 So, today we were going to revise the concepts that we have already discussed in the energy economics course, we will apply these to an example. So, we have already discussed the cost of saved carbon and the cost of saved carbon we said that when we look at a renewable option, we will take the incremental annualized life cycle cost that means the annualized life cycle cost of the project minus the annualized life cycle cost of the base case, also we will calculate the annual carbon dioxide savings which will be the CO2 which will be there in the base case if you did not have any intervention and in the project we have some CO2 savings. So, the incremental annualized life cycle cost divided by the annual carbon dioxide savings will be the cost of saved carbon. So, let us take an example and calculate this for this example. So, we all across the country we have a large number of telecom towers and the cell phones and mobile phones are available in all areas including several remote areas. Amongst these telecom towers there are many locations where the electricity supply is not there, there is no electricity grid or even if the electricity grid is there, there are many disruptions or there is load shedding. So several of the telecom towers have a provision for backup power. So, this is a slightly old number about 5 or 6 years back we had about 425,000 towers in which we had 16.5 billion kilowatt hours of electricity and 5 billion litres of diesel being used. These numbers would have increased but just to give you a sense that this is an important end use where a reasonable amount of electricity and for the backup power diesel is being used. We will try and take an example of a particular telecom tower with a peak requirement of 5 kilowatt and an average requirement of 2 kilowatt. Average requirement of 2 kilowatt means throughout the day if we look at the average there will be a power rating will be 2 kilowatts and we are looking at continuous operation of the telecom tower. We want to consider the economics of 2 options. The first one is where we have a diesel engine generator and the second one is where we have a PV battery system. In both these cases we will presume that there is no grid supply and this is a standalone supply where it is going to meet the requirement. So this will be designed to meet the requirement of an average amount of 2 kilowatt. Now we are given the following data for both these options. Option A, if you have a diesel engine with a rating of 5 kilowatt the capital cost is rupees 1.7 lakhs. This is there in your tutorial sheet problem number 4, the life is 10 years, efficiency is 35 percent. The diesel price today is about 70 rupees per kg. We have the net calorific value of diesel roughly around 40 megajoules, 42 megajoules per kg and the composition of diesel has 86 percent carbon by weight. So all of this we will use and then there is a operational and maintenance cost in addition to the fuel cost which is a non-fuel O&M cost which is 30 paisa per kilowatt are generated. So we will again use this in terms of making the calculation. This is for option A which is diesel engine generator and so the engine generator will be using diesel and depending on the load it will be operating at a particular rating. The second option is where we have a PV battery system. We have a PV system and please note here that the peak rating of the PV system is 12 kilowatt when we actually need an average of 2 kilowatt. Please remember that we are using 2 kilowatts on an average for 24 hours for the solar energy and the generation is going to be only available during the sunshine hours. So that is why you have this kind of rating. The cost of 12 kilowatts of modules at present prices is of the order of about 6.5 lakhs. We will take the module life at 25 years. We have also planned to have in order to provide the requirement of the telecom towers throughout the day. We are going to provide batteries and we said that 2 kilowatts into 24 hours means 48 kilowatt hours. So we planned for one day autonomy that means for one day if there is no sunshine and no generation the battery should be able to provide the requirement. So we are looking at a battery rating of about 50 kilowatt hour and an average cost of about 4.5 lakhs with a life of 5 years. We also have a balance of system and that balance of system is this will be like your maximum power point tracker, your power electronics and your controllers. The balance of system life is typically of the order of about 10 years. We are taking a cost of about rupees 2.5 lakhs and the ONM cost for the PV system there is no fuel cost for PV because the solar is free, solar insulation is available and we are looking at an ONM cost of about 25 paisa per kilowatt hour slightly lower than the non-fuel ONM for the diesel but almost of a similar nature. So for this what has been asked is we are supposed to first calculate what is the simple payback period for the incremental investment in B and then using a discount rate of 30 percent compute the cost of electricity generated in both cases which one would we prefer would the PV project be eligible for carbon credits and then compute the amount of annual carbon dioxide saved what is the cost of saved carbon for B compared to A and if the discount rate is instead of 30 percent if it is 10 percent how does it affect the results. So let