Transition to renewable energy – An attempt to model the mix of existing and future generation technologies for 2035 and 2050

doi:10.21203/rs.3.rs-1991342/v1

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Transition to renewable energy – An attempt to model the mix of existing and future generation technologies for 2035 and 2050

https://doi.org/10.21203/rs.3.rs-1991342/v1

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Pioneered by most advanced countries a global trend is taking place to eliminate fossil fuels (including green natural gas) and in some extent, nuclear plants, for electric energy generation. Part of these efforts aim at improving known and proven technologies such as wind, solar, hydro and biomass, by increasing their efficiency, as well as decreasing the contamination they produce in a greater or a lesser degree. Examining the abundant existent literature on future needs and projections of sources for energy generation, there are certainly publications that estimate the share of each technology, but they are mostly based on estimates grounded mainly on prices and trends. See for instance, Energy Information Agency (EIA) (2019). In this proposal it is suggested that said estimate should not be based only on one or two criteria like prices and contamination, but on a set of multiple criteria, related with economics, society, environment, new technologies, sustainability, efficiency, risks, geographic characteristics, climate change, etc. Consequently, alternatives or technologies should be selected based on this set of criteria, and thus, from different points of view.

However, relative evaluation must not be done individually, but considering simultaneously all technologies and the different periods, which is a complicated endeavor. This paper suggests a methodology, based on sound mathematics applied to government plans, as well as forecasted demands, to define the most convenient and efficient mix of technologies for 2035 and 2050.

Demand

renewable sources

energy matrix

technologies mix

MCDM

SIMUS

The objective of this paper is to propose a methodology to determine the mix of renewable technologies able to satisfy a given demand for 2035 and 2050, using 2022 as a base for projections.

It refers to a country, but of course, could be applicable everywhere. Thus, it involves the present, the decarbonization by mid 21th century of energy generation, the replacement of those utilities to be decommissioned, and the most convenience mix of technologies for 2035 and 2050.

Bloomberg NEF (2019) projects that wind and solar will supply almost 50% of world electricity by 2050.

Once defined the objective, section 2 analyzes the state of the art of present-day technologies, section 3 explains the proposed methodology, section 4 evaluates different technologies as well as examining their present-day sharing in the mix, which is the starting point of the proposed method. Section 5 applies the SIMUS method (Sequential Interactive Modelling for Urban System) (Munier, 2011), to forecast the mix of technologies for the mentioned dates, followed by a discussion and analysis of results and their comparison with present day estimates for the same dates. Section 6 examines the computed forecasted mixes and values, and finally, section 7, briefly explains how the SIMUS method works.

Considering the different sources of renewable energy, wind turbines, solar photovoltaic and solar thermal, biomass and hydro, there is a need to also consider the new comers for electric generation, i.e., hydrogen cells, green natural gas, and nuclear DT or DT (deuterium-tritium). Most country governments agree that about 2075 the planet must be completely decarbonized for electric generation, as well as for most developments, including transportation. This is a goal of paramount importance because it is the only way to reduce or stop climate change/global warming, which can cause the sinking of numerous inhabited islands and the coastal flooding of almost all countries with maritime coasts.

It is also vital for reducing the ozone hole, for keeping people in good health especially considering pulmonary diseases, and to preserve monuments that are World Heritage. No less important is saving a country valuable natural capital like coal, oil and gas, that can be put to a better use.

Existing technologies based on renewables, as well as using new ones that use abundant and inexhaustible resources such as sea water, to produce hydrogen, as well as deuterium for DT reactors, is the unavoidable future and that needs to be scheduled today.

The methodology proposed here is based on actual data on trends, demands, and present-day energy matrix, i.e., involving fossil fuels and renewables, and from it, aims at designing an energy matrix for 2035 and 2050, with progressive decarbonization and targeting only at renewable sources. The proposed methodology can be applied anywhere, but the selection is not universal since every country has different demands, preferred alternatives for energy generation, different type of resources as well as climate, and diverse geographic issues.

However, to achieve this decarbonization, it is necessary to select among renewables which will be used in that future, and determining their mix. Considering the existing array of technologies for generation from renewable sources, the percentages of generation assigned to each one, their multiple mix of feasible combinations, and the fact that they can’t be considered in isolation, it is evident the impossibility to reach the most convenient mix without the help of mathematical tools.

For this reason, this proposal resorts to a mathematical procedure called ‘Multi Criteria Decision Making’ (MCDM), that will select the best technologies that most efficiently satisfy demand, subject to a set of restrictions or evaluation criteria, involving technical, economic, social, safety and environmental issues. At present, MCDM includes more than a hundred of different methods, and thus, selecting the best one is another decision problem, but that also offers hints for the choice, most related with their respective capacity to solve a complex scenario like this.

The result of this application is not of course definitive or mandatory; it is only a solid platform where scientists can base their different positions about the mix of technologies, allowing them to examine and study at will hundreds of different mixes and percentages, involving traditional and new sources like hydrogen and DT.

In this paper the SIMUS method, is chosen, because it does not require assigning subjective weights to evaluate criteria, as is practically normal in all other methods, and which modify data. It also allows the performance of a rational sensitivity analysis, based on mathematically generated marginal values. This feature, quantitatively assesses the degree in which each objective is achieved, which is a vital element in evaluating technologies as well as compliance of different objectives.

The suggested result from the SIMUS method is thoroughly evaluated regarding its stability or strength, when diverse parameters, for instance, demand, price, or efficiency, may vary, in a great or lesser degree.

In few words, this paper proposes a platform, a guide, to forecast which could be the future composition of the energy mixes, or energy matrix, in two dates, which of course, can be changed. The forecast is grounded on different aspects like a country policy to continue or discontinue all types of fossil fuel plants, as well as existing fission nuclear plants, also, naturally, to the forecasted growth of the electrical demand, people approval, and state of the art of present and incoming technologies.

Accordingly, this proposal is based on known policies and plans from countries that are well advanced, at world level, in their decarbonization plans, like Germany. Needless to say, even when this paper is based on actual data and estimates from reputable sources, it is not a working paper, because of the complexity and uncertainty of the problem; it is only a guide.

Most efforts are focused in developing new technologies like using hydrogen cells (Proton Exchange Membrane Fuel Cells, PEM), and DT in power generation. The PEM has been developed in a certain extent mainly for use in transportation, like the 200 kW units for marine vessels and 30 kW for trucks, but little has been done for production of large quantities of electric energy for power plants, although there are in the market, scalable stationary units that can deliver up to 1.2 MW, and very apt to serve isolated communities. This is very important, because they can greatly reduce the energy fed to the national grid.

There is at present heavy activity, at research level, in developing hydrogen production for power plants, in many countries, like Argentina, Australia, Austria, Brazil, Canada, China, etc., as well as large industrial companies like Siemens in Germany or General Electric in France. According to Natural Resources Canada – Government of Canada (2020), ‘More than 350,000 Canadians from coast to coast could be working in the hydrogen sector’. Consequently, hydrogen utilization could be an important issue in job generation, which will account for 1% of country population in 2021.

DT is under development since the second half of the last century in small units, most of them with a negative efficiency, since the energy output was less that the energy input. A large pilot plant of 500 MW, (ITER), is under construction in Europe, under an international project effort. It probably will be in operation in 2025, but not to generate electricity, although its output will be more than ten times the energy inputted; ITER will provide a unique opportunity to test mock-up in-vessel tritium breeding blankets in a real DT environment.

