element analysis procedure that we have adopted is okay and now for any complication either in geometry or ampere turn distribution you know we can use this procedure because in one of the very first lectures I told you one of the major advantages of FEM is it is more or less independent of you know geometrical complications. The procedure is same and that gives you know the distinct advantage to this numerical technique finite element method. So this is how you know you can validate your finite element analysis procedure by taking a simplified you know flux distribution by doing some approximations and comparing the values and get confidence and then go on to solve more complex problems. So we will stop here and start a new topic in the next lecture. Thank you.


The title of our sermon this morning is a Romans review. This will be the first review of what may be several, but a Romans review, Romans chapter one verses one through 17. So this morning as we continue our verse by verse exposition of Paul's letter to this church at Rome, we arrive at a significant point in our progress. We've now worked through Paul's greeting to the church at Rome versus one through seven. We've considered Paul's general introduction to this letter in verses eight through 15. And then we spent time in consideration of Paul's theme versus 16 and 17, which is as Paul has stated, the gospel of Jesus Christ. And the book of Romans is essentially an exposition of the gospel. We're gonna spend a lot of time talking about the gospel. Now those three sections, the greeting, the general introduction and the theme comprise the prologue of the letter, meaning that we are now ready to begin the body of the letter in chapter one verses 18. Seems like it's been a long time coming, hasn't it? So we've arrived at verse 18. We're ready to begin the main body of the letter. As we take our journey together, I want you to know where we are on the map. So that's why we talk about an outline that we can get a perspective of where we are. However, as you well know, we've been traveling along our path rather slow. So not including our introduction to this letter, we've taken 17 sermons to cover the first 17 verses. That is a blessing and a benefit to us. This is not a sprint, it's a marathon. I think with me you would agree that we've learned a lot going through these verses in this way. So what I've planned for us to do this morning is a little bit different and it's a bit of an experiment. You'll have to let me know how it turns out when it's all said and done. I want to pull off the highway as it were and stop at a scenic overlook and take a vista view of the ground that we've covered so far. Get a more bird's eye view of what we've covered. And sometimes looking at details along the way, we can lose sight of the whole, can't we? It's like you're traveling along a path at Squirrel.  We want to come back to the path, so to speak, and we want to get a bird's eye view of what's going on. And so I thought that a review might be helpful for us as we end one section and begin a transition into another section. I could use some help learning how to move a little more quickly. You could possibly benefit by the review. And so I intend this morning with the Lord's help to take a look at verses one through 17 in their entirety in hopes that that'll help you retain what we've learned there a little better, maybe lock some of that information down. If you're visiting with us, this is ideal time for you because you'll get a one hour summary of 17 sermons on this opening section, this opening prologue to the book at Romans. We're not in any hurry, right? And in the way that the texts are laid out in the next section, the pace of this is going to quicken. It may be beneficial to us in completing large sections of the letter to stop at each of the ends of those sections and review what we've covered. So with all that said and done, let me know if this is of benefit to you. We are in the prologue of Paul's epistle to the Romans, chapter one, verses one through 17. Now we've said the opening prologue divides nicely into three sections, the greeting, the introduction and the theme. First, consider with me Paul's greeting in verses one through seven. It's the greeting in which we see Paul's reason for writing. Okay, Paul wants it known at the outset of this letter that he writes in service to the Lord Jesus Christ as a minister of the gospel. Paul's an apostle, his mission is the gospel and he wants that known at the beginning of this letter. Who he is and who he represents is the reason why he's coming to this church at Rome with this letter. It's a loving letter, but it's not a casual correspondence. Paul has a purpose in mind. He's not politicking with the Romans to boost his reputation. He's not out trying to make a name for himself. He's not building his kingdom. Paul is a man on a mission. Paul is a man under obligation. Verse 14, Paul is a debtor to all men with the gospel. Verse 15, he is ready to preach the gospel to those who are in Rome also. So with the greeting, verses one through seven, we're introduced in verse one to the servant and his subject, to the servant and his subject. Paul, a bond servant of Jesus Christ called to be an apostle separated to the gospel of God. Now remember with me the three descriptions that Paul uses for himself. Paul is a bond servant. Paul is a called apostle and Paul is separated to the gospel of God. Notice first, Paul chooses to describe himself as a bond servant of Jesus Christ. It's a very important description. It's a description that we all share as believers in the Lord Jesus Christ. The Greek word is doulas and it means slave. Paul, a slave of Jesus Christ. Now again, consider the context with me. Paul once thought of himself as a Hebrew of Hebrews circumcised the eighth day of the stock of Israel, of the tribe of Benjamin. Paul would have taken great pride in all of these things. He was concerning the law of Pharisee, concerning zeal, persecuting the church, concerning the righteousness which is through the law, blameless. In other words, Paul went all the way with his religiosity. He left nothing to chance. A Roman citizen, Paul was educated at Tarsus, a Jew educated at the feet of Gamaliel, the teacher of Israel. In other words, Paul has the education, the skill set, the resume, to do anything that he wants to do, to go anywhere that he wants to go. And what does Paul rejoice in at the outset of this letter, the first description that Paul uses for himself, I