 Welcome to class 30 on topics in power electronics and distributed generation. Last class we were talking about discussing a couple of problems related to distribution systems issues. Today we will discuss a couple of problems related to DG design decisions based on economic implications. So, in the first problem we are looking at 1.6 megawatt facility consisting of 800 kilowatts of critical loads and non critical loads. The non critical loads are split into electrical and thermal. The electrical loads balance is 600 kilowatts and there is 1 megawatt of thermal load and the facility is connected to the PCC through a main circuit breaker. This particular plant experiences 40 major outages per year and each outage lasts about 20 minutes. The plant is expected to run 365 days a year, 24 hours a day and the cost of electricity for this particular plant is 8 rupees per kilowatt hour 8 units rupees per unit. And we are told the cost of the DG is 5000 rupees per kilowatt standard diesel generator set and the size of this DG if it is supposed to meet some particular critical load is size to be about 1.2 times larger than the load. And we are also told that the installation cost is 20 percent of capital cost. So, it might be commissioning and installation and there is an annual maintenance cost for the DG and that is 10 percent of the capital cost. So, this is the overall system and in the first part we are told that the overall cost of outage has been calculated for each of these 40 major outages to be rupees 100 into 10 to the power of 3 per outage 1 lakh rupees per outage and the DG is sized only to serve the critical load. And because of the outage of the non critical load there is a residual cost of 20,000 rupees per outage due to the unserved non critical loads. And you are asked to calculate the range of simple payback for installing the DG ignoring fuel cost. So, if you look at the sizing of the system we have the critical load to be 800 kilowatts the non critical load consisting of electrical and thermal the electrical part is 600 kilowatts and the thermal load is 1 megawatt. And you can see that the thermal load is being fed electrically. So, whatever thermal load is present we are assuming it is being obtained by the consumption of electricity. So, the total load non critical load is 1.6 megawatt and you add the critical load to it. So, just overall facility input is 2.4 megawatts. So, you can calculate what would be the cost of the investment the investment cost would be 800 kilowatts for the DG power. So, you have 800 kilowatts times 1.2 which is the factor we want as a margin. So, you need a DG of size 960 kilowatts and the cost assuming 5000 rupees per kilowatt. So, this translates into 48 into 10 to the power of 5 rupees the installation and commissioning cost is 20 percent of that. So, that comes up to 9.6 into 10 to the power of 5 and if you look at the cost of the outage we have outages per year 40 per year and the cost of the outages is 100000 per outage and because of the unserved non critical loads you have 20000 rupees which you do not actually benefit by having the DG and 40 per year. So, this turns out to be 32 into 10 to the power of 5. If you look at the operation and maintenance cost this is 10 percent of the capital cost because it is a cost rather than a benefit it is put with a negative sign. So, if you look at the total out go your cost of the DG plus in commissioning and installation is 57.6 into 10 to the power of 5 your annual returns is 32 minus 4.8. So, 27.2 into 10 to the power of 5. So, your payback period is into 12 months. So, this turns out to be 25.4 months. So, this is slightly larger than 2 years. So, you pay for your generator which supports your critical loads and you expect it to break even in about little bit more than 2 years. So, here we have not looked at the cost of the fuel for running this particular generator set. So, in the next question you are asked you are given the data that if diesel cost 50 rupees per litre and the energy content of 1 litre of diesel is 36 into 10 to the power of 6 36 mega joules per litre and the fuel to electricity conversion efficiency is the 32.98 percent what how would it affect your payback calculations. So, if you look at the conversion of fuel into electricity we know that our electrical load is 800 kilowatts and there are 20 minutes of outage. So, converting it into hours 20 by 60 and there are 40 outages per year. So, the units of electricity required is 10667 kilowatts of energy required per year and you are told the efficiency of conversion from your input to output is 32.9 your efficiency and this is your output energy requirement. So, your input turns out to be 32343 units and converting from kilowatts to joules this turns out to be 1.16 into 10 to the power of 11 joules and you know that your fuel cost is 50 rupees per litre and there are 36 mega joules per litre. So, your fuel consumption per year is your E n divided by 36 into 10 to the power of 6. So, this turns out to be about 3200 litres and at 50 rupees per litre this turns out to be about 1.6 lakhs. So, rupees 1.6 lakhs. So, the net annual benefits would reduce because you have to pay for your fuel. So, if you look at the new annual benefits you now take an additional reduction because of the fuel. So, if you look at compared to the capital cost say 40 outages per year and 20 minutes per outage that roughly works out to be about 12 hours