Regarding wind, solar, biomass, geothermal and hydro, they are matured technologies, with a large background after thousands of installations around the world, both standalone and combined. There is an advantage in combining wind and solar because their peaks are unsynchronized (Siemens, 2022). Something similar happens with some hydro and tidal plants (or instance, La Rance, Tidal Barrage, France), where energy is produced between 12 and 15 hrs., corresponding to high tide, and pumped from 9.30 and 13.00 hrs., corresponding to low sea level, when electricity is used for reverse pumping, although the pumps have to de powdered by renewable energy.

Research in DT plants, or DT has been active for many years, and at present (2022), is under construction in France a large plant for energy generation. Efforts by universities and USA government are on the way (see Greenwald, 2021) for the design of a DT plant by 2025 to operate in the 2035–2040 time period. DT uses deuterium, an isotope of hydrogen; it is produced by distillation of water, followed by electrolysis. It also needs lithium, likewise an abundant and easily extracted element. Due to hydrolysis, renewable energy sources must precede DT, because they need the energy for hydrogen and deuterium-tritium fuel. A very large advantage of DT is the little radiation waste (radwaste), which is one of the largest unsolved problems in fission reactors.

Goldston et al (2021), give a concise and documented description on work being done and for advances in the design of DT power plants. See their publication ‘The international ITER project in France, which counts China, India, Europe, Japan, Russia, South Korea, and the United States as its partners, is starting to assemble the world’s most powerful DT’. ‘The United Kingdom has recently announced a plan to build a prototype DT power plant by 2040. China has a plan to begin operation of a DT engineering test reactor in the 2030s, while the European Union foresees operation of a demonstration DT power plant in the 2050s’.

Going DT is mainly a country decision, and thus, some countries will prefer to continue for whatever reasons, with the actual scheme of energy production, while others, taking as examples, China, Russia, the USA, Germany, as well as organizations promoting this change like United Nations, and OECD, among others, decide to transform the actual scenario, and have established plans for banning fossil fuels at certain dates, in the not-too-distant future.

Since it is expected, according to trend, that demand of energy will increase substantially in the future, and due to the decommissioning of nuclear fission plants, there could be a deficit of energy generation, which must be forcefully compensated by renewable sources of energy in variable mixes.

Beyond those dates the scenario for years 2075 and 2100 presents more uncertainties, and then, it is too risky to make forecasts, and one of the reasons, is that at present, we can’t forecast at those dates using our actual knowledge and sources, since in that future there could be new tools, that we can’t even envisage. However, there is confidence for 2035 and 2050, because exists a certain certainty - grounded on the abundant information of works being performed - that in 2035, most probably, hydrogen power plants will be a reality, and that for that date, DT will be enough advanced as to hope its implementation in the 2035 and 2050 interval.

Even when uncertainty is always present related to the future, there is something certain, which is the core of this proposal. It is the fact that whatever the method to design the future energy matrix, it always will be necessary to make a selection of available technologies subject to a set of conditions or criteria, and for that, at present, there is only one procedure, and it is using Multi Criteria Decision Making (MCDM), something, that in this author’s knowledge, has never been done.

Forecasting the composition of the energy matrix for a country or a region is a hot issue, with many unknowns. Projecting the performance of technologies for electricity generation that are in the developing stage, as DT, and in a lower scale hydrogen, is certainty difficult and uncertain. However, contrary to DT, there is at present enough experience for hydrogen, at a small scale, applied to transportation, but not to be considered in a country energy matrix.

2.1 Mature technologies

It has been already said that wind, solar, biomass, thermal, hydro, geothermal and fission are mature technologies with many years of operation. Needless to say, not all technologies have the same grade of maturity, and thermal, even considering its long time in service, is not in its complete maturity, since new advances and configurations are in place, such as co-generation, gas turbines or new types on condensers.

Wind, solar and hydro have achieved high efficiencies, although the two first are still improving in efficiency and costs. As in any other technology, a complete analysis must include their contribution to contamination, not in their operation, but in the process of fabrication of cells and solar collectors, and in their disposal. There are also technologies that have reached the largest values for reduction in capital costs. Figure 1 shows the capital costs for solar and wind; it is evident that solar, falls more rapidly that wind, both in average.

(By author, with data extracted from curve A-6, in CER - Canada ‘s Energy Future 2021 - Energy Regulator – Scenarios and Assumptions – Accessed January 07, 2022- CER – cer-rec.gc.ca)

Wind Turbines- Turbine installed at the top of a high steel column, which blades capture the kinetic energy of the wind, and convert it into mechanical energy, which is the prime mover of an electric generator. It produces clean energy, with no side effects, but some noise and eventual death of birds. They can be built on land or offshore, the best example for the latter is Denmark.

They can work continuously, that is, day and night, however, electricity generation is usually variable, either for lack of wind or for variation in its strength. Blades are designed to work in a range of wind forces, up to a limit or rated speed; when the wind is very strong, surpassing this limit, the device is automatically shut-off to avoid damage to the blades. Generated energy is inputted to the grid, or can be stored in lead batteries as a potential energy, and used when needed. There are also most advanced proposed solutions, (see in Science Daily, the concept of ‘Information Batteries’).

Contamination during operation: There is no contamination, although environmentalists are concerned about the death of birds struck by the blades.

Reliability: High

Solar (Photovoltaic (PV) and Thermal) -These two technologies use the same source, the sun light, that is, energy, but with different procedures. Both technologies are mature and reliable, and together with wind turbines are the backbone of electric generation by renewable sources.

PV can be tracked back to the middle of the1950s., and converts a stream of light into electricity through the photovoltaic effect using semi-conductors (Einstein, Nobel Prize, 1921). Photons strike the cells and knock their electrons loose, generating a flow of electrons (electric current). It generates continuous current (cc), which in most cases is further converted by inverters to alternate current (ac). According to some researchers, PV is the most used renewable source of energy, although it can only generate a few hours a day, when the sun shines.

Contamination during operation: None.

Reliability: High

Average life span: 30 years

Solar Thermal technology can be tracked back to 1968, and even when it also depends on sunlight, can generate for hours after sunset.

Solar thermal demands a far more complex arrangement than PV; it consists in arrays of reflective parabolic mirrors or dishes that follow the sun journey, concentrate the stream of light, and send it many times increased to a tower, (thermal receiver), where is used to heat a salted solution of sodium nitrate and potassium nitrate to a very high temperature, in excess of 500 degrees Celsius, and which is also used as a heat reservoir. The heat is used to produce superheated steam in a steam generator, which drives an electric generator, producing alternate current (ac), which can be directly injected into the electric grid. Because the heat reservoir, the system can generate electricity hours after sunset.

Contamination during operation: None.

Reliability: High

Average life span: 30 years

Thermal - Under this general denomination is the old and reliable technology used since 1884. It consists in a boiler, a steam turbine and an ac generator. The superheated steam from the boiler drives a turbine attached to the generator. The boiler is fueled by wood, gas, coal or oil (fuel oil). The gases in the flue are mainly composed by CO₂, CO, SOx, NOx, particulates, and others gases, with dangerous effects on persons, animals, buildings and especially the environment. Particulates are also hazardous, and they can be eliminated using baghouses, which are very efficiently (99%) in removing them.