am a slave of the Lord Jesus Christ. Praise God, right? Philippians chapter three, verse seven, what things were gained to me, Paul says, these I have counted loss for Christ. Now think about that. Paul's heritage, the time, the education, all of Paul's attainments, all of Paul's achievements, he says they're nothing. I've counted them as loss. Yet indeed, I also count all things lost. Why, Paul? For the excellence of the knowledge of Christ Jesus, my Lord, for whom I have suffered the loss of all things and count them as garbage, right? I count them as rubbish that I may gain Christ, right? May we be able to say the same thing. May it be said of us, right? There's nothing in this world worth holding onto, grasping onto. What will you give in exchange for your soul, right? What does it profit a man if he gains the whole world and loses his own soul? Give it up for Jesus Christ. Count it as a common thing. Count it as rubbish to gain him, amen? Notice next, not only does Paul consider himself a slave, Paul is a man, a slave with a very high calling. Paul is called to be an apostle. Literally in the Greek, a called apostle. The word called there, an adjective. It's describing the kind of apostle that Paul is. In other words, Paul is not a self-appointed apostle. Paul is not a man-made apostle, like many apostles that we see today, right? Apostle Joe, apostle Frank, apostle Sally. Those aren't apostles, all right? Paul is not a self-appointed apostle, not a man-made apostle. Apostle Paul is a called apostle. Paul is not an apostle by his own will or by the will of another. Paul is only an apostle through the will and commandment of the Lord Jesus Christ. Paul uses the word in the same way. In 1 Corinthians chapter one, verse one, where Paul literally there again, a called apostle of Jesus Christ through the will of God. In Galatians chapter one, verse one, Paul, an apostle, not from men nor through man, but through Jesus Christ and God the Father who raised him from the dead. In other words, Paul is what he is. Paul does what he does through the determined will and commandment of God and of the Lord Jesus Christ. Paul is a called apostle. In the most basic sense, the word apostle simply refers to one who is sent. Here it's an official title, designation that refers to a specific office. In this case, it's one sent by Jesus Christ in a specific capacity, sent with the Lord's authority, sent with the Lord's power, with the Lord's supply, with the Lord's strength. Paul is a sent one, an apostle. These apostles, one of the things that distinguished these apostles from other sent ones was that these were eyewitnesses to the historical facts of the gospel. You know, our faith isn't a blind faith. Our faith isn't an empty faith. It's not the figment of some man's imagination like so many other faiths, all faiths are. Our faith is rooted and grounded in historical fact. I remember I had these Jova's witnesses, they were Mormons that came to my door to witness to me one day. I opened the door, started talking to them. And in my conversation with them, I didn't mention anything in the beginning about being a pastor or anything like that. I said to them, I've often considered and I have the truth claims of other religions like Islam and like Buddhism or Hinduism and consider their truth claims, their assertions, their claims of truth. And I said, it's fascinating to me Islam, how Muhammad goes into a cave by himself. No one there to witness any of this stuff. And he says he gets direct revelation from God and the people just believe him. And the whole time what I'm doing is I'm setting it up because that's exactly what Joseph Smith did. He sticks his face in a hat to translate some plates that only he could translate. And you're gonna put your never dying soul in the hands of some man who's dreamed this up out of the figment of his own imagination. It is absurd. It's absurd. Our faith is a determined faith that is rooted and grounded in historical facts with eyewitnesses. These are men who saw the risen Lord. John chapter one, verse one, that which was from the beginning, which we have heard, which we have seen with our eyes, which we've looked upon, our hands have handled concerning the word of life, concerning Jesus Christ. The life was manifested and we have seen and we bear witness and declare to you that eternal life which was with the Father and was manifested to us. That which we have seen and heard, we declare to you so that you also may have fellowship with us. And truly our fellowship is with the Father and with his son Jesus Christ. And these things we write to you that your joy may be full. These were eyewitnesses of the facts of the gospel. Paul was a lowly slave with a very high calling. Lastly, Paul is separated to the gospel of God. Paul was a man entirely devoted to that singular cause. The word separated means set apart or appointed. It means consecrated. The grammar there is very important. The word is a perfect passive participle. I like the alliteration, right? Perfect, meaning that this was accomplished completely in the past, but has ongoing or present effect in Paul's life. The perfect tense refers to something completion, completed in the past with ongoing effects, passive, meaning it wasn't something that Paul did for himself, but rather this was something that was done to Paul. We call this a divine passive. In other words, it was God himself in the past that set apart or consecrated, appointed Paul to the gospel. And Paul is now living his life in accord with that calling in accord with that consecration or that separation. John Murray said that all bonds of interest and attachment alien or extraneous to the promotion of the gospel have been cut asunder. And he is set apart by the investment of all his interests by the investment of all his ambitions in the cause of the gospel. Charles Spurgeon called this gospel labor, the life business of the Christian, okay? It is, that's something that we should be considering. Paul is consecrated. He is set apart, commissioned to preach the gospel. And like Paul, listen, brothers and sisters, you and I are the same, right? There are ways in which we differ from Paul, but you and I are slaves of the Lord Jesus Christ called to his service, to his cause, separated to the gospel in the same way you and I. It's here in our greeting that now Paul transitions from servant to subject. What is the subject? What is our subject? It's the gospel. It's what we've been talking about, right? Verse one, Paul