per year half a day a year. So, with half a day per year you are talking about 3 percent of capital cost is your cost of the fuel it does not change your numbers by a large amount. Your new payback period is this now. So, this is 27 months. So, you are talking about a two month difference when you are between the calculations ignoring fuel while and while considering fuel, but you need to keep in mind this is for a very short duration of energy outage considered. So, if you consider outages of couple of days a year instead of 3 percent you may be talking about 5 percent or 10 percent, but still that is not too large a number to alter your payback period significantly if you are using your genset only for backup of small loads. Whereas, if we will look at the later questions which are considering not just running it during the outage duration, but it is running for substantially longer period. So, in case your outage duration is half a day you have on it you have outage on a daily basis and it is 12 hours a day then this number can rise quite significantly. So, in the next problem you are asked instead of just backing up your critical loads if you make have a much larger DG which covers both your critical and not critical loads for the facility assuming the DG ratings, initial cost, maintenance or scale with the power requirement what would be the new DG sizing and also what would be the fuel consumption corresponding to this larger sized DG unit. So, if you now look at larger sized DG, so with the larger sized DG you can completely eliminate all penalties of not operating any part of your plant. So, you can actually operate your full plant. So, your PDG is now 1.2 times 2400 kilowatts. So, you are talking about 2.88 megawatt DG and if you look at now your simple payback period because of your larger DG your capital cost is much higher. So, it was originally it was 48, so it is gone up to 144. You can see that correspondingly your installation cost has also gone up. Your power quality benefits which was originally 32 into 10 power of 5 now goes up to 40 because you do not get too much additional benefit of backing up non-critical loads. So, your net investment has gone up to 172 about 173 into 10 power of 5 and your benefits is about 25.6 into 10 power of 5. So, your new payback period is 81 months. So, instead of the 2 years we had it is about close to 7 years that you would have in this case. So, it does not make sense to actually oversize your generator to meet the non-critical loads. That is essentially why many times when you install a DG it would be good for you to separate out your wiring into what is important and what is not critical. So, the next part is to look at the fuel consumption. So, the fuel consumption we will use. So, your energy out is again 40 outages 20 minutes duration. So, this is 32 into 10 power of 3 kilowatt hours. So, your energy in using the same efficiency number is 970 to 8 kilowatt hours and this corresponds to 3.4 9 into 10 power of 11 joules and again using the joules per liter to. So, this corresponds to a consumption of about 9700 liters per year and this would correspond to 48 4.8 into 10 power of 5 rupees per year at 50 rupees per liter. So, if you look at your net returns your net returns now reduced by this 4.8 into 10 power of 5. So, your total returns reduced to a smaller number and your payback period is now about 100 months or about 8 years. So, you can see that if you now start considering fuel cost with a much larger facility your fuel consumption is going to go up. So, that also adds on to your penalty on your system which reduces now from 7 years to almost 8 years it has increased your payback period. So, it may not make sense from a payback point of view to implement such a scheme. So, in the next problem we are looking at the cost of energy. So, we are going back to the DG that is sized only to meet the critical load rather than the entire plant. However, instead of just running it during the outage we are looking at running it at full power and we know the cost of the fuel and the energy content what would be the annual diesel consumption and what would be the cost of energy from the plant assuming a fixed charge rate of 10 percent per year on capital cost. So, essentially the assumption is that your capital is being purchased based on some loan from may be a bank and you are paying back 10 percent of that particular loan as payment to the bank on an annual basis. So, if you look at the calculations in this case your DG cost is rupees 48 into 10 power of 5 from the previous calculation the installation and commissioning is 20 percent. So, 9.6 into 10 power of 5. So, the total sum of this is 57.6 into 10 power of 5 rupees per year rupees and your operation and maintenance cost is rupees 10 percent of your DG your equipment cost. So, this is 4.8 into 10 power of 5 per year and if you look at your annual fuel consumption. So, again assuming you operate it like the plant 365 days a year you have the rating of the of the gen set is 9.6 T the efficiency of input to output is 32.98 and kilowatts. So, 10 to the power of 3 3600 minutes per hour into 24 hours 365 days and the energy content per liter is 36 into 10 power of 6. So, this gives you the liters of fuel consumption per year. So, this is 2.55 into 10 to the power of 6 liters per year. So, at 50 rupees per liter this would correspond to rupees 1275 into 10 to the power of 5 per