This contamination is the reason the world wants this technology banned. When using natural gas, the emissions are much cleaner, however, the latter produces heavy atmosphere contamination of CO₂ and CH₄ (methane), during the extraction process by fracking (hydraulic fracturing), both being the main responsible of greenhouse effect and global warming.

However, CO₂ may be captured and stored in deep caverns, while CH may be used as a fuel for reciprocating engines driving electric generators.

There are several means to reduce pollution from the boiler flue, for instance, using electrostatic precipitators, as well as cyclones, while some other noxious gases can be eliminated by other means, all of them costly. For instance, fluidized bed boilers, using combustion technology, and working at near1000 degrees centigrade, are able to get rid of NOx.

Another important type of thermals are gas turbines, fed with natural gas. Large diesel engines burning diesel oil are also included in this category. At present, it is being replaced by liquified natural gas (LNG), or compressed natural gas (CNG), in transportation, especially in large trucks as 18 wheelers.

Contamination during operation: May be high due to the flue gas.

Reliability: Very high

Average life span: 50 years

Biomass – Its history is as old as humankind, but the date for its use in power generation electricity is uncertain. They are able to use a variety of raw materials for fuel such as tree wastes, waste paper and garbage. There is a controversy about considering biomass as renewable, because it discharges CO₂ into the atmosphere. Defenders of this technology, claim that this discharge adds nothing to contamination, because it is just returning to the atmosphere the CO₂ from where it was early absorbed by green vegetation for plant food, and in the process generating oxygen, by photosynthesis., i.e., a closed cycle.

Even when this may be true, biomass burning produces pollutants as follows: NOx, CO, CO₂, Particulate matter, SO₂, Volatiles, etc. According to PFPI, (Partnership for Project Integrity, 2011), a 100 MW biomass plant in Florida enmities 1,232,225 tons per year, or 1232 ton of CO₂.

Reliability: High, provided availability of materials to burn. It can work 24 hours a day, and does not depend on external factors like sun shining, winds blowing or water flowing. However, even if it does not depend on natural phenomena, is affected by costs derived from transporting materials, and then, it could be more expensive that winds and solar. In addition, in could encourage forest logging and thus, producing land erosion.

They can be built anywhere, however, the traffic a plant generate, odors and pollutants are factors than limit their construction close to cities, and normally, their construction is rejected by people.

Advantages: Save space in landfills.

Average life span: 30 years

Geothermal – Uses heat stored in the Earth’s core and at about 300 degrees Celsius, and are able to generate clean, renewable energy. Suitable sites for its exploitation exist in many countries, most in USA, and with diverse power, the largest with 1600MW.

Contamination during operation: None

Average life span: 30 years

One main disadvantage is that it is site specific, i.e., they can be built only in certain places. It is very expensive, and in operation they can release certain contaminant gases from depths of the earth, and it is less cost-effective than other technologies.

Nuclear fission power plants are based on splitting the nucleus of the atom formed by neutrons and protons. When this happens, the resulting elements have less mass than they had in the nucleus. Consequently, the missing mass is converted in energy (Einstein. mass-energy equation e = mc²). This type of energy generation con be traced to about 1960. According to Statista Research Department, there were 441 nuclear power reactors in 2021 in 31 countries.

Splitting atoms is performed through a chain reaction and thus generating very large quantities of heat, which is further used to drive steam turbines. Their role is similar to the work of boilers in conventional power plants. Nuclear reactors are safe but accidents can be catastrophic, Chernobyl, Three Miles Island and Fukushima bear witness of the consequences of failures, which are extremely serious in human life and for the environment. For this reason, they are feared and rejected by the majority of population as well as by many scientists, and some countries have decided to progressively shut them down. As a matter of fact, the European Union banned in 2017 the construction of new nuclear plants in the member countries. Wüstenhagen (2022).

Contamination during operation: They don’t contaminate; however, their spent radioactive elements (rods) do, and due to that they must be stored in especially built constructions and constantly monitored. Until these days no solution has been found to get rid of this radioactive waste or use or recycle it, which effects can last thousands of years.

Reliability: They are reliable

Average life span: 70 years

DT or Deuterium-Tritium (DT) power plants. It is a rector working with plasma, an ionized gas considered the fourth state of matter, which the Massachusetts Institute of Technology (MIT) defines as ‘Superheated Matter’. Plasma is confined in a toroidal chamber reactor called ‘Tokamak’, invented by Andrei Sakharov, a Russian physicist. The plasma is hold in the chamber by powerful magnetic forces. The first Tokamak was built about 1968 by Natan Yavlinsky. Up to recently, Tokamaks needed more energy than generated, however, it appears that new reactors could generate 20 to 30 times more energy than imputed.

The fuel for DT is deuterium (D) and tritium (T); both are isotopes of hydrogen, abundant in sea water. DT, as well as thermals, biomass, fission and hydrogen cells, needs a continuous flow of material inputted; in this case, D and T. The other technologies, such as wind, solar, hydro and geothermal, once built, do not need anything, since they receive naturally a continuous flow of natural resources, such as wind, sunlight and very hot water from depth on earth.

DT reactors follow a very complex procedure to generate energy, which is synthetized as follows:

Opposite to fission, DT is based on binding or fusing two light atoms, and as a result making a heavier one, which is heavier than the two original atoms, then, this difference of mass is converted in energy. (Einstein, mass-energy equation e = mc²). Deuterium and tritium, both abundant in Earth, don’t exist in natural state, i.e., they must be ‘fabricated’. DT technology is difficult, because to produce DT it is necessary to heat plasma at 150 million degrees Celsius, 10 times higher than the temperature in the Sun, that produces DT at about 15 million degrees Celsius. The large difference with the Sun is due to the pressure in its core. Since we don’t have such a pressure in Earth, we must get the DT effect working at much higher temperatures.

From our point of view, it is very important to consider a project that is being developed; it is coded ITER (The ‘Way’ (to a new energy), in Latin), being built under the ITER Agreement, consisting in the construction of the largest Tokamak, with an output of 500 MW, and located in south-east France, scheduled to be completed by 2025. According to scientists ITER will have a relation 1:10, that its output will be 10 times larger than the input.

“As signatories to the ITER Agreement, the ITER Members China, the European Union, India, Japan, Korea, Russia and the United States will share in the cost of project construction, operation and decommissioning, and also share in the experimental results and any intellectual property generated by the project” ITER (ITER Webpage).

If successful, it will be probably the most important landmark in the 21 Century. when completed, in 2025, it will be used to test the technology to manufacture large scale reactors and thus, paving the way for the construction and commercial operation, perhaps in 2050.

A measure of its importance can be understood by the fact that mankind can get immense amount of clean energy, from inexhaustible sources, and be forever free of fossil fuels and wood that have been our energy staple for centuries.

DT can generate abundant and clean electricity without the dangerous radiation levels of fission energy, which needs its highly radioactive wasted rods be stored in especial places and with its radioactivity lasting for thousands of years.

Fuel cells -They appeared in 1932 by the work of William Grove.

They work with hydrogen, producing clean energy with clear water as a residue.

