rus
Issue #4/2025
E. A. Ionova, K. A. Ovchinnikov, D. A. Malevskiy
Evaluation Criterion of Full-Spectrum Modules for Solar Power Engineering
Evaluation Criterion of Full-Spectrum Modules for Solar Power Engineering
DOI: 10.22184/1993-7296.FRos.2025.19.4.324.332
The use of highly efficient (efficiency > 40%) full-spectrum solar cells in the ground-based
solar power engineering is associated with the sophisticated design of the solar power plant
that can lead to the increased capital costs not covered by the boosted energy yield. It is
proposed to use the relative LCOE (Levelised Cost of Energy) as a criterion for evaluating
the competitiveness of a power plant with full-spectrum solar cells at its initial stage of development. It is shown that if the power plant is located at the geographic point with the coordinates (51N, 108E), the power plant competitiveness with full-spectrum solar cells
shall be ensured already when the capital costs per 1 m2 of the module aperture exceed the
capital costs per 1 m2 by no more than 1.9 times in comparison with a silicon module.
The use of highly efficient (efficiency > 40%) full-spectrum solar cells in the ground-based
solar power engineering is associated with the sophisticated design of the solar power plant
that can lead to the increased capital costs not covered by the boosted energy yield. It is
proposed to use the relative LCOE (Levelised Cost of Energy) as a criterion for evaluating
the competitiveness of a power plant with full-spectrum solar cells at its initial stage of development. It is shown that if the power plant is located at the geographic point with the coordinates (51N, 108E), the power plant competitiveness with full-spectrum solar cells
shall be ensured already when the capital costs per 1 m2 of the module aperture exceed the
capital costs per 1 m2 by no more than 1.9 times in comparison with a silicon module.
Evaluation Criterion of Full-Spectrum Modules for Solar Power Engineering
E. A. Ionova 1, K. A. Ovchinnikov 2, D. A. Malevskiy 1
Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia
Peter the Great St. Petersburg Polytechnic University, Saint-Petersburg, Russia
The use of highly efficient (efficiency > 40%) full-spectrum solar cells in the ground-based solar power engineering is associated with the sophisticated design of the solar power plant that can lead to the increased capital costs not covered by the boosted energy yield. It is proposed to use the relative LCOE (Levelised Cost of Energy) as a criterion for evaluating the competitiveness of a power plant with full-spectrum solar cells at its initial stage of development. It is shown that if the power plant is located at the geographic point with the coordinates (51N, 108E), the power plant competitiveness with full-spectrum solar cells shall be ensured already when the capital costs per 1 m2 of the module aperture exceed the capital costs per 1 m2 by no more than 1.9 times in comparison with a silicon module.
Key words: solar power plant, solar cell, multi-junction solar cell, power generation, efficiency, LCOE (Levelised Cost of Energy)
Article received: February 26, 2025
Article accepted: April 26, 2025
INTRODUCTION
The solar power engineering includes the low-power generating facilities that can be considered as a part of distributed power generation. Within the framework of this industrial development concept, the centralized system is supplemented by the energy production close to its consumers. The distributed electric power industry can be related to the smart power transmission networks that allow for prompt changes in the current specifications in the electric network, while reducing the energy costs by the load redistribution between the sources. The smart networks shall allow for the integration of solar power plants (SPP) into the power engineering sector specified by a wide range of both installed capacity values (from several kW to tens of MW), and energy production during the day, while ensuring their operation in a centralized system or in an isolated mode [1–2].
At present, the solar cells (SC) with several (3–6) active p-n junctions and a total spectral range of spectral response of 380–1850 nm are already available or in the final stages of development [3–6]. They absorb the solar spectrum in terms of its energy content almost completely, unlike the silicon SCs operating in the spectral range of 350–1100 nm, and other SCs with an even narrower range of spectral response. Although the efficiency of SCs only partly depends on the spectral response range, the multijunction SCs have the highest efficiency (40% and higher), the works are being carried out for its further increase. The modules based on such multi-junction SCs, shall be further called the full-spectrum modules (FSM) by using this attribute as a determinant one.
The problem of using the FSM-based solar power plants in the solar power engineering to implement the advantages of their high efficiency is of not only practical but also scientific interest, since the FSMs have significant differences from silicon and other solar cell batteries. Moreover, the market entry of the FSM-based solar power plants shall be different, at least since its stall shall be “conquered” due to its competitive advantages.
