The stubbornly recurrent LCOE

 

I am thinking about those results I got in my last two research updates, namely in “The expected amount of what can happen”, and in “Contagion étonnement cohérente”. Each time, I found something intriguingly coherent in mathematical terms. In “The expected amount of what can happen”, I have probably nailed down some kind of cycle in business development, some 3 – 4 years, as regards the FinTech industry. In “Contagion étonnement cohérente”, on the other hand, I have seemingly identified a cycle of behavioural change in customers, like around 2 months, which allows to interpolate two distinct, predictive models as for the development of a market: the epidemic model based on a geometric-exponential function, and the classical model of absorption based on the normal distribution. That cycle of behavioural change looks like the time lap to put into an equation, where the number of customers is a function of time elapsed, like n(t) = e0,69*t.  Why ‘0,69’ in n(t) = e0,69*t? Well, the 0,69 fits nicely, when the exponential function n(t) = eß*tneeds to match a geometric process that duplicates the number of customers at every ‘t’ elapsed, like n(t) = 2*n(t-1) + 1.

I have identified those two cycles of change, thus, and they both look like cycles of behavioural change. It takes a FinTech business like 3+ years to pass from launching a product to stabilizing it, and it apparently takes the customers some 2 months to modify significantly their behaviour – or to take a distinctive, noticeable step in such behavioural change – regarding a new technology. I am trying to wrap my mind around each of those cycles separately, as well as around their mutual connection. It seems important for continuing to write that business plan of mine for the EneFinproject, that FinTech concept for the market of energy, where households and small businesses would buy their energy through futures contracts combined with participatory deeds in the balance sheet of the energy provider.

Now, before I go further, a little explanation for those of you, who might not quite grasp the way I run this blog. This is a research log in the most literal sense of the term. I write and publish as I think about things and as I channel my energy into the thinking. This blog is the living account of what I do, not a planned presentation. As for what I do the latter category, you can find it under the heading of “Your takeaways / Vos plats à emporter“. The approach I use, the one from the side of raw science on the make, is the reason why you can see me coming and going about ideas, and this is why I write in two languages: English and French. I found out that my thinking goes just sort of better when I alternate those two.

Anyway, I am trying to understand what I have discovered, I mean those two intriguing cycles of behavioural change, and I want to incorporate that understanding in the writing of my business plan for the EneFinproject. Cycle of change spells process: there is any point of talking about a cycle if it happens like recurrently, with one cycle following a previous cycle.

So, I do what I need to do, namely I am sketching the landscape. I am visualising urban networks composed of wind turbines with vertical axis, such as I started visualising in « Something to exploit subsequently». Each network has a different operator, who maintains a certain number of turbines scattered across the city. Let this city be Lisbon, Portugal, one of my favourite places in Europe, which, on the top of all its beauty, allows experiencing that shortest interval of time in the universe, i.e. the time elapsing between the traffic lights turning greed, for vehicles, and someone from among said vehicles hooting impatiently.

We are in Lisbon, and there are local operators of urban wind turbines, and with the wind speed being 4,47 m/s on average, each turbine, such as described in the patent application no. EP 3 214 303 A1, generates an electric power averaging 47,81 kilowatts. That makes 47,81 kilowatts * 8760 hours in the normal calendar year = 418 815,60 kilowatt hoursof energy a year. At €0,23 for each kWh at the basic price for households, in Portugal, the output of one turbine is worth like € 96 327,59. According to the basic scheme of EneFin, those € 96 327,59 further split themselves in two, and make:

€ 50 257,87in Futures contracts on energy, sold to households at the more advantageous rate of €0,12, normally reserved for the big institutional end users
€ 46 069,72in Participatory deeds in the balance sheet of the operator who currently owns the turbine

Thus, each local operator of those specific wind turbines has a basic business unit – one turbine – and the growth of business is measured at the pace of developing such consecutive units. Now, the transactional platform « EneFin» implants itself in this market, as a FinTech utility for managing financial flows between the local operators of those turbines, on the one hand, and the households willing to buy energy from those turbines and invest in their balance sheet. I assume, for the moment, that EneFin takes 5% of commissionon the trading of each complex contract. One turbine generates 5%*€ 96 327,59 =  € 4 816,38 of commission to EneFin.

I am progressively make the above converge with those cycles I have identified. In the first place, I take those two cycles I have identified, i.e. the ≈ 2 months of behavioural change in customers, and the ≈ 3+ years of business maturation. On the top of that, I take the simulations of absorption, as you can see in « Safely narrow down the apparent chaos». That means I take into account still another cycle, that of 7 years = 84 months for the absorption of innovation in the market of renewable energies. As I am having a look at the thing, I am going to start the checking with the last one. Thus, I take the percentages of the market, calculated « Safely narrow down the apparent chaos», and I apply them to the population of Lisbon, Portugal, i.e. 2 943 000 peopleas for the end of 2017.

