We keep going until we observe

I keep working on a proof-of-concept paper for my idea of ‘Energy Ponds’. In my last two updates, namely in ‘Seasonal lakes’, and in ‘Le Catch 22 dans ce jardin d’Eden’, I sort of refreshed my ideas and set the canvas for painting. Now, I start sketching. What exact concept do I want to prove, and what kind of evidence can possibly confirm (or discard) that concept? The idea I am working on has a few different layers. The most general vision is that of purposefully storing water in spongy structures akin to swamps or wetlands. These can bear various degree of artificial construction, and can stretch from natural wetlands, through semi-artificial ones, all the way to urban technologies such as rain gardens and sponge cities. The most general proof corresponding to that vision is a review of publicly available research – peer-reviewed papers, preprints, databases etc. – on that general topic.

Against that general landscape, I sketch two more specific concepts: the idea of using ram pumps as a technology of forced water retention, and the possibility of locating those wetland structures in the broadly spoken Northern Europe, thus my home region. Correspondingly, I need to provide two streams of scientific proof: a review of literature on the technology of ram pumping, on the one hand, and on the actual natural conditions, as well as land management policies in Europe, on the other hand.  I need to consider the environmental impact of creating new wetland-like structures in Northern Europe, as well as the socio-economic impact, and legal feasibility of conducting such projects.

Next, I sort of build upwards. I hypothesise a complex technology, where ram-pumped water from the river goes into a sort of light elevated tanks, and from there, using the principle of Roman siphon, cascades down into wetlands, and through a series of small hydro-electric turbines. Turbines generate electricity, which is being stored and then sold outside.

At that point, I have a technology of water retention coupled with a technology of energy generation and storage. I further advance a second hypothesis that such a complex technology will be economically sustainable based on the corresponding sales of electricity. In other words, I want to figure out a configuration of that technology, which will be suitable for communities which either don’t care at all, or simply cannot afford to care about the positive environmental impact of the solution proposed.

Proof of concept for those two hypotheses is going to be complex. First, I need to pass in review the available technologies for energy storage, energy generation, as well as for the construction of elevated tanks and Roman siphons. I need to take into account various technological mixes, including the incorporation of wind turbines and photovoltaic installation into the whole thing, in order to optimize the output of energy. I will try to look for documented examples of small hydro-generation coupled with wind and solar. Then, I have to rack the literature as regards mathematical models for the optimization of such power systems and put them against my own idea of reverse engineering back from the storage technology. I take the technology of energy storage which seems the most suitable for the local market of energy, and for the hypothetical charging from hydro-wind-solar mixed generation. I build a control scenario where that storage facility just buys energy at wholesale prices from the power grid and then resells it. Next, I configure the hydro-wind-solar generation so as to make it economically competitive against the supply of energy from the power grid.

Now, I sketch. I keep in mind the levels of conceptualization outlined above, and I quickly move through published science along that logical path, quickly picking a few articles for each topic. I am going to put those nonchalantly collected pieces of science back-to-back and see how and whether at all it all makes sense together. I start with Bortolini & Zanin (2019[1]), who study the impact of rain gardens on water management in cities of the Veneto region in Italy. Rain gardens are vegetal structures, set up in the urban environment, with the specific purpose to retain rainwater.  Bortolini & Zanin (2019 op. cit.) use a simplified water balance, where the rain garden absorbs and retains a volume ‘I’ of water (‘I’ stands for infiltration), which is the difference between precipitations on the one hand, and the sum total of overflowing runoff from the rain garden plus evapotranspiration of water, on the other hand. Soil and plants in the rain garden have a given top capacity to retain water. Green plants typically hold 80 – 95% of their mass in water, whilst trees hold about 50%. Soil is considered wet when it contains about 25% of water. The rain garden absorbs water from precipitations at a rate determined by hydraulic conductivity, which means the relative ease of a fluid (usually water) to move through pore spaces or fractures, and which depends on the intrinsic permeability of the material, the degree of saturation, and on the density and viscosity of the fluid.

As I look at it, I can see that the actual capacity of water retention in a rain garden can hardly be determined a priori, unless we have really a lot of empirical data from the given location. For a new location of a new rain garden, it is safe to assume that we need an experimental phase when we empirically assess the retentive capacity of the rain garden with different configurations of soil and vegetation used. That leads me to generalizing that any porous structure we use for retaining rainwater, would it be something like wetlands, or something like a rain garden in urban environment, has a natural constraint of hydraulic conductivity, and that constraint determines the percentage of precipitations, and the metric volume thereof, which the given structure can retain.