The peculiarity of the FSM-based solar power systems is that they almost always include optical concentration of solar radiation and the Sun position tracking. The specificity is demonstrated both due to the concentration and tracking processes that occur simultaneously with the power generation, and due to the availability of the relevant structural elements (see the figure).
Tracking is necessary as a result of the direct solar radiation concentration on the surface of multijunction solar cells, and concentration is required due to the small size of such solar cells and due to the increased conversion efficiency in the case of radiation concentration. It should be noted that the solar power plants based on other solar cells almost never use the solar radiation concentration. However, the Sun tracking (often uniaxial process) can take place: to increase the daily power generation.
Another feature of such solar power plants is that the FSM development is complicated by the extensive variability of design parameters by the type and dimensions of its components: a concentrator, a solar cell, a tracking support. As a consequence of this variability, a scientific mission is determined to create a special FSM evaluation criterion with due regard to both the design properties and possible integration of the solar power plants based on them into the distributed power generation industry.
Relative LCOE as a criterion for developing the FSM-based solar power plants
At present, the main criterion in the development of solar modules is conventionally the standardized efficiency for the solar cell and for the module (ASTM G 173-03). Focusing on this criterion makes it possible to conduct research aimed at reducing the transmission losses during the radiation concentration process, and increasing the photovoltaic conversion efficiency. If the additional criterion is the Sun tracking accuracy, then, upon ensuring its acceptable value, a tracking support with the highest efficiency modules shall represent completion of the SPP prototyping stage. The next stage of the SPP project involves calculation of the plant capacity factor at the SPP location and calculation of the aggregated economic indicators in the well-known market conditions to justify the project feasibility. For example, the following indicator is widely used to compare the power engineering technologies: LCOE (Levelised Cost of Energy).
However, the module improvement process based on the efficiency criterion may imply reaching the maximum value to the detriment of economic factor: the increase in the cost of components and technological processes may have a predominant contribution to the LCOE value, not covered by the increased energy yield.
In addition, in the case of full-spectrum conversion, the dependence of energy yield on the spectral composition of solar radiation during the year is demonstrated to a greater extent [9]. It shall have impact on the plant capacity factor value, but not the nominal efficiency, since the latter as a development evaluation criterion includes information only about the module operation in a spectrum of AM1.5 according to ASTM G 173-03.
Finally, the efficiency maximization of solar cells and FSMs as the main criterion does not solve the optimal design issue in terms of the component type and dimensions, since the maximum efficiency shall result from improving the production technology of a design option selected once at the earliest design stage that makes it impossible to develop with due regard to the current or expected market conditions.
In our opinion, the above tasks can be solved by taking into account the future SPP competitiveness already at the initial stage of its design development. One of the main optimization criteria can be the LCOE (RUB/kWh). The LCOE value in absolute terms depends on the market conditions at the economic project justification stage and on the results of its forecasting, as well as, just as much, on the insolation conditions of the solar power plant location. The time lag from the start of development to the economic project justification and the lack of information about where the solar power plant will be located make it impossible to determine the LCOE value in absolute terms at the initial stage.
In this regard, it is proposed to evaluate the LCOE of the FSM-based SPPs in relation to the LCOE of one of the commercially successful SPPs, thereby solving the competitiveness evaluation issue in the same and well-known conditions that have similar predictive potential, manifested under the similar atmospheric conditions affecting the insolation process.
The LCOE indicator (RUB/kWh) shall consider the costs of power production, distributed throughout the life cycle of the solar power plant, and represent the average estimated manufacturing costs of a unit of electric energy with due regard to the investment conditions.
LCOE = Σ Σ , (1)
where the costs during the year t shall be of the following types: CAPEXt – specific capital outlays, RUB/kW; OPEXt – specific operating costs, RUB/kW; E1 – specific power generation during the first year of power plant operation, kWh/kW; r – discount rate, % per year; n – number of operating years; d – power plant degradation factor, % per year [10]. The capital costs shall be one-time: CAPEX1 = CAPEX, CAPEX2 = CAPEX3 = …= CAPEXt = 0, the operating costs for each year can be taken to be the same: for t = 1 .. n OPEXt = OPEX. Then formula (1) shall be as follows:
LCOE = · +
+ · = RCAPEX + ROPEX, (2)
where RCAPEX is the capital component of the power cost, and RОPEX is the semi-constant component of the cost.