year. If you look at the energy being produced from this particular generator your annual energy production is 960 kilowatts into 24 into 365. So, this is 8.4 into 10 power of 6 kilowatts. So, now with this data you can actually calculate your cost. So, your cost of the capital was 57.6 into 10 to the power of 5. So, this is 10 percent is your fixed charge rate. So, you get 5.76 your operation and maintenance cost is 4.8 into 10 to the power of 5 and your fuel cost is 272 or 1275 into 10 to the power of 6. So, if you look at the cost of capital that was 57.6. So, this is about 20 more than 20 times the capital cost. So, you can see that if you are running this plant on a continuous basis you are dominated by the cost of the fuel. The cost of your initial equipment is actually much smaller your energy production was calculated into 84 into 10 to the power of 5. So, the cost of energy this works out to be rupees 15.29 per kilowatt hour and we saw that the cost of energy from the grid was 8 rupees per kilowatt hour. So, what you just generate from the gen set is much more expensive it would not make sense to just run the gen set all the time. So, you can see that the fuel cost in the case when you are running it just for a day a year is probably in the range of 10 percent, but here this is actually 22 times your capital cost. So, depending on the number of days per year usage on your gen set you can end up with a substantial cost as fuel. So, in this case you can say to decide on whether to upgrade this particular generator from just a generating electricity to combined heat and power. So, CHP unit so that the waste heat from the generator is used to provide for the thermal load. So, you need to add some heat recovery equipment to this particular generator and we calculate that the efficiency from your fuel input to thermal output is about 45 percent which is fairly good. The cost of the thermal system including heat exchangers is again 3500 rupees per kilowatt thermal load requirement and the installation cost is again 20 percent of the capital cost. And we will assume that the operation of maintenance is also the same 10 percent of the capital cost. What is the cost of energy for the CHP DG under three conditions one when it is running at its rated power level which is 960 kilowatts. The second when it is running at a lower power at 800 kilowatts. The third when it is running in such a manner that the output thermal power is matched and whatever is being generated electrically is just being put out to the grid. And we want to see which of these cases leads to lowest cost of energy. So, in the first case we will first look at the cost of the CHP DG the cost of the thermal system there is 1000 kilowatts of thermal load and it is 3500 rupees per kilowatt thermal. So, this turns out to be 35 into 10 power of 5. So, your total cost considering installation is 20 percent of that. So, that turns out to be 7 into 10 power of 5 and your equipment cost is 42 from your electrical system or 42 from your thermal system plus 57.6 from your electrical system that you had previously calculated. So, this is rupees 99 and your operation and maintenance cost is 10 percent of your capital cost without the installation. So, this turns out to be rupees 8.3 into 10 power of 5 rupees per year. And the cost of energy from the grid is 8 rupees per kilowatt hour and your efficiency thermal is from fuel to thermal is 45 percent. So, when your thermal output is at P electrical being 960 kilowatts. So, your input power coming in is 960 by your electrical efficiency which is 32.98 this is the input power times 0.45 is your thermal power thermal output. So, this turns out to be 1310 kilowatts. So, out of which your load in the facility will consume 1000 kilowatts and the remaining 310 goes as waste. So, because now your facility is being fed from your from your DG Genset rather than previously it was being consumed from your point of common coupling electrically you now have thermal savings. So, you can calculate your thermal savings per year is 1000 kilowatts into 24 hours per day 365 days per year and 8 rupees per kilowatt hour. So, this turns out to be 700 into 10 power of 5 rupees per year. So, if you look at now your calculations your annual payment of for capital we saw the capital was 99.6. So, this is 10 percent of that which is your annual payment your operation and maintenance is 8.3 into 10 to the power of 5 your fuel cost which we calculated in the last problem was 125 1275 into 10 to the power of 5, but now you have benefits because you are not consuming electricity for your thermal loads your annual energy production stays 84 into 10 to the power of 5 units. So, your cost of energy can now be expressed by this which turns out to be equal to 7.06 rupees per kilowatt hour. So, you can see that now you have a number which is less than 8. So, it starts making sense to see whether you can actually run it because the cost is less than what your service provider is providing you which is 8 rupees per kilowatt hour. So, we will look at the next case where the DG is run instead of at 960 kilowatts at a lower power rating if the DG is run at 800 kilowatts your thermal output is 800 divided by 32.998 which is your efficiency electrical efficiency 0.45 is the efficiency from input to thermal output. So, this is 1092 again your thermal load is 1 megawatts. So, you 92 kilowatts goes out as a loss your annual