The results of this particular step in my calculations are shown in Table 1 below. Before I go interpreting and transforming those numbers, further below the table, a few words of reminder and explanation for those among the readers, who might now have quite followed my previous updates on this blog. Variability of the population is the coefficient of proportion, calculated as the standard deviation divided by the mean, said mean being the average time an average customer needs in order to switch to a new technology. This average time, in the calculations I have made so far, is assumed to be 7 years = 84 months. The coefficient of variability reflects the relative heterogeneity of the population. The greater its value, the more differentiated are the observable patterns of behaviour. At v = 0,2it is like a beach, in summer, on the Mediterranean coast, or like North Korea, i.e. people behaving in very predictable, and very recurrent ways. At v = 2, it is more like a Halloween party: everybody tries to be original.

Table 1

Number of customers acquired in Lisbon
[a] [b] [c] [d]
Variability of the population 12th month 24th month 36th month
0,1 0 0 0
0,2 30 583 6 896
0,3 5 336 25 445 86 087
0,4 29 997 93 632 212 617
0,5 61 627 161 533 310 881
0,6 85 978 206 314 365 497
0,7 100 653 229 546 387 893
0,8 107 866 238 238 390 878
0,9 110 200 238 211 383 217
1 109 574 233 290 370 157
1,1 107 240 225 801 354 689
1,2 103 981 217 113 338 471
1,3 100 272 208 016 322 402
1,4 96 397 198 958 306 948
1,5 92 525 190 184 292 331
1,6 88 753 181 821 278 638
1,7 85 134 173 925 265 878
1,8 81 695 166 513 254 020
1,9 78 446 159 577 243 014
2 75 386 153 098 232 799

Now, I do two things to those numbers. Firstly, I try to make them kind of relative to incidences of epidemic contagion. Mathematically, it means referring to that geometric process, which duplicates the number of customers at every ‘t’ elapsed, like n(t) = 2*n(t-1) + 1, which is nicely (almost) matched by the exponential function n(t) = e0,69*t. So what I do now is to take the natural logarithm out of each number in columns [b] – [d]in Table 1, and I divide it by 0,69. This is how I get the ‘t’, or the number of temporal cycles in the exponential function n(t) = e0,69*tso as to obtain the same number as shown in Table 1. Then, I divide the time frames in the headings of those columns, thus, respectively, 12, 24, and 36, by the that number of temporal cycles. As a result, I get the length of one period of epidemic contagion between customers, expressed in months.

Good, let’s diagnose this epidemic contagion. Herr Doktor Wasniewski (this is me) has pinned down the numbers shown in Table 2 below. Something starts emerging, and I am telling you, I don’t really like it. I have enough emergent things, which I have no clue what they mean, on my hands. One more emergent phenomenon is one more pain in my intellectual ass. Anyway, what is emerging, is a pattern of decreasing velocity. When I take the numbers from Table 1, obtained with a classical model of absorption, and based on the normal distribution, those numbers require various paces of epidemic contagion in the behaviour of customers. In the beginning, the contagion need to be f***ing fast, like 0,7 ÷ 0,8 of a month, so some 21 – 24 days. Only in very homogenous populations, with variability sort of v = 0,2, it is a bit longer.

One thing: do not really pay attention to the row labelled ‘Variability of the population 0,1’. This is very homogenous a population, and I placed it here mostly for the sake of contrast. The values in brackets in this particular row of Table 2 are negative, which essentially suggests that if I want that few customers, I need going back in time.

So, I start with quite vivacious a contagion, something to put in the scenario of an American thriller, like ‘World War Z no. 23’. Subsequently, the velocity of contagion is supposed to curb down, to like 1,3 ÷ 1,4 months in the second year, and almost 2 months in the 3rdyear. It correlates surprisingly with that 3+ years cycle of getting some stance in the business, which I have very intuitively identified, using Euclidean distances, in «The expected amount of what can happen». I understand that as the pace of contagion between clients is to slow down, my marketing needs to be less and less aggressive, ergo my business gains in gravitas and respectability.