The competitiveness condition of any new and reference solar power plant design shall be as follows:
LCOE ≤ LCOEref или RCAPEX ≤ Rref CAPEX − (ROPEX − RrefOPEX). (3)
That is, the capital component of the power cost of the developed SPP shall not be greater than the similar parameter of the reference SPP minus the difference between the semi-constant cost components of the new and reference technologies. The operating expenses (OPEX) for the SPP with the tracking function are definitely higher. It is expected that ROPEX shall be greater than RrefOPEX, but it may also be the other way around if the power production during the first operating year of the new technology Е1 shall significantly exceed the similar parameter of the reference technology. In the latter case, the competitiveness condition (3) of the new technology shall be softened.
The feature of SPP technologies is such that the operating costs are much lower than the capital costs. Therefore, without restricting the generality, the ratio of the capital power cost components of new and reference technologies (4) can be used as a competitiveness condition.
RCAPEX ≤ RrefCAPEX (4)
The competitiveness condition of new technology under the equal financial conditions (r), degradation factors (d) of the estimated service life (n) shall be as follows:
CAPEX ≤ CAPEX ref · E1Eref1 (5)
To be competitive, the specific capital costs of a technologically new solar power plant shall not exceed the specific capital costs of a reference solar power plant multiplied by the coefficient СЕ = E1 / Eref1 that indicates the increase (СЕ > 1) or shortfall (СЕ < 1) of annual power production using the new technology.
The specific (per unit of installed capacity) annual power production E1 is related to the plant capacity factor: Е1 = plant capacity factor · 365 · 24 h · 1 kW.
The installed capacity is determined for a solar radiation flux density of 1 kW/m2. Since a unit of installed capacity is considered, the effect of efficiency difference of the solar power plant and other technical parameters of the compared solar power plants is demonstrated by the difference in the total area of module apertures that is required to generate 1 kW when absorbing radiation with a power density of 1 kW/m2. For a preliminary evaluation, it can be assumed that the actual power generation is changed with a natural change in the power density of incoming radiation linearly with a proportionality coefficient of one. Then the coefficient СЕ is equal to the ratio of the solar energy actually received per year, P and Pref, kWh/m2 per unit of installed capacity of the compared solar power plants.
СЕ = E1 / Eref1 = plant capacity factor / plant capacity factorref =
= P / Pref, (6)
For greater accuracy in determining СЕ, it is recommended to estimate the specific power generation during the first operating year of power plants E1 and Eref1.
The formulas (3–6) are suitable for estimating the costs of changing the location of a well-known solar power plant or for determining the feasibility of installing the well-known solar modules (usually of static type) on the tracking systems. In this case, P is the energy of incident solar radiation on a solar power plant with a tracking device, falling on a site perpendicular to the rays, and Pref is the energy of solar radiation falling on a statically fixed surface.
To express the capital expenses (CAPEX) per 1 m2 of SPP aperture, it shall be assumed that CAPEX per 1 kW of installed capacity is greater than CAPEX per 1 m2 of apertures by the same number of times as the area of apertures in m2 that isrequired to generate 1 kW of installed capacity.
CAPEX / CAPEXm2 =
= 1 kW (installed capacity) /
/ (1 kW/m2 (solar radiation) × η), (7)
where CAPEXm2 – capital costs per unit area of the apertures of photovoltaic modules, η – efficiency of the photovoltaic module. Then, based on the formulas (5) and (6),
CAPEXm2 ≤ CAPEXrefm2 · P / Pref · η / ηref. (8)
When designing the FSM-based solar power plant, it is proposed to focus mainly on its reliability as the ability to maintain the required properties and perform the intended functions during the specific period of time. In the case of a solar power plant, this period is approximately 25 years. Thus, the attention of developers shall be directed to ensuring the installation failure-free operation, maintainability and durability that, unfortunately, cannot be currently determined due to the lack of statistical data confirming the reliability parameters.
The remaining specifications of the solar power plant, namely, annual energy yield and capital costs, including the cost of components and technologies (at the current stage of development), are proposed to be considered as the basic and dependent variables when calculating and minimizing LCOE. The calculated LCOE as a competitiveness criterion of the design of a FSM-based solar power plant shall comply with the inequalities (1–8). The comparison can be made with the solar power plants that have left the development stage and obtained the well-known exact LCOE and CAPEX values, as well as with the solar power plants that are at the development stage, then these parameters shall be of an evaluative nature. The CAPEX value of the FSM-based SPP being developed shall also partially have an evaluative nature in view of its future reduction due to the scale effect during the production concentration.