us start with this problem, let us start with option A, option A is a diesel engine generator DG and it is given to you that the capital cost is, capital cost is rupees 1.7 lakhs. So the capital cost is 1.7 lakhs for the diesel engine generator as compared to this let us look at the capital cost for option B. So option B has 3 components, there are the PV modules with a capital cost of rupees 6.5 lakhs. We have the battery and in most of the PV battery systems you will find lead acid batteries some of the recent ones you may find that we are using lithium ion batteries. So in the case of batteries we are talking of rupees 4.5 lakhs for the batteries and the balance of system all the power electronics we are saying this is rupees 3 lakhs. So let us just add this up, this is coming to rupees 14 lakhs. So you should note that the capital cost in case B is 14 lakhs as compared to 1.7 lakhs for the case A. So what is the difference, what is the incremental investment, incremental capital cost, incremental capital cost, this is going to be rupees 14-1.7 lakhs and that is thing but 12.3 lakhs. So keep this in mind and let us now calculate what is the difference in the annual cost. So in the case of A for the DGE system let us first find out for both these cases what is the kind of annual generation. So annual generation is 2 kilowatt per hour that means in an hour 2 kilowatt hour into 24 hours in a day into 365 since this is the average and this is nothing but 2 into 8760 is 17520 kilowatt hours. Now in order to meet 17520 kilowatt hour in the case of the diesel engine we are using diesel we are firing diesel in the engine we want to find out how much diesel are we using. So the output that we have is 17520 kilowatt hour 1 kilowatt hour is 1 kilowatt is kilojoules per second into 60 seconds per minute into 60 minutes per hour which means into 3600 that is 3600 kilojoules. This is the required output in kilojoules divide this by the efficiency of the diesel engine which is given to us as 35 percent so 0.35. Now this is the energy input in kilojoules. Now remember every kg of diesel that we are talking of has a net calorific value of 42 megajoules 42 megajoules means 42 into 10 raise to 3 42,000 kilojoules. So now this is in kg of diesel you can calculate this and you will find that this turns out to be 4291 kg of diesel per year. So once we get this now we know how much we have given that the price of diesel is 70 rupees. So we just take the annual fuel cost is 70 into 4291 approximately equal to rupees 3 lakhs. So if we now look at this in terms of the, in the case of what about the annual ONM cost we said the annual ONM non-fuel ONM is 30 paisa per kilowatt hour. So this is 0.3 into total of 17520 kilowatt hour which is generated and this turns out to be rupees 5250. So it is actually very small the total annual cost annual fuel plus ONM total annual cost is just instead of 3 lakhs now it becomes rupees 3.05 lakhs. In the case of in the second case where we are looking at the PV what is the fuel cost the fuel cost is 0 because we do not have to pay for the solar insulation. So that entire annual fuel cost is saved there is an annual ONM cost in case of B and that we can calculate annual ONM cost is nothing but 0.25 rupees per kilowatt hour into 17520 and this turns out to be rupees 4380. So the annual savings which we have if we opt for PV battery is the difference in these two cost that is difference between 3.05 lakhs and this is 0.04 lakhs. So the annual savings is rupees 3.01 lakhs. So now we can calculate straight away what is the simple payback period. Simple payback period and this is just going to be the incremental investment which was 12.3 lakhs divided by 3.01 lakhs which turns out to be approximately 4.1 year okay. Now depending on the company as we had said if you look at the company which has a payback period of 3 years or so then this is not viable. Now of course in such a case we will not just look at the simple payback period we will look at the other indices. We have also been asked to now calculate what is the cost of electricity generated in both the cases. So let us for this cost of electricity generated we will use the annualized life cycle cost. So when we look at annualized life cycle cost let us first calculate annualized life cycle cost for option A okay. We are given that discount rate is 30%. So let us first see what is the annualized capital cost, annualized capital cost for the diesel engine. This is going to be 1.7 into CRF, discount rate is 30%, life is 10 years. So this is 1.7 as per the formula that we had, 1.3 raise to 10, 1.3 raise to 10 minus 1, 1.7 into 0.323, this comes out to be rupees 0.549 lakhs right. This is the annualized capital cost and we have already calculated what is the annual fuel cost and annual O and M cost that turns out to be 3.05 so the total annualized life cycle cost is 0.549 plus 3.0 we had seen this was 3.0 plus 0.05. So you see these components you can see the relative magnitudes, this is the annualized capital cost, this is the annualized fuel cost, this is the annual fuel cost, this is the non-fuel O and M cost and this is the annualized capital cost, annualized capital. So you can see in the case of the diesel engine it is the fuel cost, the diesel cost which is predominating, the capital is relatively low and overall we are looking at the total cost that we