Table 2

The length of one temporal period « t » in the epidemic contagion n(t) = 2*n(t-1) + 1 ≈ e0,69*t, in the local market of Lisbon, Portugal
[a] [b] [c] [d]
Variability of the population 12th month 24th month 36th month
0,1  (0,34)  (1,26)  (6,55)
0,2  2,44  2,60  2,81
0,3  0,96  1,63  2,19
0,4  0,80  1,45  2,02
0,5  0,75  1,38  1,96
0,6  0,73  1,35  1,94
0,7  0,72  1,34  1,93
0,8  0,71  1,34  1,93
0,9  0,71  1,34  1,93
1  0,71  1,34  1,94
1,1  0,71  1,34  1,94
1,2  0,72  1,35  1,95
1,3  0,72  1,35  1,96
1,4  0,72  1,36  1,97
1,5  0,72  1,36  1,97
1,6  0,73  1,37  1,98
1,7  0,73  1,37  1,99
1,8  0,73  1,38  2,00
1,9  0,73  1,38  2,00
2  0,74  1,39  2,01

The second thing I do to numbers in Table 1 is to convert them into money, and more specifically into: a) the amount of transaction-based fee of 5%, collected by the EneFin platform, when b) the amount of capital collected by the suppliers of energy via the EneFin platform. I start by assuming that my customers are not really single people, but households. The numbers in Table 1, referring to single persons, are being divided by 2,6, which is the average size of one household in Portugal.

In the next step, I convert households into energy. Easy. One person in Portugal consumes, for the strictly spoken household use, some 4 288,92 kWh a year. That makes 11 151,20 kWh per household per year. Now, I convert energy into money, which, in financial terms, means €1 338,14a year in futures contracts on energy, at €0,12 per kWh, and €1 226,63in terms of capital invested in the supplier of energy via those complex contracts in the EneFin way. The commission taken by EneFin is 5%*(€1 338,14+ €1 226,63) =  €128,24. Those are the basic steps that both the operator of urban wind turbines, and the EneFin platform will be taking, in this scenario, as they will attract new customers.

People converted into money are shown in Tables 3 and 4, below, respectively as the amount of transaction-based fee collected by EneFin, and as the capital collected by the suppliers of energy via those complex contracts traded at EneFin. As I connect the dots, more specifically tables 2 – 4, I can see that time matters. Each year, out of the three, makes a very distinct phase. During the 1styear, I need to work my ass off, in terms of marketing, to acquire customers very quickly. Still, it does not make much difference, in financial terms, which exact variability of population is the context of me working my ass off. On the other hand, in the 3rdyear, I can be much more respectable in my marketing, I can afford to go easy on customers, and, in the same time, the variability of the local population starts mattering in financial terms.

Table 3

Transaction-based fee collected by EneFin in Lisbon
Variability of the population 1st year 2nd year 3rd year
0,1 € 0,00 € 0,00 € 1,11
0,2 € 1 458,22 € 28 752,43 € 340 124,01
0,3 € 263 195,64 € 1 255 033,65 € 4 246 097,13
0,4 € 1 479 526,18 € 4 618 201,31 € 10 486 926,46
0,5 € 3 039 639,48 € 7 967 324,44 € 15 333 595,20
0,6 € 4 240 693,13 € 10 176 019,80 € 18 027 422,81
0,7 € 4 964 515,36 € 11 321 936,93 € 19 132 083,67
0,8 € 5 320 300,96 € 11 750 639,54 € 19 279 326,77
0,9 € 5 435 424,51 € 11 749 281,67 € 18 901 432,22
1 € 5 404 510,95 € 11 506 577,11 € 18 257 283,50
1,1 € 5 289 424,10 € 11 137 214,92 € 17 494 337,16
1,2 € 5 128 672,87 € 10 708 687,77 € 16 694 429,35
1,3 € 4 945 700,41 € 10 259 985,98 € 15 901 851,61
1,4 € 4 754 575,54 € 9 813 197,53 € 15 139 607,38
1,5 € 4 563 606,09 € 9 380 437,89 € 14 418 674,83
1,6 € 4 377 570,97 € 8 967 947,88 € 13 743 280,35
1,7 € 4 199 088,86 € 8 578 519,11 € 13 113 914,13
1,8 € 4 029 458,58 € 8 212 936,36 € 12 529 062,43
1,9 € 3 869 177,26 € 7 870 840,04 € 11 986 204,76
2 € 3 718 261,64 € 7 551 243,62 € 11 482 385,83