is separated to the gospel of God, which he promised before through his prophets in the holy scriptures, concerning his son, Jesus Christ, our Lord, who was born of the seat of David according to the flesh and declared to be the son of God with power according to the spirit of holiness by the resurrection from the dead. That word gospel literally means good news, you on Galeon, a good message, a good word. Notice first the source of this good news. It is the gospel of God, specifically speaking here of God the Father. It is the good news that originates with, is promised by, revealed by, given by God himself. In other words, this is God's gospel. It's not a gospel of human origin. It's not a gospel revealed by man. It's not to be tampered with by man or messed with by man. Paul is set apart to the gospel of God. It's God's gospel, okay? Therefore, this message isn't to be dressed up or dressed down to suit our convenience. It's not to be tampered with, altered, watered down, washed out, spruced up, it can't be adjusted, can't be modified to suit your circumstances. It's absurd to think that you can make it more relevant. There's nothing more relevant to begin with and you can't do anything to make it more palatable to this wicked culture. It's a gospel. The gospel is a word from God the Father to sinful man. We shouldn't be messing with it. And what you find is churches and preachers all over the place who do. They water it down, they wash it out. That message concerns his son, Jesus Christ, our Lord. It is to be proclaimed in his name, given with his authority, authenticated by the work of his spirit. Paul told the church at Corinth, when I came to you, brethren, I didn't come to you with excellence of speech or of wisdom declaring to you the testimony of God. In other words, I didn't drum a message of my own making. I'm not at liberty to change things. I'm not at liberty to withhold things or to add things. I don't get to stand back. We, brothers and sisters, don't get to stand back and make decisions about what we say and what we don't say. What's important or not important? What may offend or not offend? You see, we can't do that. We've been given a message. We have to be true and faithful to that message. Paul levels a pretty strict anathema, a curse against anyone who would mess with it. We're not to change the message. Paul says, I didn't come to you with excellence of speech. I gotta think now carefully about how I can manipulate and persuade to get people to say yes to what I'm selling, what I'm peddling. We're not peddling anything here. I determined, Paul said, to know nothing among you except Jesus Christ and him crucified. I was with you in weakness and fear and in much trembling. That doesn't mean that Paul was scared to do that. Paul's not ashamed of the gospel. Paul wasn't fearful to preach the gospel. When Paul says I was with you in weakness and in fear and in much trembling, Paul is talking about the weight of what he is doing, presenting a message of salvation to lost and dying hellbound sinners. Souls are on the line.  That's why Paul was in fear and in weakness. Who's sufficient for such things? We are in weakness. We are in fear and in much trembling. We know what it is we're talking about. Paul says, my speech then, my preaching. Some people are so arrogant and so full of themselves with respect to the gospel, they believe they can sell it. They're like snake oil salesmen, right?  Who are you to make it anything? But what God makes it in His word, preach the truth of the gospel, right? We don't have the liberty to do that nonsense. Paul says, not with persuasive words of human wisdom, but in demonstration of the spirit and of power. When the word of God is preached, the spirit of God works through the word of God upon the people of God to effect the fruit that God intends from it. And we see that in the demonstration of the spirit and of power. Your wisdom, your faith should not be in the wisdom of men, it should be in the power of God is what Paul is saying. There is no salvation apart from the proclamation of a true and full gospel which God has given. And Paul says, I'm not shrunk back to declare it to you, right? Innocent of the blood of all men because I'm not shrunk back from declaring to you the gospel. We better not tamper with it, amen? Now notice next, the substance then of that good news, the source of the good news, it is the gospel of God. The substance of that good news, the gospel concerns a promise. That promise concerns a person and a purpose, okay? The promise, verse two, that which God promised before through his prophets in the holy scriptures. The person, verse three, concerning his son, Jesus Christ, our Lord. The purpose, obedience to the faith among all nations for his name. In other words, what Paul was preaching was what God had always intended. What God himself had promised long before. It's in Galatians chapter three that Paul says that the scriptures foreseeing that the Gentiles would be saved by faith preached the gospel to Abraham saying, in you all the nations of the world will be blessed. In other words, the gospel was something that was preached to them. The gospel preached throughout the Old Testament. These truths given to them as well. This was something that God promised long before. The first example of that promise we find in Genesis chapter three, verse 15, right? Where a promised seed of the woman would crush the head of the serpent. This was promised long before through his prophets in the Old Testament scriptures. That's what Paul is speaking of. Now these Old Testament scriptures given to us through Old Testament prophets who wrote concerning his son, our Lord Jesus Christ. In confrontation with the Jewish leaders in John chapter five, verse 39, the Lord says, you search the scriptures, speaking of the Old Testament for in them you think that you have eternal life and these are they which testify of me. The Old Testament testifies of Jesus Christ with the disciples on the road to Emmaus in Luke 24 beginning with Moses and all the prophets Jesus Christ expounded to them in all the scriptures. And what is he speaking of? He's speaking of the Old Testament scriptures. He expounded to them in all the scriptures the things concerning himself. In other words, the Old Testament concerns who? Jesus Christ. How then are we to read the Old Testament? How should you read your Old Testament? We are to read the Old Testament as scriptures that reveal the person and work of Jesus Christ. If