The cell has made remarkable advances in small and large applications, however, hydrogen does not exist free in nature as other elements, such as Al, Cu or Lithium, and in a form that permits its immediate use, consequently, it must be ‘fabricated’, or extracted. Fortunately, it is one of the most common elements in Earth, however, hydrogen extraction has a high cost in electricity, therefore, researchers agree that renewable sources like PV, solar, hydro, etc., are appropriate supply sources.

The way to generate electricity by a fuel cell is very simple. Stored hydrogen and air from the atmosphere are inputted in a device with two electrodes, cathode an anode, separated by an electrolyte; a very similar structure as in a battery. When hydrogen is fed to the anode and air to the cathode, the hydrogen molecules in the anode are separated, through a catalyst, (platinum), into a proton and an electron. The flow of electrons constitutes the electric current which is sent to an external circuit such as the electric motor of a car. The flow of protons migrates to the cathode, where combines with oxygen producing water.

According to Toshiba the fuel cell has a 55% efficiency, and Wintle (2020), CGTN (China Global Television Network), envisages a generation capacity of 6 GW by 2024 and 40 GW by 2030.

Platinum is one of the most expensive elements and deteriorates with use. Recent research indicates that it can be replaced by ‘Hydrogen-oxygen polymer electrolyte membrane fuel cells (PEMFCs)’, developed by Ramani et al (2020). This is a very important advance in the future use of hydrogen cells, and most probably will pave the way for construction of large stationary units.

There is in operation a range of fuel cells for different uses, from small to large output. For instance, Ballard, installed 1 MW containerized fuel cell system in France. They can also be used for urban and long-distance trains. Due to all these advantages, it seems that hydrogen cells will be a leading technology.

However, it appears that for large stationary generation plants, the ideal is a combination of green natural gas and hydrogen.

Nowadays, billions of dollars are spent in research as well as looking for novel ways to produce the so called ‘green hydrogen’, using different processes, mainly involving electrolysis, with power generated by renewable sources, as well as from treating and processing paper waste (see Choo, 2021).

Electrolysis is costly, however, one of the main drawbacks for using hydrogen is its storage, since it requires very high pressure. This, together with its low density, presents some problems in transportation, but probably not in stationary power plants.

Contamination during operation: None

Reliability: Very good

Cons: It depends on hydrogen, that must be produced.

Hydro power plants. The first one was built in 1882 in Wisconsin (USA). These are normally very expensive constructions. A concrete or earth dam is built across a river, and consequently, creating a lake or pond behind. The dam houses hydraulic turbines, driven by water discharging from the lake through a steel conduct or tunnel called penstock. Dams are very strong constructions and their life spans for more than a century.

Contamination during operation: None. However, construction of a large hydro plant normally involves the flooding of agricultural land and forests, and the removal of people leaving in those areas.

According to some scientists the large volume of water in the artificial lake may have geological effects and produce tremors and earthquakes.

Reliability: They are very reliable

Average life span: 100 + years

2.2 Comparison of technologies

Since we use several different technologies, it is evident the need to compare them and select the most important from different points of view. However, it is not easy or possible, even when analyzed under the same set of criteria. The reasons are:

* We don’t have a common base for comparisons. The most logical is efficiency, however, there are several efficiencies, for instance, thermal efficiency is related to thermal energy in the fuel, while mechanical efficiency measures the capacity of a device to convert inputted energy in mechanical work.

* To generate electricity from fossil fuels as well as from nuclear fission, there is not only one mechanism but several. In a conventional power plant, there is a series of different devices such as boilers, superheaters, turbines, alternators, condensers, and pumps, and each one with its own efficiency.

In a PV solar plant, the efficiency refers to a ratio between the amount of electricity generated and that received from the sun. In natural gas plants there is thermal and mechanical efficiency using the turbine and the electric generator. In a hydro plant it is the ratio between electricity delivered by the hydraulic turbines and dynamic energy of the water flow.

An overall efficiency value may be computed for each system; however, it does not take into account aspects such as capital and operation costs, land use, jobs creation, contamination, etc.

If we want to compare electric generation systems, we need to contrast the different systems when each one is considered in full., and even its life cycle.

* We could use a metric such capital cost/MW, but it appears not to apply to all technologies, because the different work needed for some technologies in preparing the necessary ‘raw materials’ such as enriched uranium, or natural gas to get ‘green gas’, or ‘green hydrogen’, or collection of material for biomass, and that should be included in capital costs, as well as the cost of dismantling installations such as nuclear plants or thermos electricals.

* Not all technologies have the same useful life, and thus hydro usually last for more than 100 years, while thermoelectric probably 50 years, or 30 years for solar.

* Not all technologies have the same capacity factor. Some can work day and night for years, while others work only when sun shines or wind blows.

* We may have a hint, but there is no way for us to know with certainty which new technologies will appear in the next 50 years.

* Technologies can be used standing alone or in thermal combined arrangements, as well as solar and thermal.

* No less important is the fact that some technologies may change in the future increasing their efficiency, while others may decrease their costs, as is envisaged for wind and solar for 2035 and 2050. Consequently, a single change in one technology may trade-off better than another one, which in principle was superior in the last period.

Since the energy matrix represents a system involving different technologies, all of them subject to the same criteria or objectives, the analysis must consider simultaneously all potential variations for each alternative, expressed by the respective performance value in each criterion. This is the reason by which we can’t consider, analyze and predict the performance of each technology independently, and then, adding them up, because a system can’t be partitioned, since the result is not always equal to the sum of the components. This is the core of this proposal.

3.1 Analyzing the problem

The large variety of technologies, their relative advantages and disadvantages, the uncertainty regarding when new technologies may be available and in continuous operation, future demands, their dependency to a set of restrictions or criteria, and their comparison that was explained in section 2.2, make very difficult to select a technology over another, let alone a set of technologies for each period, and this is the reason why mathematical models are needed. As mentioned, this proposal works with a mathematical discipline named Multi Criteria Decision Making (MCDM).

There are more than 120 methods in MCDM, and most of them need to determine weights for criteria, such as investment, unit cost per MW, alternative feasibility, job generation, alternative efficiency, environment, etc., since in most cases they don’t have the same relative importance. Unfortunatelly, these weights are computed subjectively, and thus, highly disputable, and most important, impossible to verify.

Among the different methods, SIMUS was chosen because it releases scientists from the heavy task of estimating those weights for criteria, especially considering that normally there is a team that must be in agreement on a large quantity of values that don’t have any mathematical support. When hundreds of scenarios must be considered, it is understood the difficulty of this task. In SIMUS, those weights are mathematically computed.

Another advantage of the method is that it determines automatically the degree of compliance of each criterion or objective. For instance, how much, in percentage, objective ‘Minimize investment’ is achieved with this selection of alternatives?

It also allows the performance of a sensitivity analysis that examines how strong is a solution reached. This strength is related to the stability of the best solution when some criteria change in significance.

That result depends on circumstances or criteria that can change, due to different reasons.

Consequently, it is important to determine how much a criterion affecting the best solution can vary, increasing or decreasing, without affecting the position of the best alternative. For instance, let’s assume that the best alternative is hydro-electricity, and that one of the criteria is ‘Effect of global warming on alternatives’, with an expected maximum limit of 1.5 degrees Centigrade increase in the next 50 years; it is important to analyze how that increase will affect some hydro-power schemas to be built in the future, regarding water availability.