Bortolini & Zanin (2019 op. cit.) bring forth empirical results which suggest that properly designed rain gardens located on rooftops in a city can absorb from 87% to 93% of the total input of water they receive. Cool. I move on and towards the issue of water management in Europe, with a working paper by Fribourg-Blanc, B. (2018[2]), and the most important takeaway from that paper is that we have something called European Platform for Natural Water Retention Measures AKA http://nwrm.eu , and that thing have both good properties and bad properties. The good thing about http://nwrm.eu is that it contains loads of data and publications about projects in Natural Water Retention in Europe. The bad thing is that http://nwrm.eu is not a secure website. Another paper, by Tóth et al. (2017[3]) tells me that another analytical tool exists, namely the European Soil Hydraulic Database (EU‐ SoilHydroGrids ver1.0).

So far, so good. I already know there is data and science for evaluating, with acceptable precision, the optimal structure and the capacity for water retention in porous structures such as rain gardens or wetlands, in the European context. I move to the technology of ram pumps. I grab two papers: Guo et al. (2018[4]), and Li et al. (2021[5]). They show me two important things. Firstly, China seems to be burning the rubber in the field of ram pumping technology. Secondly, the greatest uncertainty as for that technology seems to be the actual height those ram pumps can elevate water at, or, when coupled with hydropower, the hydraulic head which ram pumps can create. Guo et al. (2018 op. cit.) claim that 50 meters of elevation is the maximum which is both feasible and efficient. Li et al. (2021 op. cit.) are sort of vertically more conservative and claim that the whole thing should be kept below 30 meters of elevation. Both are better than 20 meters, which is what I thought was the best one can expect. Greater elevation of water means greater hydraulic head, and more hydropower to be generated. It pays off to review literature.

Lots of uncertainty as for the actual capacity and efficiency of ram pumping means quick technological change in that domain. This is economically interesting. It means that investing in projects which involve ram pumping means investment in quickly changing a technology. That means both high hopes for an even better technology in immediate future, and high needs for cash in the balance sheet of the entities involved.

I move to the end-of-the-pipeline technology in my concept, namely to energy storage. I study a paper by Koohi-Fayegh & Rosen (2020[6]), which suggests two things. Firstly, for a standalone installation in renewable energy, whatever combination of small hydropower, photovoltaic and small wind turbines we think of, lithium-ion batteries are always a good idea for power storage, Secondly, when we work with hydrogeneration, thus when we have any hydraulic head to make electricity with, pumped storage comes sort of natural. That leads me to an idea which looks even crazier than what I have imagined so far: what if we create an elevated garden with strong capacity for water retention. Ram pumps take water from the river and pump it up onto elevated platforms with rain gardens on it. Those platforms can be optimized as for their absorption of sunlight and thus as regards their interaction with whatever is underneath them.  

I move to small hydro, and I find two papers, namely Couto & Olden (2018[7]), and Lange et al. (2018[8]), which are both interestingly critical as regards small hydropower installations. Lange et al. (2018 op. cit.) claim that the overall environmental impact of small hydro should be closely monitored. Couto & Olden (2018 op. cit.) go further and claim there is a ‘craze’ about small hydro, and that craze has already lead to overinvestment in the corresponding installations, which can be damaging both environmentally and economically (overinvestment means financial collapse of many projects). Those critical views in mind, I turn to another paper, by Zhou et al. (2019[9]), who approach the issue as a case for optimization, within a broader framework called ‘Water-Food-Energy’ Nexus, WFE for closer friends. This paper, just as a few others it cites (Ming et al. 2018[10]; Uen et al. 2018[11]), advocates for using artificial intelligence in order to optimize for WFE.

Zhou et al. (2019 op.cit.) set three hydrological scenarios for empirical research and simulation. The baseline scenario corresponds to an average hydrological year, with average water levels and average precipitations. Next to it are: a dry year and a wet year. The authors assume that the cost of installation in small hydropower is $600 per kW on average.  They simulate the use of two technologies for hydro-electric turbines: Pelton and Vortex. Pelton turbines are optimized paddled wheels, essentially, whilst the Vortex technology consists in creating, precisely, a vortex of water, and that vortex moves a rotor placed in the middle of it.

Zhou et al. (2019 op.cit.) create a multi-objective function to optimize, with the following desired outcomes:

>> Objective 1: maximize the reliability of water supply by minimizing the probability of real water shortage occurring.

>> Objective 2: maximize water storage given the capacity of the reservoir. Note: reservoir is understood hydrologically, as any structure, natural or artificial, able to retain water.

>> Objective 3: maximize the average annual output of small hydro-electric turbines

Those objectives are being achieved under the corresponding sets of constraints. For water supply those constraints all turn around water balance, whilst for energy output it is more about the engineering properties of the technologies taken into account. The three objectives are hierarchized. First, Zhou et al. (2019 op.cit.) perform an optimization regarding Objectives 1 and 2, thus in order to find the optimal hydrological characteristics to meet, and then, on the basis of these, they optimize the technology to put in place, as regards power output.