you're not reading your Old Testament in that way, if you're not reading your Old Testament to see how Jesus Christ is revealed there, then you're reading your Old Testament like an Old Testament Jew, right? The veil is lifted in Jesus Christ. We have progressive revelation and isn't it glorious, right? To see the Old Testament in that light in all the ways in which the Old Testament reveals the person and work of Jesus Christ. It's awesome and all of that lends itself to this unified, grand, progressive, redemptive revelation. All fits in one glorious story from beginning to end from Genesis to Revelation and it is beautiful. Now, introducing the person and work of Jesus Christ in Paul's greeting from chapter one, Paul first references his humiliation in verse three and then Paul references his exaltation in verse four, okay? Concerning his humiliation, what theologians have called his humiliation, we might refer to it also as his incarnation. Concerning his humiliation, Jesus Christ was born of the seed of David according to the flesh, verse three. Literally translated, the text would read, having become the seed of David according to the flesh. In other words, the eternal Son of God, co-equal, co-eternal with the Father began to be something that he was not before. The one who is the Son of God, Jesus Christ our Lord became of the seed of David. Now, Paul is talking here about the incarnation. That's what Paul means by the modifying phrase in verse three, according to the flesh. It means that Jesus Christ came into being as it were in the likeness of our essential humanity. Hebrews chapter two, 14 speaks of this very issue. In as much then as the children have partaken of flesh and blood, he himself likewise shared in the same. Note the emphasis, right? So that through death, he might destroy him who had the power of death, that is the devil, right? Crush the head of the serpent and release those who through fear of death were all their lifetimes subject to bondage. For indeed, he does not give aid to angels, but he does give aid to the seed of Abraham. Those who with Abraham trust in Christ for the promise. Again, this is referred to as the Lord's humiliation. In part, Philippians chapter two, verse six, tells us why being in the form of God, he did not consider it robbery to be equal with God. Why are those two statements true? Because Jesus Christ is God. Jesus Christ is God in the flesh. Being in the form of, in other words, Jesus Christ had within himself all of the essential attributes of deity contained within the Lord Jesus Christ is the fullness of the Godhead bodily. So he was in every way God did not consider it robbery at all to be equal with God, but made himself of no reputation, taking the form of a slave and coming, same word, becoming in the likeness of men. It was his humiliation. Jesus Christ came into this world. He assumed the dirt, the mud of our humanity, so to speak, as the promised seed of David. Jeremiah chapter 23, verse five, the prophet Jeremiah says, Behold, the days are coming says the Lord that I will raise to David a branch of righteousness. He is the promised seed of David. A king shall reign and prosper, execute judgment and righteousness in the earth. In his days, Judah will be saved. Israel will dwell safely. By the way, in his days, who is Judah? Who is Israel? All those who have the faith of Abraham, right? All Israel will dwell safely. Now this is his name by which he will be called the Lord our righteousness. We're there for Lord is Yahweh. Jesus Christ is Yahweh our righteousness. Being found in appearance as a man, the Lord Jesus Christ humbled himself, became obedient to the point of death, even the death of the cross. It was there that the Lord bore the sins of his people and his body on the tree. It was there at the cross that he took our sin, our guilt, our shame, took that upon himself and the Lord Jesus Christ suffered in our place, the just for the unjust. All of that, brothers and sisters, so that you and I could be forgiven, that we might be reconciled to God. He made him who knew no sin to be sin for us, that we might become the righteousness of God in him. What should be the response of any rationally thinking person? What is the only reasonable response, J.I. Packer? Look to Christ, speak to Christ, cry out to Christ just as you are.  Ask him to give you a new heart. Working in you true repentance and affirmed faith, ask him to take away your evil heart of unbelief and to write his law within you that you may never henceforth stray again from him. Turn to him, trust him as best you can. Pray for grace to turn and to trust him more. Use the means of grace expectantly. Looking to Christ to draw near to you as you seek to draw near to him. Watch, pray, read, hear God's word, worship, commune with God's people, and so continue till you know in yourself beyond doubt that you are indeed a changed being. A penitent believer, the new heart which you desired has been put within you. Amen, praise God. If that's you here this morning, cry, flee to Christ. Amen. Upon the completion of his work for sinners in his humiliation, we then see the reward of his labors in his exaltation. Romans chapter one, verse four, he was declared to be the son of God with power according to the spirit of holiness by the resurrection from the dead. We've noted that the gospel of God concerns a promise, verse two, that which God promised before through his prophets and the holy scriptures. We've also noted that the gospel of our God concerns a person in verse three that concerns God's son, Jesus Christ our Lord. And concerning Jesus Christ, we see the gospel magnified in his humiliation, verse three, he was born of the seat of David according to the flesh and we see the gospel magnified in his exaltation, verse four, he was declared to be the son of God with power according to the spirit of holiness by the resurrection from among dead ones. That's what that means. Paul then summarizes the purpose of the gospel in verse five, through him we have received grace and apostleship for obedience to the faith among all nations. Well, that sounds legalistic. I'm just reading the Bible, right? For obedience, obedience, obedience. Paul says to Titus, remind them of these things constantly that they should be careful to maintain good works for obedience to the faith among all nations for his name among whom you also are the called of Jesus Christ. God expects as the fruit of faith, obedience for his name as a fruit of faith, not in order to