energy production we can just scale it from the previous number the previous number was 84 into 10 to the power of 5 that was when it was running at 960 kilowatts, but now it is being run at 800 kilowatts. So, this is 7.01 into 10 to the power of 6 kilowatts. Because this is now equal to 1092 your thermal savings is still the same number as calculated previously. So, your cost of energy in the second case in the new case when it is running at 800 kilowatts your annual payment stays the same your maintenance stays the same which is what we are assuming, but now your fuel cost has come down because it is running at lower power your heating benefits stays the same because you anyway are generating excess heat which meets your facility requirement your annual energy production has come down from 84 to 70 into 10 to the power of 5 units. So, if you look at the cost of energy in this particular case this turns out to be rupees 5.42 per kilowatt hour. So, you can see that the costs are coming down and then your asked in part 3 what would be the cost if your operating such that your thermal load is just being met. So, the thermal load is 100 kilowatts then you can calculate what would be your corresponding electrical output. So, this is 1000 kilowatt thermal your thermal efficiency is 0.45 your electrical efficiency is 32.98 percent. So, this turns out to be 733 kilowatts and again you can scale your annual energy production. So, with this you can also look at your fuel cost annual fuel cost which can also be scaled was 1275 into 10 to the power of 5 into 733 divided by 960. So, with this information you can again go back and calculate your cost of energy. So, your capital cost stays the same operation and maintenance has stayed the same your fuel cost has come down further your heating benefit is just sufficient to match your load requirement which still stays at 700 into 10 to the power of 5 your energy production has gone down. So, if you do the overall the calculations this turns out to be equal to rupees 4.53 per kilowatt hour. So, you can see that the cost of electricity has come down substantially from the 8 number. However, that depends critically on the fuel cost which is a big number over here. So, if the fuel cost fluctuates quite a lot then the cost of energy would also tend to jump quite a bit. So, you if you now take your power level further down you will see that your energy production goes down your thermal benefits would also go down and your cost of the fuel would just go down proportionately. So, again if you go below this particular point you will see that your cost of energy starts going back up. So, your typical combined heat and power systems are run. So, that your thermal loads are matched and whatever you generate as electricity is actually a byproduct of the end of the process. So, in the next problem you are told that there are couple of options for now connecting this particular genset to the electrical grid or to electrical loads when the grid is not available. One is using the a fixed speed synchronous machine and that is typically the way most diesel generator sets operate you have a internal combustion engine followed by a synchronous machine which whose output is connected to loads. So, because your output frequency is 50 hertz your electrical frequency requirement is 50 hertz the rpm of the of your IC engine is determined essentially by your frequency requirement of your electrical load. So, the speed in that particular case is fixed. The second option is to actually connect make the IC engine operate at variable speed and whatever electrical output is generated by your speed is the IC engine that is running you run it to variable speed generator the variable speed generator might consist of may be a permanent magnet generator followed by inverter which means that the inverter can produce 50 hertz irrespective of the frequency of your IC engine. So, essentially we are looking at a variable speed generator versus a fixed speed generator and the effective electrical efficiency of the VSG option is 35.15 percent which is higher than the 32.9 percent that we considered for the fixed speed generator. The capital cost of the variable speed gen set is 10000 rupees per kilowatt. So, higher much higher than the fixed speed generator. Using the assumptions that the DG is running to match the thermal load which is the best operating point we like to do a comparison between the cost of energy when you are running with a variable speed generator and with a fixed speed generator. So, if you look at the configuration of the fixed speed versus a variable speed can see that from the mechanical from the fuel to thermal point of view your efficiency is same your synchronous machine by itself can have a higher efficiency in this particular case you have a PM generator plus a high efficiency inverter. However, its overall efficiency might actually be lower than just a simple single stage synchronous machine, but because you are able to operate at variable speed you can operate at the maximum efficiency point of your IC engine. So, your efficiency of the IC engine goes from 34 percent to 33 percent your efficiency of your electrical interface comes down, but you get a bigger boost coming from your IC engine now being operating at its optimum point. So, if you look at the structure of this particular system use of variable speed. So, you get a higher efficiency from your P N