The general tool for optimization used by Zhou et al. (2019 op.cit.) is a genetic algorithm called NSGA-II, AKA Non-dominated Sorting Genetic Algorithm. Apparently, NSGA-II has a long and successful history of good track in engineering, including water management and energy (see e.g. Chang et al. 2016[12]; Jain & Sachdeva 2017[13];  Assaf & Shabani 2018[14]). I want to stop for a while here and have a good look at this specific algorithm. The logic of NSGA-II starts with creating an initial population of cases/situations/configurations etc. Each case is a combination of observations as regards the objectives to meet, and the actual values observed in constraining variables, e.g. precipitations for water balance or hydraulic head for the output of hydropower. In the conventional lingo of this algorithm, those cases are called chromosomes. Yes, I know, a hydro-electric turbine placed in the context of water management hardly looks like a chromosome, but it is a genetic algorithm, and it just sounds fancy to use that biologically marked vocabulary.

As for me, I like staying close to real life, and therefore I call those cases solutions rather than chromosomes. Anyway, the underlying math is the same. Once I have that initial population of real-life solutions, I calculate two parameters for each of them: their rank as regards the objectives to maximize, and their so-called ‘crowded distance’. Ranking is done with the procedure of fast non-dominated sorting. It is a comparison in pairs, where the solution A dominates another solution B, if and only if there is no objective of A worse than that objective of B and there is at least one objective of A better than that objective of B. The solution which scores the most wins in such peer-to-peer comparisons is at the top of the ranking, the one with the second score of wins is the second etc. Crowding distance is essentially the same as what I call coefficient of coherence in my own research: Euclidean distance (or other mathematical distance) is calculated for each pair of solutions. As a result, each solution is associated with k Euclidean distances to the k remaining solutions, which can be reduced to an average distance, i.e. the crowded distance.

In the next step, an off-spring population is produced from that original population of solutions. It is created by taking relatively the fittest solutions from the initial population, recombining their characteristics in a 50/50 proportion, and adding them some capacity for endogenous mutation. Two out of these three genetic functions are de facto controlled. We choose relatively the fittest by establishing some kind of threshold for fitness, as regards the objectives pursued. It can be a required minimum, a quantile (e.g. the third quartile), or an average. In the first case, we arbitrarily impose a scale of fitness on our population, whilst in the latter two the hierarchy of fitness is generated endogenously from the population of solutions observed. Fitness can have shades and grades, by weighing the score in non-dominated sorting, thus the number of wins over other solutions, on the one hand, and the crowded distance on the other hand. In other words, we can go for solutions which have a lot of similar ones in the population (i.e. which have a low average crowded distance), or, conversely, we can privilege lone wolves, with a high average Euclidean distance from anything else on the plate.  

The capacity for endogenous mutation means that we can allow variance in all or in just the selected variables which make each solution. The number of degrees of freedom we allow in each variable dictates the number of mutations that can be created. Once again, discreet power is given to the analyst: we can choose the genetic traits which can mutate and we can determine their freedom to mutate. In an engineering problem, technological and environmental constraints should normally put a cap on the capacity for mutation. Still, we can think about an algorithm which definitely kicks the lid off the barrel of reality, and which generates mutations in the wildest registers of variables considered. It is a way to simulate a process when the presence of strong outliers has a strong impact on the whole population.

The same discreet cap on the freedom to evolve is to be found when we repeat the process. The offspring generation of solutions goes essentially through the same process as the initial one, to produce further offspring: ranking by non-dominated sorting and crowded distance, selection of the fittest, recombination, and endogenous mutation. At the starting point of this process, we can be two alternative versions of the Mother Nature. We can be a mean Mother Nature, and we shave off from the offspring population all those baby-solutions which do not meet the initial constraints, e.g. zero supply of water in this specific case. On the other hand, we can be even meaner a Mother Nature and allow those strange, dysfunctional mutants to keep going and see what happens to the whole species after a few rounds of genetic reproduction.

With each generation, we compute an average crowded distance between all the solutions created, i.e. we check how diverse is the species in this generation. As long as diversity grows or remains constant, we assume that the divergence between the solutions generated grows or stays the same. Similarly, we can compute an even more general crowded distance between each pair of generations, and therefore to assess how far has the current generation gone from the parent one. We keep going until we observe that the intra-generational crowded distance and the inter-generational one start narrowing down asymptotically to zero. In other words, we consider resuming evolution when solutions in the game become highly similar to each other and when genetic change stops bringing significant functional change.