earn your salvation. This is not a salvation by works. It's a salvation that works, right? Obedience for his name, saving faith bears fruit to all who are in Rome, beloved of God, called to be saints, verse seven, grace to you in peace from God our Father and the Lord Jesus Christ. With that, Paul closes out his greeting and moves on to his general introduction verses eight through 15. And in the introduction here in verses eight through 15, we see Paul's relationship to these believers at Rome. Paul, since his conversion, has not been to Rome as an apostle, he's not visited there, he doesn't know these people, he's met a couple of them, but he doesn't know these people, doesn't know these church, and by this church, and by reading these verses, it's as if they are long lost friends, right? He loves them, it's as if he knows them very well. And as we look at this particular section of the text, Paul's general introduction from verses eight to 15, we see this under three headings and all of it related to Paul's prayer for them. How does Paul relate to these believers in Rome, having not been there himself, he prays for them. He loves them and love bears fruit in Paul's prayers. We see point one, Paul's prayer of thanksgiving, point two, Paul's prayer of intercession, and point three, Paul's prayer of supplication. And in these verses, we should see brothers and sisters in a pattern for us, our own prayer. This should inform how we pray for others, pray for one another. First, we come to Paul's prayer of thanksgiving in verse eight. First, I thank my God through Jesus Christ for you all, that your faith is spoken of throughout the whole world. What was it, verse eight, that compelled Paul to offer thanksgiving to God for them? It was because their faith is spoken of. It was witnessed to, it was evident to the whole world. How do you see someone's faith, right? James says, show me your faith without your works. If you could do such a thing, which you can't, I'll show you my faith by my works, right? So how is it that their faith is spoken of throughout the whole world? Because these believers are rendering the obedience of faith to the glory of his name. And the rest of the world sees it. That's because they've come to faith in Jesus Christ. It's because they've evidenced that faith through obedience to the gospel. And precisely because that faith is so obviously manifest that Paul prays to God and gives thanks to God for them. They're living it, aren't they? The next, we come to Paul's prayer of intercession from a prayer of thanksgiving to a prayer of intercession, verse nine. For God is my witness, whom I serve with my spirit in the gospel of his son, that without ceasing, I make mention of you always in my prayer, you see those descriptors, right? Without ceasing and always, most basic, most fundamental to Paul's service to God in the ministry of the gospel is unceasing always prayer for those to whom he ministers. We don't build this house ourselves, right? We labor in vain unless the builder builds.  Most basic to our service needs to be this activity of prayer. The word serve in verse nine, for God is my witness whom I serve with my spirit is the word latruo. It means to worship. It was an act of worship on the part of Paul to pray, to serve God in this way. By spirit in verse nine, Paul is not speaking of a holy spirit, Paul is speaking of his own spirit. He's serving with earnestness, right? In my spirit, with my spirit. Serving with fervency, he's serving with sincerity, with a heart level earnestness and eagerness in the gospel Paul is serving. In other words, Paul isn't merely checking boxes and doing his duty. This is not base duty on the part of the apostle Paul. This is from the heart. In a third, consider with me Paul's prayer of supplication then, Paul's prayer of petition. In verse 10, Paul begins to tell the church at Rome what he's been praying for. Making request, if by some means now at last I may find a way in the will of God to come to you for I long to see you, that I may impart to you some spiritual gift so that you may be established. That is, that I may be encouraged together with you by the mutual faith both of you and me. The root of the verb in verse 10, making request, is used in the noun form for supplication. This is Paul's prayer of supplication. Notice first, again, Paul's heart. Paul employs several emotive phrases here. He's wearing his heart on his sleeve. Paul is sincere, Paul is earnest, right? Verse 10, if by some means now at last I may find a way, verse 11, I long to see you. Verse 12, that I may be encouraged together with you by our mutual faith. Right, in other words, Paul's expressing his love for these people, expressing his heart for these people. This isn't dead ritual. This is a spirit wrought grace, is it not? The spirit of God among the people of God cultivates this kind of love in the heart of God's people, right? For one another. And praise God, we witness that here. We need to abound in this grace. We need to ask, pray fervently, fervently that the Lord would increase this among us. That we would love one another more fervently and that we would love him more fervently, right? Please, Lord, grow our love that we need it. Now Paul here loves these people. God, please, may I find a way in your will to come to them, to make it to Rome. I long to see these dear people. But notice second, the substance. What is Paul praying for? The substance of Paul's supplication. That I may come to you, verse 10. That I may impart to you some spiritual gift, verse 11. That you may be established, right? Established in the faith through apostolic preaching, established, strengthened. That I may be encouraged together with you, verse 12. He wants to have fruit among them, verse 13. And he is ready to preach the gospel to them, verse 15. So, although Paul longs for that encouragement, that comes from fellowship, Christian fellowship with the saints, Paul's concern is not sightseeing in Rome. Paul's concern is not the good coffee and donuts that are served in the Narthex of the church at Rome. Paul's concern is not what he can receive from them but what he desires from the heart to do for them. And that, brothers and sisters, is a model of ministry for all of us. We hear it all the time, don't we? Like I, you pick a church, you go to church because I wanna be fed, right? And well and good, we need to go to a church that feeds our soul, right? The church has a responsibility from the word of God to feed the souls of God's