are now looking at is 3.6 lakhs, this is the annualized life cycle cost. Now the cost of generated electricity that we have will be taking cost of generated electricity, we take the annualized life cycle cost ALCCA by the annual electricity generation, electricity generated per year. So this is going to be 3.6 lakhs, 3.6 into 10 raised to 5 divided by 17520 and what will be the units, this is going to be rupees per kilowatt hour. When you put this and calculate you will find that this is rupees 20.54 per kilowatt hour, this is the cost that we are getting for generating electricity from diesel. Now is this reasonable, we can try and see, this is higher than the price at which we get electricity from the grid which is reasonable because otherwise instead of your power plants we would actually just have diesel engines. And we have a rating of a diesel engine, the diesel price is high. So this is higher than the price at which you get grid electricity and that is why you prefer grid electricity to diesel power but if you have no other option and you have an isolated system then this is a system which has low capital cost but high running cost because of the diesel price. So now let us keep this in mind and go ahead and calculate for case B. In case B we have when we talk about the ALCC, again this ALCC will have here 2 components annualized capital cost, capital cost plus annual ONM cost, there is no fuel cost here. So in the case of annualized capital cost, we have 3 components here and remember these 3 components have different lives. So because of that when we take the capital and annualize it they will have different capital recovery factors that we are going to use. So this will be equal to CpV which is the capital cost for the PV into capital recovery factor, discount rate is 0.3 and the PV module life is 25 years. So this is this plus C battery, CRF 0.3 but battery life is less than the life of the panels or the life of the power electronics. So this is the 5 years and see this is the advantage that we have when we use an annualized capital life cycle cost method because we can actually just simply add up the annualized capital cost for different components which have different lives and it just means that the capital recovery factors we use are going to be different. And then the third component which is C balance of system into capital recovery factor 0.3 and 10. So now let us calculate these capital recovery factors, CRF 0.325 is 0.3 into 1.3 raise to 25 divided by 1.3 raise to 25 minus 1 and this turns out to be approximately 0.3. Then CRF 0.35 and this is going to be the highest value, this is going to be 0.3 into 1.3 raise to 5 divided by 1.3 raise to 5 minus 1 and that turns out to be 0.41 and CRF 0.310 is something we have already calculated in our earlier examples, this is 0.323. So you see the lowest value is where the life is highest 0.3 in 0.310 years it is 0.323 if it is only 5 years it means the capital recovery factor is higher. Now let us use these and plug in the values to get the final value of the annualized capital cost. Annualized capital cost is going to be we have to calculate this in lakhs 6.5 lakhs into 0.3 plus 4.5 lakhs into 0.41 plus 3 lakhs into 0.323. So this comes out to be 1.95 plus 1.5 you can check these numbers there may be some rounding of issues 0.97 and this turns out to be 4.769 lakhs to this. So when you look at the ALCC we will add 4.769 plus what we had calculated which was 4400 something of that sort 4380 but we can just take it as 0.044. So it comes out to be 4.81 rupees lakhs that is the ALCC. Now let us calculate the cost of generated electricity. So just similar to cost of generated electricity for case B generated electricity let us calculate this will be 4.81 into 10 raise to 5 because it is lakhs divided by 17,520 and the units as we said was rupees per kilowatt hour. When we do this we get rupees 27.47 per kilowatt hour ALCC B turns out is ALCC B turns out to be greater than ALCC A cost of electricity for B turns out to be greater than that for A. So with a discount rate of 30% this means that the company will not opt for solar PV. Now let us calculate what happens when we look at if we have do we get carbon dioxide savings and if we get carbon dioxide savings would it be eligible for carbon credits. So generally what happens is in the case of PV there is some CO2 emissions because of the embodied materials. If you look at the silicon or you look at the glass and you look at the kind of energy used and the kind of CO2 which has come in in making that material we can make that calculation but typically these values are relatively less. So it turns out to be 20, 30 grams per kilowatt hour for our purpose for our calculation we can neglect it and say that all the CO2 there is it is like negligible and we will just take whatever is the CO2 that is being saved because we are not using diesel is the kind of CO2 saving which is obtained. So let us calculate now how much CO2 we are saving. So we have we want to calculate what is the annual CO2 emissions in A in case A. Case A uses diesel and we have calculated already the amount of diesel that we are using we are using 4291 kgs of diesel per year. So this will involve we know also that 4291 kgs each kg of diesel has 86 percent carbon. So this is 0.8 into 0.86 you get 3690 kgs of carbon annually are being burned. Now we know