T R thermal is 45 percent T R electrical output is 35.15. So, you can calculate the cost of capital for this DG system with the combined heat and power unit. So, capital cost is 960 kilowatt electrical into 10 the power of 4 10,000 rupees per kilowatt R plus your thermal load is 1000 kilowatts into 3500 rupees per kilowatt cost of the heat exchangers. So, this would be the cost of your capital equipment 131 into 10 power of 5 20 percent for installation, installation plus commissioning might be 20 percent that works out to 26 into 10 power of 5. So, your overall total capital plus installation is rupees 157.2 into 10 power of 5 your operation and maintenance cost on an annual basis is 10 percent of the equipment cost. So, that is 9.6 into 10 power of 5 plus 13.1 into 10 power of 5. So, because you are operating your DG in the thermal tracking mode your output electrical power is your thermal requirement is 1000 kilowatts your thermal efficiency is 0.45, but now your electrical efficiency has gone up 35.15 percent. So, your thermal output your electrical output is now 781 kilowatts. So, it has gone up from 733 to 781 your annual energy production is again you could scale it kilowatt 6.84 into 10 power of 6 kilowatt hours per year and your annual fuel cost stays at 973 into 10 power of 5 rupees per year, because your thermal requirement stays the same. So, you could then calculate your cost of energy. So, your 10 percent of your capital 15.72 into 10 power of 5 your operation and maintenance cost 13.1 into 10 power of 5 your annual fuel cost stays the same, because your thermal load has to be satisfied your heating benefits is 700 into 10 power of 5 your annual energy production has gone up a bit, because your your electrical output has gone up from 733 to 784. So, if you look at now your overall cost of energy you get an expression 9.96. So, essentially the sum of these two amounts. So, this calculates out to be equal to rupees 4.4 per kilowatt hour. So, you can see that there is a further reduction in cost of energy if you by going into the variable speed option. However, your capital cost has gone up. So, if you are willing to have access to the higher capital then potentially your cost of energy can be brought down further by looking at a variable speed option compared to a fixed speed option when you are considering a system which is running continuously for a long duration of time. So, in the next problem you are asked to look at a net present value or the effective initial cost calculations not for the entire system, but only for the electrical part of the system. So, essentially whatever is contained in this particular block we are looking at the net present value again from a design perspective someone who might be coming in might be looking at different subsystems. So, if someone is interested in looking at what sort of inverter or what sort of generator what is acceptable you want to look at a particular subsystem and make a decision. So, for the effective initial cost calculation you are given this is the system that comes from the shaft of your IC engine to the AC electrical output and the data that is given to you is that the DG capital cost is 5000 rupees per kilowatt consists of two parts 2500 rupees per kilowatt for the IC engine and 2500 rupees per kilowatt for your synchronous machine. The efficiency of 32.98 can be considered of to be 34 percent for the IC engine and 97 percent for your synchronous machine and for the variable speed gen set the capital cost is 10000 rupees per kilowatt again consisting of 25 rupees 2500 rupees per kilowatt for the IC engine and 7500 for per kilowatt for your PM machine and again the efficiency of 35.1 percent can be considered to be 37 percent from the IC engine because it is operating at a more efficient operating point and your inverter is now at a lower efficiency of 95 percent and a few factors that are being considered that you can get a benefit for the IC engine because it is able to operate at variable speed often engines have once they go up to its best operating point have a flat torque versus speed characteristics. So, you could operate at a slightly higher speed and get a benefit say of 20 percent and the output power is required is 100 kilowatts. So, the system that you are designing is 100 kilowatts operating on a continuous basis 365 days a year. You are looking at a effective interest rate of 5 percent a product life of 5 years and cost of energy to be 8 rupees per kilowatt hour. So, we want to installation cost is ignored for the effective initial cost calculation O and M cost of both configurations are assumed to be similar and calculate the effective initial cost or the net present cost including electrical efficiency fuel considerations and sizing of the engine. So, for doing this calculation we will we will we can actually look at each particular part of it. So, if you look at cost of interface. So, it is 2500 rupees per kilowatt for the IC engine into 100 kilowatts. So, this is 2.5 into 10 power of 5 for your fixed speed for the variable speed it is 7500. So, there is a increase in cost on the VSG side of about 5 into 10 power of 5 for your electrical interface IC engine power requirement your efficiency of your machine is here I have considered 96 percent. So, this is 104 kilowatts if you are considering your IC engine variable speed option your interface efficiency reduces to 95 and you have a 20 percent