people. But our heart attitude should not only or merely be to go to a church where I'm going to be fed, we should have from the heart a desire to serve God's people. We need to emulate Paul in this, imitate him as he imitates Jesus Christ, who for the joy set before him, despising the shame, counting in a small, common, insignificant thing, endured the cross. Brothers and sisters, we need to serve one another following that good example. Notice in the substance of his supplication, it's the fruit of serving God's people, the Lord's church, that Paul then expects to receive a blessing himself. And isn't that in God's grace always the case, right? When I serve him, I'm blessed. And you know, if you really trust the Lord in that, it can almost be self-serving, right? Listen, I'm gonna come and love you because I love you and the Lord loves me through. It's all good. Like the Lord takes care of us in that way. It's very gracious. It says in verse 12, that is that I may be encouraged together with you by the mutual faith both of you and me. This is not a one-sided affair. Paul's gonna be encouraged too, right? Here's the mindset. Here's the hope, the hope, the heart of the apostle Paul and the purpose of his prayer. He knows that when he goes to the church at Rome with the heart and mind to love and to serve selflessly and sacrificially serve those people, when he is there among them as one who serves, when he fulfills his responsibility to pray for them, to build them up, to establish them, to spiritually bless them, he knows that due to the grace of God, they won't be the only ones built up or encouraged. Paul himself will be encouraged together with them through their mutual faith. This is a means of grace, right? Everything that God commands turns into a means of grace for our own blessing, for our own benefit. Just obey the Lord, trust him, serve him in faith and let the Lord do you good in that, right? When you begin to think to yourself that somehow the church has failed you, I don't get invited to fellowships like I think I should or these people aren't loving me the way that I feel as though I should be loved. Not having warm feelings anymore like I once had, then you get busy serving and loving this church and these people, right? We concluded the introduction then by noting Paul's obligation to serve. First, we took note of Paul's sense of obligation. Verse 14, Paul says, I am a debtor. I am a debtor. We're used to thinking of that word debtor as a financial term, being a debtor indebted to someone means that you owe them money, okay? However, I thought of more fully, the range of that word also includes someone who's under a sense of obligation. I'm indebted. A person who's under obligation is bound, bound to the payment of some price or bound to the rendering of some service to some course of action. He's duty bound to pay it, duty bound to perform it. Paul says, I am a debtor. We took note of Paul's submission under obligation from verse 13. He says that I do not want you to be unaware, brethren, that I often planned to come to you but was hindered until now. Paul says, I often planned, but I'm a man under submission. I'm a man under obligation. I go where the Lord directs. I often planned to come to you, but I've been hindered. I might have some fruit among you also just as among the other Gentiles. We noted God's sovereignty there over Paul's circumstances. We noted Paul's responsibility then in those circumstances to trust, to pray, and to obey. You wanna know how to be happy in Jesus? You trust, pray, and obey. Trust, pray, and obey. That's what Paul was doing. He is a man under obligation. Under obligation to the Lord and he is in submission to the Lord in his obligation. So are you and I. We are not the captain of our souls, right? The masters of our fate. We are not that. We are not our own. We are bought at a price. We are to glorify him in our decisions, in our actions. Here, Paul is doing just that. Now, next, we took note of the scope of his obligation. Also in verse 14, Paul says, I'm a debtor, both to Greeks and to barbarians, both to wise and unwise. Greeks representing those within the quote unquote, cultured boundaries of the Roman Empire, barbarians representing everyone else. It was at that time mostly that if you were in the Roman Empire, if you looked west, you saw culture. If you looked east, you saw dark uncultured, right? Not unlike the way that some view it even now. Today in our day and age, west is civilization, east is not. Back then it was Greeks and barbarians, right? Barbarians representing everyone else outside the Roman Empire, those not privileged to be within the boundaries of Greek culture, the Barbaros. And in the second pairing, Paul then refers to the wise and unwise. These are overlapping. To wise and unwise, Paul is referring to the learned and the unlearned, the privileged and the underprivileged, the advantaged and the disadvantaged. But notice, the scope of Paul's obligation doesn't end with Greeks and barbarians wise and unwise or lost Gentiles, verse 15. So as much as it's in me then, Paul says, I am ready to preach the gospel to you who are in Rome also. In other words, the gospel, the scope of Paul's obligation extends to believers, even believers with the gospel. Paul is obligated by the Lord to feed, to tend his flock, to feed his sheep. And you and I, we need to be constantly reminded of the glorious truths of our redemption. One of the ways in which you and I live day by day, week by week, year by year in the faith, is by continuously reminding ourselves of the great truths of our redemption. Continuously reminding ourselves of what God has done in Jesus Christ for us. The preaching of the gospel is a universal and a perpetual need. We'll be glorifying God for the gospel for the rest of eternity. This is our obligation, brothers and sisters, to preach the gospel. The Great Commission in Matthew chapter 28 alludes to that very thing, right? We are to go there for and make disciples. How do you make a disciple?  