that C the basic stoichiometry C plus O2 giving us CO2 which means 12 kgs gives 44 kgs. So if we want to calculate how much CO2 we are getting by annually from the diesel we can see that this will be 3690 into 44 by 12 is the CO2 emissions annually in option A. So this turns out to be if we do the calculation you will find that this is 13,531 kgs of CO2. In option B we are saving this much amount of CO2. So the incremental cost that we have now if we are looking at the cost of saved carbon if you remember we talked of that as the ALCC with the project that means ALCC of B minus ALCC of A divided by the CO2 emissions of A minus CO2 emissions of B. We will assume that the CO2 emissions of B is negligible if we have that value we can add it up this will be typically of the order of 20, 30 grams per kilowatt hour so it is relatively small. So this is going to be now 4.81 minus 3.05 that is the incremental capital cost into 10 raised to 5 divided by 13,531 and what are the units this is rupees per kg of CO2 saved that is why it is called the cost of saved carbon. And if you see this this comes out to be 1.76 lakhs is incremental divided by 13,531 that comes to rupees 13 per kg of CO2 often when we talk in terms of carbon savings and carbon the cost of saved carbon we usually talk in terms of certified emission reduction 1 certified emission reduction or CER is 1 ton of CO2 saved. So let us calculate you can just take this this is per kg we can make it per ton it will be 13,000 rupees per ton of CO2 saved annually and if you convert this to US dollars this divided by 70 you will get this as about 186 US dollars per ton. And you can compare that with the carbon credits of the carbon price you find the carbon price is actually much much lower this is a relatively high value. So this gives us an idea that at these costs with the cost number that we have said if the company has a discount rate of 30% it would not be viable it would not prefer to go for the PV option of course if it has an incentive in terms of carbon credit and that carbon credit is priced then it might happen. Let us also do we had also said that what if the it is a public sector company or it has an access to a fund green fund where the interest rate is lower and we can look at it as a situation where we are talking of a discount rate not of 30% but a much lower discount rate of 30% 10%. So if the discount rate is 10% case A economics remains the case A also the economics will change but let us look at what will happen in terms of case B. Case B we will have the CRFs which will change CRF 0.125 is you can calculate this and this will turn out to be 0.1 into 1.1 raise to 25, 1.1 raise to 25 minus 1 this is just about 0.11 CRF 0.15 again in a similar fashion we can make the calculation is 0.1, 1.1 raise to 5, 1.1 raise to 5 minus 1 if you calculate it you will get it as 0.264 CRF 0.110 and this comes out to be 0.1627. So now your ALCC for B turns out to be 6.5 into 0.11 plus 4.5 into 0.264 plus 3 into 0.1627 and this turns out to be 2.39 lakhs and to add to that the ONM of which is 0.44. So we are talking of 2.43 lakhs. The cost of generated electricity now is 2.43 into 10 raise to 5 by 17520 and this turns out to be 13.87 rupees per kilowatt hour. This is of course much cheaper than the option B when we calculated for 30% it also happens to be cheaper than option A but of course please remember that option A economics also changes because now the discount rate is 10%. So the capital cost that we had calculated earlier for the diesel engine that will also change. So now the ALCC for option A will become 1.7 into CRF 0.110 which is 0.1627 plus the other values that we had 3 plus 0.05. So instead of the value here we will get a lower value but even then this ALCC now ALCCB turns out to be less than ALCCA. So the interesting thing is that now in this particular case PV is more viable than the diesel engine generator and this is because we have a lower cost of capital, we have a lower discount rate and so with this we can sum up. We have looked at the way in which we can do the economic calculations and we have then also taken an example by which we have shown how we can calculate the annualized life cycle cost and the effect we can compare both the options and select that option which has a lower ALCC. This decision for the telecom towers we found that at a discount rate of 30% it is preferable to go for diesel engine generators and that is why you see mostly it is diesel engine generators across the country relatively low in terms of capital, convenient in terms of usage but not good in terms of emissions. We then also calculated what are the CO2 emissions which are coming based on that option and then seen the difference in that cost divided it by the emissions and calculated the cost of safe carbon. So with this we can actually get the curve that we showed for different options how much what is the cost per ton of CO2 that we are saving. We also saw that if the discount rate is lower then it is possible the company would be interested in making that additional investment and it is viable to go for the PV battery systems. So you can try out the other tutorial problems and see that you can use the different kinds of indices when you have different components in a system with different lives. Life cycle cost is a convenient way of doing the calculation. Thank you.