Table 4

Capital collected by the suppliers of energy via EneFin, in Lisbon
Variability of the population 1st year 2nd year 3rd year
0,1  € 0,00  € 0,00  € 10,63
0,2  € 13 948,06  € 275 020,26  € 3 253 324,36
0,3  € 2 517 495,89  € 12 004 537,77  € 40 614 395,82
0,4  € 14 151 834,00  € 44 173 614,09  € 100 308 629,20
0,5  € 29 074 492,97  € 76 208 352,96  € 146 667 559,88
0,6  € 40 562 705,95  € 97 334 772,00  € 172 434 323,50
0,7  € 47 486 146,88  € 108 295 598,06  € 183 000 528,68
0,8  € 50 889 276,10  € 112 396 186,64  € 184 408 925,42
0,9  € 51 990 445,74  € 112 383 198,48  € 180 794 321,60
1  € 51 694 754,11  € 110 061 702,11  € 174 632 966,74
1,1  € 50 593 935,49  € 106 528 711,32  € 167 335 299,39
1,2  € 49 056 331,91  € 102 429 800,96  € 159 684 091,36
1,3  € 47 306 179,81  € 98 137 917,98  € 152 102 996,27
1,4  € 45 478 048,96  € 93 864 336,33  € 144 812 044,65
1,5  € 43 651 404,71  € 89 724 941,73  € 137 916 243,78
1,6  € 41 871 957,84  € 85 779 428,52  € 131 456 019,80
1,7  € 40 164 756,47  € 82 054 498,57  € 125 436 061,23
1,8  € 38 542 223,78  € 78 557 658,50  € 119 841 889,05
1,9  € 37 009 114,98  € 75 285 468,80  € 114 649 394,41
2  € 35 565 590,09  € 72 228 493,11  € 109 830 309,84

 Now, I do one final check. I take the formula of LCOE, or the levelized cost of energy, as shown in the formula below:

LCOE

Symbols in the equation have the following meaning: a) Itis the capital invested in period t b) Mtstands for the cost of maintenance in period t c) Ftsymbolizes the cost of fuel in period t and d) Etis the output of energy in period t. I assume that wind is for free, so my Ftis zero. I further assume that It+ Mtmake a lump sum of capital, acquired by the supplier of energy, and equal to the amounts of capital calculated in Table 4. Thus I take those amounts from Table 4, and I divide each of them by the energy consumed in the corresponding headcount of households. Now, it becomes really strange: whatever the phase in time, and whatever the variability of behaviour assumed in the local population, the thus-computed LCOE is always equal to €0,11. Always! Can you understand? Well, if you do, you are smarter than me, because I don’t. How can so differentiated an array of numbers, in Tables 1 – 4, yield one and the same cost of energy, those €0,11? Honestly, I don’t know.

Calm down, Herr Doktor Wasniewski. This is probably how those Greeks hit their π. Maybe I am hitting another one. I am trying to take another path. I take the number(s) of people from Table 1, I take their average consumption of energy, as official for Portugal – 4 288,92 kWh a year per person – and, finally, I take the 47,81 kilowattsof capacity in one single wind turbine, as described in the patent application no. EP 3 214 303 A1, in Lisbon, with the wind speed 4,47 m/s on average. Yes, you guessed right: I want to calculate the number of such wind turbines needed to supply energy to the given number of people, as shown in Table 1. The numerical result of this particular path of thinking is shown in Table 5 below.

The Devil never sleeps, as we say in Poland. Bloody right. He has just tempted me to take the capital amounts from Table 4 (above) and divide them by the number of turbines from Table 5. Guess what. Another constant. Whatever the exact variability in behaviour, and whatever the year, it is always €46 069,64. I can’t help it, I continue. I take that constant €46 069,64 of capital invested per one turbine, and I divide it by the constant LCOE €0,11 per kWh, and it yields  418 815,60 kWh, or 37,56 households (2,6 person per household) per turbine, in order to make it sort of smooth in numbers.

Table 5

Number of wind turbines needed for the number of customers as in Table 1
Variability of the population 1st year 2nd year 3rd year
0,1 0 0 0
0,2 0 6 71
0,3 55 261 882
0,4 307 959 2 177
0,5 631 1 654 3 184
0,6 880 2 113 3 743
0,7 1 031 2 351 3 972
0,8 1 105 2 440 4 003
0,9 1 129 2 439 3 924
1 1 122 2 389 3 791
1,1 1 098 2 312 3 632
1,2 1 065 2 223 3 466
1,3 1 027 2 130 3 302
1,4 987 2 037 3 143
1,5 948 1 948 2 994
1,6 909 1 862 2 853
1,7 872 1 781 2 723
1,8 837 1 705 2 601
1,9 803 1 634 2 489
2 772 1 568 2 384

Another thing to wrap my mind around. My brain needs some rest. Enough science for today. I am consistently delivering good, almost new science to my readers, and love doing it, and I am working on crowdfunding this activity of mine. As we talk business plans, I remind you that you can download, from the library of my blog, the business plan I prepared for my semi-scientific project Befund  (and you can access the French versionas well). You can also get a free e-copy of my book ‘Capitalism and Political Power’ You can support my research by donating directly, any amount you consider appropriate, to my PayPal account. You can also consider going to my Patreon pageand become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

 

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