Rivers that have their sources from melting ice high in the mountains, may be badly affected because global warming, due to the melting of glaciers and less snowfalls. Considering that hydro dams are built to last 100 + years, there is the possibility that operation of hydro plants will be highly reduced, and even become not suitable for power generation, because reduced water flow, and thus, it could be that hydro electricity ceases to be the best alternative. Therefore, there is a pressing need to determine how much increase in global warming can sustain hydro dams and keep being the best alternative.

The same may apply to deforestation of the Amazonia and other large wooded areas, which to a great extent determine global rainfalls.

This analysis must be performed for the best, the second and the third best solutions, considering all criteria that affect them the most, for instance, EROI, NPV, investments, etc. Obviously, not a calculation for a human mind.

From this information, scientists, with data on demand, can determine the capacity of each alternative for each period.

Example

An example is proposed with real data extracted from various sources. This author wants to emphasize that this exercise is not intended to represent reality; its only purpose is to explain the methodology. A real case must consider more alternatives and many more criteria, but the process is exactly the same, independently of the quantity of data and even adding especial criteria.

The process starts with the present-day energy matrix, i.e., with data on total capacity installed, technologies used, percentage of each one, and capacity estimates for 2035 and 2050, to satisfy demand. In this case, for 2022 it is assumed that demand is 1000 MW. For 2035, a 30% increase is chosen in accordance with estimates from several sources, and thus, the installed capacity must be 1300 MW. An increase of 35% for 2050 gives 1755 MW.

These estimates are based on current trends that also consider future sharp increments due to many factors like demography, climate change, population living longer, reconversion of cars to electricity, and new initiatives as the mining of crypto currencies, industry robotization, etc.

Criteria don’t need to be the same for all periods; we can delete or add some of them, and this depends on time, i.e., the model must take into account potential changes along time for some criteria that perhaps, because lack of information, were not considered in former analysis. For instance, it could very well be that for 2035 aiming at 2050, there will be new criteria, or some of the existent modified.

An example for the latter: In options such as hydrogen cells, an actual criterion could address feasibility for large output units, for which we don’t have experience and values. This author navigated the Web trying to find the reason by which there is no information about this issue in spite of the extensive range of applications. Apparently the largest is 1 MW, which is out of the range regarding large power stations.

Perhaps the reason is the hydrogen storage and the inherent risk associated, or the very expensive amount of platinum needed, or it could also be the high cost for getting green hydrogen, compared with other fuels.

Who knows, perhaps in the future scientists find a way to use the hydrogen cells in power stations. They could use tools and procedures that we don’t know or even hint now.

Table 1 shows the composition of the initial energy matrix for 2022, and estimates for 2035 and 2050, as per present-day knowledge.

In columns are the different technologies, and in rows nine criteria that will be used for their evaluation. These criteria (Ci), are:

Percentages of participation (C1),
Capital cost (US$) (C2),
Operation and Maintenance cost (US$) (C3),
Capacity factors (%) (C4). It is the ratio between the energy generated in the working hours /day, and the energy that would be generated in 24 hours at full rate,
Land needed (km²) (C5)
Efficiency (%) (C6),
Availability per day (hours of operation) (C7),
Useful life (years) (C8),
Contamination they produce in CO₂, NOx, CH₄, etc.(ppm) (C9).
Percentages of participation (C1) (not shown, because it is the result of a further computation), The shares by each energy sources give a better approximation of final energy consumption (Ritchi et al, 2020).
Capital cost (US$) (C2),
Operation and Maintenance cost (US$) (C3),
Capacity factors (%) (C4). It is the ratio between the energy generated in the working hours /day, and the energy that would be generated in 24 hours at full rate,
Land needed (km²) (C5)
Efficiency (%) (C6),
Availability per day (hours of operation) (C7),
Useful life (years) (C8),
Contamination they produce in CO₂, NOx, CH₄, etc.(ppm) (C9).

Table 1 Initial decision matrix and proposed matrices for 2035 and 2050

	2022					2035				2050
	Wind	PV	Biomass	Hydro	Thermal	Wind	PV	H₂	Thermal	Wind	PV	H₂	D-T
Percent age of participation C1	20.1 8.8 7.5 3.4 43.2 Percentages are from Clean Energy Wire for 2021, which shows that the installed capacity and energy mix					Estimates from researchers based on SIMUS results for 2035				Estimates from researchers based on SIMUS results for 2050
Capital cost C2	1700	1750	2600	30	1181	1800	600	42	950	800	500	500	663	MIN
Operation & Maintenance C3	40	25	91	0.125	35	29	11.5	0.0062	29	30	10.9	0.0059	67	MIN
Capacity factor C4	0.35	0.17	0.67	0.4	0.7	0.4	0.42	0.9	0.8	0.42	0.46	0.9	0.7	MAX
Land used C5	2.46	0.16	5.85	0.01	0.076	2.46	0.16	0.004	0.076	2.44	0.14	0.9	0.081	MIN
Efficiency C6	0.34	0.3	0.45	0.9	0.4	0.36	0.35	0.9	0.5	0.36	0.35	0.9	0.8	MAX
Hours per day C7	19	5	24	24	24	19	5	24	57	13	5	24	24	MAX
Life C8	20	30	30	100	50	20	32	30	50	20	32	30	50	MAX
Contamination CP	0	0	0.8	0	0.5	0	0	0	0.5	0	0	0	0	MIN

Notice that criteria include economic, technical, social and environmental aspects. The number of criteria can be greatly increased, if necessary, and there is no limit. The role of these criteria is to evaluate the technologies considering the degree of participation of each one in the criteria. This participation is expressed in values that conform reality, and are mostly objective, for instance, capital cost, capacity factor, etc., which values (performance values), are known for each alternative.

This is the format of the initial decision matrix in MCDM, and it is designed to model mathematically the real scenario as close as possible. For this reason, a new component must be added, which is the specification of the action of each criterion, for instance, capital cost must be minimized, efficiency maximized, and there could also equality, if investment (not here), must be equal to a certain amount.

In applying a MCDM method, in this case SIMUS, its result indicates the relative importance of each alternative, for each period. This information is paramount, because it allows the definition of polices to determine which technologies must be improved, to be included in the package of technologies for the next period, and looking for the greatest efficiency.

For instance, assume that solar (PV and Solar Thermal), have the highest score. Then, it indicates that it is worth to investigate these technologies in comparison to others, because their large efficiency. Since it the next period, percentages must be forcefully increased, this analysis shows that solar must be given particular attention.

At present, large international organizations ponder the percentages of participation of different technologies for 2035 and 2050, normally based on trends and assumptions, and thus, showing increases of respectively 30% for 2035, and 35 % for 2050. However, this procedure would be misleading, due to the potential change of data in criteria between current dates and 2035 and 2050, i.e., data in criteria normally change along the years, especially in technical aspects.

For instance, capital costs for wind and solar have been in constant decline (Figure 1). Data from CER (2020) allows comparing capital cost for them. The first decline, has a linear trend, see formula, from 2020 to 2050, while for solar the decline is logarithmic, and as 2050 capital cost for solar are much lower than for wind.