When they turn from their sin and put faith in Jesus Christ, they become a disciple. What are you to do then? Great commission, Matthew chapter 28. We are to teach then those, baptize them in the name of the Father, Son, and the Holy Spirit. In other words, bring them into the membership of the church and you teach those disciples. Not those infants that you sprinkled. You teach those disciples whom you've baptized. You teach those disciples to observe all things Jesus says that I have commanded. How do you do that? You preach the gospel to them. You continue to preach the gospel. Paul's sense of obligation, the scope of Paul's obligation. What is the substance of Paul's obligation? We've already talked about it. What Paul has been given, what has been committed to Paul's trust, what has been committed to our trust. What like Paul, we also are obligated to give to Greeks and barbarians and wise and unwise like the gospel of Jesus Christ. So having written a customary greeting that in general introduction to his letter, Paul now transitions to this primary theme, which is the subject of his letter. We see that in verses 16 and 17. The subject that will occupy his thought, his time in writing to them, will be the gospel of Jesus Christ and this letter gloriously filled with those gospel truths that we take great joy in looking at. Romans is essentially an exposition or an explanation of the gospel. In the statement of his theme, Paul builds an argument on a series of explanations. And I want you to see that. He starts in verse 15, as much as is in me, I am ready, I'm determined, resolved to preach the gospel to you who are in Rome also. Why these explanations each begin with that little preposition for, I think better translated because, for the sake of English, why are you ready to preach the gospel to those who are in Rome also? Paul says, because I am not ashamed of the gospel of Christ. Why, Paul, are you unashamed? Because the gospel is the power of God to salvation for everyone who believes, to the Jew first and also to the Greek. Why is the gospel, the power of God to salvation? Because in it, in the gospel, the righteousness of God is revealed from faith to faith, just as it is written, the just shall live by his faith. But why, why is then the righteousness of God revealed in the gospel? Because the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men. The word for ashamed in verse 16 doesn't speak of public shaming. The word refers to a personal, a private sense of disgrace. It refers to a feeling of embarrassment or of lost status. People are ashamed of the gospel. In the parable of the unjust steward from Luke 16, the steward said within himself, what shall I do? My master is taking the stewardship away from me. I cannot dig, I'm ashamed to beg. You and I can relate right to that kind of shame. Well, that kind of shame, Paul says, is a temptation even amongst believers in preaching the gospel. Paul is aware of the reality that believers will be tempted to be ashamed of the gospel. And that was happening in Rome because of how Rome treated Christian. There are two basic reasons for this shame, this temptation to shame. Two basic external reasons, two basic internal reasons. The two external reasons for this temptation to be ashamed of the gospel is one, because the world hates the gospel.  That was what was going on in Rome, right? In Rome, the Romans used to mock the Christians for being cannibals because they took the Lord's supper, eating of his flesh and drinking of his blood. They accused Christians in Rome of being atheists because Christians disavowed all the pantheon of Roman gods and said those gods were all fake. They didn't exist. And oh, by the way, we're not offering any kind of incense or applause to Caesar either. We believe in the one true and living God. And so they accused the Christians of being atheists.  Well, Paul was often shamed and he bore the marks of that in his back. Paul was beaten, left for dead in Lystra, right? He was shipwrecked in peril continuously. First Corinthians, or second Corinthians chapter 11. So Paul was often shamed, but Paul was never ashamed. And it's because of the gospel, it's the power of God of salvation for everyone who believes to the Jew first and also for the Greek. There are also two basic internal reasons for why believers are tempted to be ashamed of the gospel. One is a lack of faith or unbelief. The other is a lack of love. Faith strengthens us, right? The spirit of God through the means of faith strengthens his people, supplies them with holy spirit, wrought power and enabling empowerment. Second Timothy chapter one, verse eight. Paul exhorts Timothy in verse six. Listen to what he says to Timothy. Therefore I remind you to stir up the gift of God which is in you through the laying out of my hands for God has not given us Timothy a spirit of fear but of power and of love and of a sound mind. Those are fruits of the spirit. Therefore Timothy do not be ashamed of the testimony of our Lord nor of me his prisoner but share with me in the sufferings for the gospel according to the power of God. Not according to your own power but according to the power of God. Now, Paul invites us to share with him in this very same work, right? Paul as much as to Timothy here says to us do not be ashamed of the testimony of our Lord or of Paul his prisoner or of all those prisoners we just prayed for but share with us in the sufferings for the gospel not according to your own power but according to the power that is given to you by God through his spirit through the means of faith. And Paul reminds him then of the truths of the gospel that Timothy believes. It's God who has saved us. Call this with a holy calling not according to our works but according to his own purpose and grace which was given to us in Christ Jesus before time began. But now has been revealed by the appearing of our savior Jesus Christ who has abolished death, brought life and immortality to light through the gospel to which I was appointed a preacher and apostle and a teacher of the Gentiles. Paul says for this reason I also suffer these things. That message is worth suffering for. Do you see? The truth of the gospel. It is the power of God to salvation. It is worth suffering for. For this reason Paul says I also suffer these things. Nevertheless, I am not ashamed. Why Paul? For I know that's faith whom I have believed and I am persuaded faith that he is able to keep that which I've committed to him until that day. He tells Timothy, hold fast the pattern of sound words which you have heard from me in faith and love. Do you see? Which are in Christ Jesus. So Paul says, listen, I'm not ashamed. I'm not ashamed of the gospel. How could anyone be ashamed of the gospel? Right? What a testimony of our own sinfulness and waywardness when we ourselves become ashamed of the gospel. Paul said, I did not shrink back. I was not ashamed. Why? Three facts, three facts. The purpose of the gospel, the power of the gospel and the people of the gospel, the people to whom it is given. First, consider quickly the power or the purpose of the gospel, the purpose of the gospel. I'm not ashamed of the gospel of Christ. For the gospel is the power of God to salvation. We cannot be ashamed of the gospel of Christ brothers and sisters because it is a message of salvation. The word salvation presupposes damnation. The Greek word translated salvation in verse 16 refers to being delivered from harm, being delivered from danger, literally to be snatched by force from some peril or danger. That's what the word is referring to. In this case, we know what the harm is. Verse 18, the wrath of God is revealed from heaven. That's the harm. Apart from salvation, Jonathan Edwards describes the danger you're in. I recall this quote to your mind.   