benefit because of your variable speed nature. So, you could maybe get by with a 94 kilowatt engine IC engine. So, if you look at the cost of IC engine that this corresponds to rupees 2.6 into 10 power of 5 here it corresponds to 2.1. So, that is about 50000 rupees difference not much if you consider the fuel cost. So, the cost as we saw when we are running a genset on a continuous basis the capital equipment cost is actually a smaller fraction of your fuel cost. If you look at the loss in your electrical system you have in one case it is 96 percent efficient. So, you have 4.2 kilowatts of losses in your synchronous machine and about 5.3 kilowatts of losses in the PM machine plus inverter. So, to calculate the annual cost of losses you take this multiply by 24 into 365 and you know it is 8 rupees per kilowatt or cost of energy. So, the cost of energy cost of the losses this corresponds to rupees 2.9 into 10 to the power of 5 per year is the cost of losses in your fixed speed generator in your variable speed generator this turns out to be 3.7 into 10 to the power of 5. And we to calculate your net present cost NPC of loss what you do you accumulate the losses from over the 5 years. So, your first year comes in then for your next year it is based on your charge rate. So, you have summation i is equal to 1 to 5 2.9 into 10 to the power of 5 divided by 1 plus 0.1 is your interest rate to the power of 5. So, this turns out to be rupees 11 into 10 to the power of 5 the corresponding number over here is rupees 13.9 into 10 to the power of 5. So, you can see that the losses in your variable speed genset case is actually higher and the equivalent cost net present value is higher in that particular case. If you look at your annual fuel consumption. So, in the first case it is 100 kilowatts 96 percent efficiency for the for your synchronous machine and 34 percent efficiency for your IC engine. So, into 3600 24 minutes seconds per hour 2400 into 365 divided by 3.6 into 10 to the power of 7 joules per liter. So, this turns out to be 2.68 liters into 10 to the power of 5 liters per year in for your fixed speed case and the corresponding number for the variable speed case is 2.49 into 10 to the power of 5 liters per year. So, if you look at the corresponding cost at 50 rupees per liter this corresponds to rupees 134 into 10 to the power of 5 rupees per year. In this particular case it is rupees 125 into 10 to the power of 5 per year and you could again do a net present value calculation for the rupees over the 5 year duration similar to how we did for your for the electricity electrical energy loss. So, the net present value turns out in this particular case of fuel turns out to be rupees 509 into 10 to the power of 5 here this is rupees 472. So, you can see that in this between these two numbers there is a difference about 36 into 10 to the power of 5. So, there is a fairly substantial difference in between your variable speed genset and the fixed speed genset if you look at the net present value of your fuel. So, you could then make use of these numbers and calculate what the differences overall are the cost of the interface is higher in case of your various variable speed genset. So, if you look at a variable speed vsg minus variable speed minus fixed speed you are talking about a difference of 5 into 10 to the power of 5. If you look at the cost of the IC engine by itself there is a small reduction. So, delta in this particular case is minus 0.5 into 10 to the power of 5 if you look at the losses in your electrical system here the delta is 2.9 into 10 to the power of 5. So, there is more losses in your variable speed case, but if you look at the delta for your fuel in this particular case it is minus 36 into 10 to the power of 5. So, 36 dominates over all the other numbers. So, if you look at your overall benefit net present cost of the overall electrical interface the fixed speed generator has a number of 525 into 10 to the power of 5 the variable speed is 496 into 10 to the power of 5. So, there is a difference of about 29. Practically this 525 is not a number that you are actually going to deal with 496 is also not a number you are dealing with what you are saying is over 5 years of operation by the use of the variable speed option you are going to get a present value of the savings corresponding to 29 lakhs. So, you can look at the case where instead of say a 5 year duration what would be the net present value if you just restricted to just a 1 year generation and you can see that even with 1 year you get a benefit for the variable speed case if you are running the gen set on a continuous basis. So, from an electrical perspective it makes sense to go to a variable speed case if you just look at the net present value of just the interface and the losses you can see that it does not make sense because you are going for something which is a higher cost and more lossy, but your benefits is coming from benefits to the balance of system in this particular case. So, you can see that these calculations can give you a feel for what might be an appropriate design for your electrical system in a more complex electrical, mechanical, thermal system and what could be the options that you could look at which can actually reduce your overall cost of energy or your benefits on an annual basis. So, these are important engineering design decisions that can benefit your overall system design. Thank you.