3.2 Factors to consider about the future of existing renewable sources for energy generation

Performance values change
Trends in Fig. 1 show that solar capital cost decreases more rapidly than wind, consequently, there could be differences in the performance values of these technologies, and in addition, these changes may influence others criteria, for instance, land needed, as well as energy generated., therefore, it could be changes in the land use.
Discontinuing existing installations.
Stakeholders, in accordance to the policy of shutting down nuclear fission plants, have the mandate to discontinue this type of installations. This leads to looking for renewable sources to compensate for the loss of the nuclear fission plant, such as wind, solar, biomass and hydro, until technologies like hydro, hydrogen and DT will be able to take the whole load. There will also be additional benefits with this final replacement, since many km² of valuable land would be freed, for agriculture, human settlements or industries, after dismantling these installations, except perhaps hydro.
Keeping existing installations

In opinion of this author, hydropower plants will continue well into de 22nd century.

Hydropower plants have been built in many countries, and have demonstrated their reliability for more than 100 years as the workhorse for energy generation. They are in general large and resistant structures than can still be of service for years to come. Plants as the Three Gorges Power plant in China, still young, has a capacity of 22,500 MW, Itaipú in Brazil, with about 20 years old, 14,000 MW, The Hoover Plant in the States, 2,080 MW, in 1935, etc. There are still many places in the world with mighty rivers where hydro plants can be built.

Consequently, even if studies supported by mathematical procedures such as MCDM, suggest their dismissal, most probable they will be kept in operation. They depend on the flow of water, and once built and in operation, need little maintenance, no replacement during long periods, high reliability, and no contamination.

However, it is necessary to consider the possibility of gradual loss of capacity due to reduced flows of water, in those rivers which sources depend on heavy snowfalls in high mountains; decrease caused by global warming. It is expected that by 2050 there will be enough knowledge and statistics about this phenomenon, on which scientists can be based to determine keeping old plants and construction of new hydro plants.

As other energy generators, they can be updated, and after 30 or 40 years of operation, improve valves, penstocks, turbines, and sluice gates, consequently, they should not be considered for shutting down, rather perhaps as a reserve for peak hours.

Hydropower stations can be shut down, but their utility can be still very significant, because the artificial lake formed behind the dam, may serve for centuries as water reservoir for agriculture, drinking water, recreation, fishing, tourism, etc.

This is a fundamental step in the process of forecasting the use of future technologies, and may be done considering two complementary procedures:1) Reasonable and educated estimates, as well as future options, still in development like hydrogen and DT, and 2) Considering technical, economic, social and environmental issues and their interrelationships according to existing and new technologies. It is believed that this second aspect, was never addressed before, and it is the main subject of this proposal.

This is a complex task, because it involves analyzing how the mix and participation of each alternative changes, when performance factors such as capital costs, contamination, capacity, etc., vary along the years.

This analysis is beyond human capacity, due to the thousands of possible permutations, and consequently, requires the use of mathematical tools to get a result with the maximum efficiency. As mentioned, this paper proposes the Multi Criteria Decision Making (MCDM) procedure to solve this problem, and within its catalogue of techniques, the SIMUS method.

It uses criteria, i.e., conditions that each energy technology must meet, and finds the best solution in form of a ranking of technologies scores, the higher the better. ‘Best solution’ means the set of technologies that better satisfy all criteria simultaneously, i.e., from the economic, social, environment and technical point of view, and for a certain demand of energy. When data changes say from year 2022 to 2035, due to new costs, demography, environment, efficiency, etc., including an increased energy demand, the percentages of participation of each technology also change, which produces a new ranking of technologies from 2035 to 2050, and also a change between 2050 and 2075.

Criteria are used to evaluate technologies. They establish conditions than technologies must satisfy to a greater or lesser degree. In this example, nine criteria are considered, but there could be many more, perhaps in the hundreds, and in this case, interrelationships among criteria will increase dramatically, and thus, becoming unmanageable, unless using mathematical aids.

4.1 Very important aspects to consider in this problem

4.1.1 Precedence

Any period (n) is affected by the work done in the precedent (n-1), depending on how well the whole system performed and advanced between (n-1) and (n).

As an example, if a planned shutting down of fossil fuel plants, during 2022/2035 is incomplete, it may mean that those plants must continue for some time in 2035/2050. Same, if for instance, putting in service during 2022/2035 a new technology like hydrogen is delayed, obviously, it will affect the set of technologies foreseen to be in operation in the next 2035/2050 period. Consequently, the two periods, 2022/2035 and 2035/2050 must be considered simultaneously, and this is done using precedence, indicating for instance, that design and construction of renewable plants must precede the shutting down of oil fired or coal fired plants.

4.1.2 Balancing

If in a period such as 2022/2035 it has been decided for instance, to shut down nuclear fission plants, most probably there will be necessity to increase generation capacity of the balance of plants and /or build new renewable ones. At the same time, probably the decommissioning of nuclear and/or thermal plants must also be executed in the same period. Therefore, a balance must exist between shutting down plants and updating existent, or building new ones. This is extremelly difficult, due to many known and unknown factors, such as government funding, manufacture and availability of new equipment, demand, land availability, state of the new technology, etc.

It is essential to work with probabilities here, and then, aggregate two new criteria: Probability of shutting down in a relative short period of 13 years, and probability that updates and new equipment will be working at 100% capacity by 2035, also in 13 years. We can say for example that probably 80% of the updates and new constructions will be in operation by 2035, and that probably only 65% of shutting down will be done by 2035. Thus, we need to add these two new criteria, and leave to the software to find the balance, of course, including the original 9 criteria.

4.1.3 Uncertainty

There is uncertainty regarding the start of new technologies operations, as well as on costs, performances, reliability, demand, prices for energy sold, government subsides, distribution, etc., and thus, with probabilistic performance values, such as time for dismantling thermal and fission plants, and to build new ones, where naturally, the second must precede the first, etc. Of course, there is a wealth of information about all of them because trends, past data and advances in technology, but sometimes that is not enough.

An example could be hydro plants. They have been built and in operation for a long time, are reliable, and expected to continue in operation for many years to come.

However, as we have examined, there is not guarantee that their electric output will continue at the same rate as present, because the mentioned global warming, which in the future could compromise the working of the plant, because lack of water. This means, that a study like this, should involve more that determining the mix of technologies, because it also must contemplate international plans and agreement for reforestation, CO₂ decrease and storage, and find uses for CH₄.

These series of uncertainties may be reduced using fuzzy logic (Zadeh,1968) (also within MCDM), for every performance value, technology and demand. That is, we can assume for instance, that probability of shutting down all nuclear plants varies between 55% and 72% and getting an average using a triangular fuzzy distribution.

In this proposal, which is not a working paper or a feasibility study, are considered, other than forecasting demands, the variations of conditions as well as precedent periods performance. In this way, the result achieved in each period serves as a platform, a reliable base, where stakeholders can use their knowledge and judgement, to forecast the mix of options and percentages for certain years in the future.

4.1.4 Examining actual values for 2022, 2035 and 2050

At present (2022), we can use statistical values for percentages of participation, regarding an arbitrarily assumed total generation capacity of 1000 MW, and forecasting for1300 MW for 2035 and 1755 MW for 2050, the respective percentages for the forecasted energy demand, i.e., with increases of 30% for 2035, and 35% for 2050, on the precedent demands, and thus, it is possible to prepare Table 2.