His wrath toward you burns like fire.  Listen, this is drawn from scripture, do you see? Like people today mock this notion of God. This is the God of the Bible. In his settled disposition against sin, ungodliness and unrighteousness, right?  He looks upon you as worthy of nothing else but to be cast into the fire. He is of purer eyes than to bear to have you in his sight.  You may ask yourself, you've not turned from your sin. You've not repented to put your faith in Jesus Christ.  The reason that he hasn't is because the Lord Jesus Christ died to redeem his people and we, he is gathering those together to himself for redemption. It's the only reason that God hasn't torn this whole place up even now. Because Jesus Christ has given himself for a people and that people is being redeemed. He is gathering his elect from four corners of the earth. That word salvation encompasses all that is necessary to redeem you, all that is necessary to reconcile you and restore you to a right relationship to God through the person and work of his own son, our Lord Jesus Christ rescuing you from the danger that you are in due to rebellion in your sin. The purpose of the gospel, second, the power of the gospel. The gospel is the power of God to salvation. One, the gospel is God's power through which he works in his power to save sinners. In other words, the gospel is not what God tells us to do so that we can grid it out in our own power to save ourselves, right? Jeremiah 13, 23, can the Ethiopian change his skin or the leopard change its spots? No. Then may you also do good who are accustomed to do evil? No. Man, it's powerless to overcome his own sinful nature. Self-help may change temporal habits but it cannot change the human heart and that which the law could not do in that it was weak through the flesh, God did by sending his own son in the likeness of sinful flesh so that the righteous requirement of the law might be fulfilled in us who do not walk according to the flesh but according to the spirit. So the gospel is God's power to salvation. Secondly, the gospel is God's power to salvation. Inherent to the gospel message is the power of an omnipotent God. That power alone, sufficient to save the chief of sinners.  Third then, note with me the people to whom the power of God and the gospel is directed. Paul says in verse 16, I am not ashamed of the gospel of Christ for it is the power of God to salvation for everyone who believes. Why would we be ashamed of the gospel? Everyone who believes will be saved. So preach the gospel and every one of them who will believe will be saved. Literally for everyone who is believing, present tense, Paul didn't have one gospel for the Jews, another gospel for the Gentiles, Paul had one gospel through which men are saved in believing. And there's no one outside the scope of that. It's for everyone who believes. Why is the gospel, the power of God to salvation for everyone who is believing? Because in it, the righteousness of God is revealed. Paul refers to that righteousness which belongs to God, God's own righteousness. It is that righteousness, the righteousness of God that is the possession of the one who believes. Amen, what an awesome blessing, an awesome gift. Richard Sibs, often think with thyself, what am I? I'm a poor, sinful creature. But I have a righteousness in Jesus Christ that answers all. I am weak in myself, but Christ is strong and I am strong in him. I am foolish in myself, but I am wise in him. What I want or lack in myself, I have in him. And that is great news, the greatest news. The greatest news you will ever, ever hear. It's the greatest news you'll ever hear, why? Because the wrath of God is revealed from heaven. The wrath of God revealed from heaven against all ungodliness and unrighteousness of men who continue to suppress the truth of God in their unrighteousness. More about that beginning next week. Paul begins this next section from chapter one, verse 18, through chapter three, verse 20, with a scathing, withering, searing, blistering indictment of human sin. And we'll be spending several months in that section of scripture dealing with that indictment of human sin. We must understand the very bad news, right? In order for us to comprehend and then apprehend the very good news. All praise, honor, and glory to be to God for the gospel. Amen, let's pray. Father in heaven, Lord, we praise you and thank you for the gospel, God. Thank you for condescending to save wretched sinners like us. Thank you for all that you have done. It's just absolutely amazing. It is rich with a depth that is incomprehensible, Lord. And we rejoice to be beneficiaries of your saving work unable certainly to save ourselves to even understand the faintest level, the depth of these glorious truths. But Lord, you've so lavished your grace upon us that having saved us, Lord, you've delivered us to this great salvation, this content of our faith, this understanding, this blessing by your spirit to now live in accord with these truths and to be blessed as worshipers of God and spirit and in truth for all eternity. So grateful to you, Lord. Grateful for our Lord Jesus Christ who went to the cross in our stead and died there in our place. We thank you for that. And thank you, Lord, for this blessing that we have now of considering these things. Help us, Lord, to understand. Help us to retain what we learn. Plant these things within our hearts and minds. Help us, Lord, to meditate on them, to consider them and to understand them and to apply them, to live according to them and to rejoice in them and to worship because of them, to praise you in response to them. We thank you, we love you. Be with us now as we go in Jesus' name, amen.