Cool. When I want to optimize my concept of Energy Ponds, I need to add the objective of constrained return on investment, based on the sales of electricity. In comparison to Zhou et al. (2019 op.cit.), I need to add a third level of selection. I start with selecting environmentally the solutions which make sense in terms of water management. In the next step, I produce a range of solutions which assure the greatest output of power, in a possible mix with solar and wind. Then I take those and filter them through the NSGA-II procedure as regards their capacity to sustain themselves financially. Mind you, I can shake it off a bit by fusing together those levels of selection. I can simulate extreme cases, when, for example, good economic sustainability becomes an environmental problem. Still, it would be rather theoretical. In Europe, non-compliance with environmental requirements makes a project a non-starter per se: you just can get the necessary permits if your hydropower project messes with hydrological constraints legally imposed on the given location.     

Cool. It all starts making sense. There is apparently a lot of stir in the technology of making semi-artificial structures for retaining water, such as rain gardens and wetlands. That means a lot of experimentation, and that experimentation can be guided and optimized by testing the fitness of alternative solutions for meeting objectives of water management, power output and economic sustainability. I have some starting data, to produce the initial generation of solutions, and then try to optimize them with an algorithm such as NSGA-II.

[1] Bortolini, L., & Zanin, G. (2019). Reprint of: Hydrological behaviour of rain gardens and plant suitability: A study in the Veneto plain (north-eastern Italy) conditions. Urban forestry & urban greening, 37, 74-86. https://doi.org/10.1016/j.ufug.2018.07.003

[2] Fribourg-Blanc, B. (2018, April). Natural Water Retention Measures (NWRM), a tool to manage hydrological issues in Europe?. In EGU General Assembly Conference Abstracts (p. 19043). https://ui.adsabs.harvard.edu/abs/2018EGUGA..2019043F/abstract

[3] Tóth, B., Weynants, M., Pásztor, L., & Hengl, T. (2017). 3D soil hydraulic database of Europe at 250 m resolution. Hydrological Processes, 31(14), 2662-2666. https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.11203

[4] Guo, X., Li, J., Yang, K., Fu, H., Wang, T., Guo, Y., … & Huang, W. (2018). Optimal design and performance analysis of hydraulic ram pump system. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 232(7), 841-855. https://doi.org/10.1177%2F0957650918756761

[5] Li, J., Yang, K., Guo, X., Huang, W., Wang, T., Guo, Y., & Fu, H. (2021). Structural design and parameter optimization on a waste valve for hydraulic ram pumps. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 235(4), 747–765. https://doi.org/10.1177/0957650920967489

[6] Koohi-Fayegh, S., & Rosen, M. A. (2020). A review of energy storage types, applications and recent developments. Journal of Energy Storage, 27, 101047. https://doi.org/10.1016/j.est.2019.101047

[7] Couto, T. B., & Olden, J. D. (2018). Global proliferation of small hydropower plants–science and policy. Frontiers in Ecology and the Environment, 16(2), 91-100. https://doi.org/10.1002/fee.1746

[8] Lange, K., Meier, P., Trautwein, C., Schmid, M., Robinson, C. T., Weber, C., & Brodersen, J. (2018). Basin‐scale effects of small hydropower on biodiversity dynamics. Frontiers in Ecology and the Environment, 16(7), 397-404.  https://doi.org/10.1002/fee.1823

[9] Zhou, Y., Chang, L. C., Uen, T. S., Guo, S., Xu, C. Y., & Chang, F. J. (2019). Prospect for small-hydropower installation settled upon optimal water allocation: An action to stimulate synergies of water-food-energy nexus. Applied Energy, 238, 668-682. https://doi.org/10.1016/j.apenergy.2019.01.069

[10] Ming, B., Liu, P., Cheng, L., Zhou, Y., & Wang, X. (2018). Optimal daily generation scheduling of large hydro–photovoltaic hybrid power plants. Energy Conversion and Management, 171, 528-540. https://doi.org/10.1016/j.enconman.2018.06.001

[11] Uen, T. S., Chang, F. J., Zhou, Y., & Tsai, W. P. (2018). Exploring synergistic benefits of Water-Food-Energy Nexus through multi-objective reservoir optimization schemes. Science of the Total Environment, 633, 341-351. https://doi.org/10.1016/j.scitotenv.2018.03.172

[12] Chang, F. J., Wang, Y. C., & Tsai, W. P. (2016). Modelling intelligent water resources allocation for multi-users. Water resources management, 30(4), 1395-1413. https://doi.org/10.1007/s11269-016-1229-6

[13] Jain, V., & Sachdeva, G. (2017). Energy, exergy, economic (3E) analyses and multi-objective optimization of vapor absorption heat transformer using NSGA-II technique. Energy Conversion and Management, 148, 1096-1113. https://doi.org/10.1016/j.enconman.2017.06.055

[14] Assaf, J., & Shabani, B. (2018). Multi-objective sizing optimisation of a solar-thermal system integrated with a solar-hydrogen combined heat and power system, using genetic algorithm. Energy Conversion and Management, 164, 518-532. https://doi.org/10.1016/j.enconman.2018.03.026

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