Table 2 Assumed percentages of utilization of different technologies in 2022

Technologies: Wind Solar Biomass Hydro Thermal Fission

Percentages: 0.22 0.09 0.08 0.04 0.44 0.13

Notice that thermal is the dominant alternative, followed by wind, and with hydro having the lowest percentage.

Table 3 Assumed percentages of utilization of different technologies in 2035

Technologies: Wind Solar Biomass Hydro Thermal H₂

Percentages: 0.32 0.17 0.06 0.03 0.32 0.10

Thermal continues being the dominant alternative, followed by wind.

It is very similar to 2022 which could mean that not significant changes will take place on the next 13 years. However, thermal has declined from 44–32%, and fission has been replaced by hydrogen, that has been developing since 2022.

It may indicate that starting on about 2050, electric generation will be dominated by wind, thermal, DT and hydrogen, keeping existing hydro as a reserve, or to reinforce the grid during some very high demand periods.

Thermal shows a continuous decline, probably due to plants taken off service. However, it should be considered the advances being done to get clean coal plants, which can be registered by adding a new criterion like ‘Highest allowed limits pollution from coal plants’, that obviously, should be very low.

Table 4 Assumed percentages of utilization of different technologies in 2050

Technologies: Wind Hydro Thermal DT H₂

Percentages: 0.32 0.03 0.21 0.20 0.24

Wind is now the dominant alternative followed by thermal, DT and hydrogen. It appears that by 2050 the country will continue using thermal, although in considerably less percentage (21%). Thus, considering the rate of participation of thermal, it may be hypothesized that thermal will continue perhaps up to 2075, and completely replaced by 2100.

It is necessary to take into account that decommissioning thermal and nuclear fission plants may take decades, not only because the complexity of the task, but perhaps more important, because updating or increasing renewable installations, may take a considerable time.

This example assumes that these updates and increase of existing installations will materialize in the 2022/2035-time interval, with the incorporation of hydrogen technology. It appears that such a complex and costly technology like DT, probably will not be ready by 2035, but probably for 2050 or later.

SIMUS is a MCDM method that starts with an initial decision matrix, very similar as depicted in Fig. 1, that is, with the set of technologies in columns and the set of criteria in rows. Given an objective, it finds the dimensional space that contains all feasible thousands of solutions of a problem. This space can be a polygon, a polyhedron or a polytope, depending on the number of technologies (2, 3, or ‘n’) respectively.

This analysis is sequential or iterative, and determines which is the optimal solution, i.e., in this case, it identifies the technology that best satisfies all criteria, in compliance with the given objective, using the Simplex algorithm (Dantzig, 1987).

It starts from the origin of the coordinate system, whatever it may be, follows a progressive path, and performs an analysis of each vertex of the dimensional space (iteration), to verify if it corresponds to the best solution, since it is always in one of the vertices, according to the Linear Programming Theorem (Kantorovich, 1959). That optimum is achieved when a vertex is tangent to the objective function. At that point, the Simplex algorithm gives the optimal scores or importance of each technology.

The SIMUS method, based on Linear Programming, converts criteria in progressive objectives, and using the Simplex algorithm finds the best technology in each case.

The collection of optimal scores is saved in a matrix called ‘Efficient Result Matrix’(ERM), and using weighted sum for each technology, computed by the algorithm, determines de importance or significance of each one. The weights are obtained mathematically as a ratio between the number of satisfied criteria and their total number. Therefore, even when data may be uncertain, the result using them, is completely objective.

Since Linear Programming works with inequations or spaces, instead of lines as in equations, it is very suitable to solve problems of this type, since criteria are not restricted to certain values. The combination of the different criteria spaces forms the dimensional space, on which vertexes the analysis is performed.

Table 4 shows the ERM matrix; the solid row depicts the different scores. Immediately below technologies are arranged in the order of importance. This is the guide for the analysis in each period; obviously, the most efficient technology, regarding compliance of all criteria, is the first candidate to update. Notice that technologies that don’t satisfy criteria are not considered.

One of the advantages of the chosen SIMUS method, is that the software takes the ERM matrix, with its collection of optimal scores obtained by repetitive use of the Simplex algorithm, and from it, applying a known MCDM procedure called ‘Weighted Sum Method’, finds a solution, i.e., selects the best alternative, and depicts a ranking in order of importance, of the remain alternatives.

After that, the software takes again the ERM matrix and applies another MCDM procedure called ‘Outranking’, finds the best alternative and depicts the ranking of the remaining alternatives.

The comparison of the two results and rankings reveals that both are identical, consequently, both procedures, check to each other.

There is no doubt that in every country, energy projections are taken seriously and based on the available present information and forecasts, but it seems that the energy matrix is composed by technologies that have been added or updated individually, just trying to satisfy the demand, looking for costs and new developments, and without realizing that the energy matrix of a country is a system, and as such, it can’t be developed independently by considering each individual technology, and then, adding them up.

It is a complex and integrated system involving demands, generation plants, transmission and distribution, and reckoning that installations for year 2035 must be based on what is done in 2022 and beyond; the same for 2050, which it will depend in a large extent on what is managed for 2035 and onwards. Consequently, this author believes that projections must be based considering that it is a dynamic system, and thus, changing as new demands and new and more efficient and environmentally friendly technologies appear. In addition, it must be deemed than once an electric generation plant is built, it must last for decades.

Based on this core concept this proposed methodology develops a working strategy than includes plans with different objectives (meaning not only electricity generation but also society, environment, resources, economics, etc.), and involving the state of the art of various technologies.

Table 5 shows the percentages corresponding to technologies estimated at present, as well as those computed by the SIMUS method considering the same set of criteria, for 2022, 2035 and 2050.

Note than in some years there are two numbers. For instance, for biomass in 2035, 0.22/0.35. The first one is what SIMUS suggests, and the second one, bolded, is what the DM could assign considering that there is need to satisfy demand. For instance, for 2035, SIMUS gives only two values, for solar (0.12) and for biomass (0.22). Since biomass has the largest score. It is assigned 13% increase, while solar gets a 2% increase. The balance, to satisfy demand goes to thermal (although decreasing its participation looking further for its elimination), hydro and wind, the latter with 6 more percent points (to favor renewables). In this way the researcher increases first the capacity of most important, and after he/she increase and decrease according the environment and plans for decommissioning.

The same procedure is applied for 2050. Observe that actual estimates assigned thermal 0.21, while computation assigned it zero. Hydro was selected by computation requiring a very large increase, for 0.03 to 0.08.

Table 5 ERM matrix showing in the solid row scores by technology

Table 6

Comparison for 2022 between actual and computed percentages
	Solar	Thermal	Hydro	Wind	Biomass	Nuclear fission	Sum
Actual for 2022	0.09	0.44	0.04	0.22	0.08	0.13	1
Computed for 2022	0.36	0.25	0.20	0.10	0.10	0	1

Table 7

Comparison for 2035 between actual and computed percentages
	Solar	Thermal	Hydro	Wind	Biomass	H₂	Sum
Actual for 2035	0.17	0.32	0.03	0.32	0.06	0.1	1
Computed for 2035	0.12/0.14	0.10	0.03	0.38	0.22/0.35		0.34/1
■ Plain: SIMUS mathematical procedure Bold: Estimation procedure

Table 8

Comparison for 2050 between actual and computed percentages
	Solar	Thermal	Hydro	Wind	Nuclear DT	H₂	Sum
Actual for 2050		0.21	0.03	0.32	0.20	0.24	1
Computed for 2050	0.12		0.08/0.11	0.29/0.35	0.20	0.22	0.37/1
■ Plain: SIMUS mathematical procedure Bold: Estimation procedure

Comparison reveals that for 2022:

Solar is too low (9%), computation increased it to 36%
Thermal is too high (44%), reduced to 25%
Hydro is too low (4%), decreased to 20%
Wind is too low (4%), increased to 10%
Biomass is too high (22%), reduced to10%
Nuclear fission from 13% to 0.

It is worth to notice that the software eliminated the nuclear fission plants, not because some countries plan to shut them down, but because it does not satisfy simultaneously all criteria. Obviously, its elimination forces to distribute its generation among other technologies.

This comparison shows that present-day energy matrix, does not take into account restriction criteria related to different anthropogenic activities.

Comparison for 2035

SIMUS finds a participation of 12% for solar, less than the 17% actual. A reason could be the disadvantage of this technology that can work only some others a day, in comparison with others that operate 24 hours. This I an aspect that possibly was not taken into account.
More wind participation of wind and lower participation of solar
More participation of biomass, from 6–22%
No participation of DT and H₂. It is difficult to assess the reason for this absence, however, it could be attributed to the low percentage of H₂ (10%)

Therefore, the software detects a very critical situation for 2035, produced by the simultaneous shutting down of many thermal and fission plants.

It appears that part of thermal should be kept in operation, as well as 100% of hydro and biomass, or that plans elaborated in 2022 revised, perhaps delaying for 2050 the total shutdown of thermal.

For instance, biomass

These scores or degree of efficiency from SIMUS have been obtained by considering simultaneously all data for 2022, 2035 and 2050.

As seen, in this SIMUS result for 2022, the nuclear fission alternative is missing. The explanation is that it is considered not important with relation to the others. However, if it is going to be shut down and decommissioned, it can be done when others types of plants can take the load, consequently, and according to the scores, the first candidate is wind. It is expected that for 2035 fission it is no longer in operation and the 1300 MW will be generated by only two sources, according the result from SIMUS, i.e., solar and biomass.

This is the mathematical result for maximizing efficiency and not to meet demand, As can be seen, the method does not indicate the mix to satisfy demand, it selects the technologies based on efficiency, and then, it allows government agencies to decide how to complete the load, and which investments and updates must be done to replace those decommissioned generation plants. This explains why the methodology must be seen as a solid platform for decision making.

As a platform, the method allows performing hundreds of tests, each one with new values, and in a brief period. This will allow to have a panorama of how different changes affect the results.

Comparison for 2050

SIMUS selected only two technologies: Wind with 29% and hydro with 8%. To achieve the total demand, and since wind has the highest score, it is increased to 35%, while hydro to 11%. Since both amount to only 37%, it is necessary to determine which other technologies will make it. The first candidate is H and then nuclear DT with 22% and 20% respectively. The loas is completed with solar (12%).

As can be seen for 2050, all electricity generators are renewable. This contrasts with former estimates made in 2022 where for 2050 there still will be thermal plants responsible for 21% of the demand.

A method is proposed for building a platform that allows taking decisions in 2022 about how to satisfy demands in 2035 and 2050. This platform provides for each period the most efficient mix of technologies for electric generation, considering not only generation and technical issues but also how each one will perform regarding society, environment and economics.

Starting in 2022 the method indicates which is the best mix of technologies to satisfy a demand in 2035, assumed to be a 30% larger than in 2022. These technologies are ranked from best to worse, and the method also suggests shutting down some installations, as well as considering new technologies, for 2035. In turn, for 2035 it suggests the best mix for 2050. In 2050, the best mix for 2075, and so on, i.e., it is a progressive assessment.

Undoubtedly, this is a very complex problem that needs a balance among many aspects. There is uncertainty in future values for demand, costs, performances of each technology, people acceptance, impact on the environment, etc., as well as how sure we are that new technologies sch as hydrogen and DT will perform in the future. Possibly, existing uncertainty in 2022 will be certainty in 2035 for hydrogen, and a much better knowledge about feasibility of using DT, that perhaps by 2050 becomes reality.

For this reason, this research works with two main concepts: The necessary and sometimes subjective forecasting from agencies and decision-makers concerning selection for the future, and the assurance that they have reality, due to mathematical results, about the consequences regarding all interactions among intervening factors. Consequently, this methodology offers a platform estimate, obtained by mathematical methods, on where decision-makers can work. It is also a tool that allows to perform rapidly many different tests and mixes of technologies, by changing and testing different technologies and by carrying performances of each one.

There is no doubt that this proposal is only a first step for a country to get rid of its polluting plants using non-renewable resources. There is work ahead to improve this methodology regarding different aspects such as to make sure that the existing renewable sources will have the capacity to produce clean power to get green hydrogen as well as deuterium, the ‘raw materials’ for the new technologies.

Sensitivity of solution found that for 2022 solar is the source with the largest significance, however, we need to determine how strong is this solution to variations for some parameters.

The ERM matrix shows that this technology depends on hours of operation, which in turn, strongly depends on criteria C4 (Capacity factor) and C6 (Efficiency). Therefore, the strength of solar is related with the allowed variations of these two criteria. The software also shows that there is little margin for increasing capacity factor and a large margin for its decreasing. Within these two margins the criteria may vary without affecting the solution found. The opposite happens with criterion C6, since it allows for a rather large increase in efficiency but with a very little decrease. Since these two criteria affect simultaneously both solar technologies, possible variations must be considered at the same time. The software, through and add-in called Input-Output Sensitivity Analysis, (IOSA), can perform this simultaneous operation.

Consequently, since there is a little margin for increasing the capacity factor for solar, it appears that another type of technology must be used for 2035. Examining the ERM for 2035, it transpires that biomass may partially assume the demand for 2035 and complementing solar. Same analysis can be done in the same way for every source and for each period.

For instance, for 2035, bio depends on operations and maintenance. The margin for decreasing operations and maintenance costs is very small, and for that reason for 2050 it is replaced by wind.

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No competing interests reported.

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Transition to renewable energy – An attempt to model the mix of existing and future generation technologies for 2035 and 2050

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Abstract

Figures

1. Actual Scenario Regarding Power Generation

2. State Of The Art In Electric Generation Technologies

2.1 Mature technologies

2.2 Comparison of technologies

3. Proposal

3.1 Analyzing the problem

3.2 Factors to consider about the future of existing renewable sources for energy generation

4. Evaluating Electric Technologies And A Mathematical Method For Processing

4.1 Very important aspects to consider in this problem

4.1.1 Precedence

4.1.2 Balancing

4.1.3 Uncertainty

4.1.4 Examining actual values for 2022, 2035 and 2050

5. How To Forecast Values For 2035 And 2050, From An Updated 2022 Using Mathematical Programming

6. Examining Computed Values For 2022, 2035 And 2050 And Comparison With Actual Data

7. Discussion And Conclusion

References

Additional Declarations

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