An example of evaluation using the formula (8) is shown for a location in the Zabaikalskiy region (51N, 108E), where the average direct solar radiation density over several years is 1636 kWh/m2/year, and the average solar radiation density falling on a static area inclined at an optimal angle is 1717 kWh/m2/year [11]. The paper [12] presents a FSM with η = 36% that is lower than the efficiency of solar cell used in this module (42.7%) due to the transmission losses during the solar radiation concentration process. A widely used silicon module with an efficiency of ηref = 18% [1] was used for a comparison. Then, as for the competitiveness in terms of cost factor, it is possible that the capital costs per 1 m2 of the FSM aperture are higher than the capital costs of the compared silicon module by no more than 1.9 times.
For a more accurate assessment of the relative LCOE of the FSM-based SPP, it is necessary to consider the spectral composition of the annual solar radiation, since in the regions with a high atmospheric turbidity index, the FSM efficiency is decreased [9]. Moreover, it is necessary to take into account the temperature changes in the SPP efficiency that is more typical for the silicon modules. The reduction of LCOE value is facilitated by optimizing the SPP design by the types and dimensions of the concentrator-SPP pair and placing the SPP in a location with a high level of direct solar radiation. It should be noted that there are some territories in the world where the annual direct radiation is higher than the annual radiation falling on an optimally inclined static site, unlike the location considered in the Zabaikalskiy region.
CONCLUSION
In order to simplify the market entry of the highly-efficient FSM-based solar power plants, it is proposed to conduct an evaluation of the average weighted cost at which the power shall be generated at the solar power plant already at the development stage and to use its ratio to the average weighted cost of the competitive solar power plant technologies as a criterion when conducting R&D. Application of the relative LCOE as the evaluation criterion for the FSM-based SPPs at the design stage shall ensure a sustainable approach to achieving the goal of the FSM development and implementation.
AUTHORS
Ionova Evgeniya Aleksandrovna, research assosiate at the Ioffe Physical-Technical Institute, Laboratory of Photovoltaic Converters, e-mail: ionova@mail.ioffe.ru; Saint Petersburg, Russia. Region of interest: concentrator photovoltaics.
ORCID: 0000-0003-2886-6706
Ovchinnikov Kirill Andreevich, Master’s student, St. Petersburg Polytechnic University, e-mail: owe4kink@yandex.ru; Saint Petersburg, Russia. Region of interest: innovation economics in power engineering.
ORCID 0009-0006-5774-0925
Malevskiy Dmitry Andreevich, research assistant, Ioffe Physical-Technical Institute, Photovoltaics Laboratory, e-mail: dmalevsky@scell.ioffe.ru; Saint Petersburg, Russia. Region of interest: concentrator power plants.
ORCID: 0000-0002-9337-4137
AUTHOR CONTRIBUTION
Ionova E. A.: concept of the article based on the methods of solving three issues: implementation of a new development in the power engineering sector, evaluation of its energy parameters, assessment of the economic project; Ovchinnikov K. A.: assessment of the economic specifications of an innovative project in the power engineering sector; Malevskiy D. A.: development of a solar energy system with the full-spectrum solar cells.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
E. A. Ionova 1, K. A. Ovchinnikov 2, D. A. Malevskiy 1
Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint-Petersburg, Russia
Peter the Great St. Petersburg Polytechnic University, Saint-Petersburg, Russia
The use of highly efficient (efficiency > 40%) full-spectrum solar cells in the ground-based solar power engineering is associated with the sophisticated design of the solar power plant that can lead to the increased capital costs not covered by the boosted energy yield. It is proposed to use the relative LCOE (Levelised Cost of Energy) as a criterion for evaluating the competitiveness of a power plant with full-spectrum solar cells at its initial stage of development. It is shown that if the power plant is located at the geographic point with the coordinates (51N, 108E), the power plant competitiveness with full-spectrum solar cells shall be ensured already when the capital costs per 1 m2 of the module aperture exceed the capital costs per 1 m2 by no more than 1.9 times in comparison with a silicon module.
Key words: solar power plant, solar cell, multi-junction solar cell, power generation, efficiency, LCOE (Levelised Cost of Energy)
Article received: February 26, 2025
Article accepted: April 26, 2025
INTRODUCTION
The solar power engineering includes the low-power generating facilities that can be considered as a part of distributed power generation. Within the framework of this industrial development concept, the centralized system is supplemented by the energy production close to its consumers. The distributed electric power industry can be related to the smart power transmission networks that allow for prompt changes in the current specifications in the electric network, while reducing the energy costs by the load redistribution between the sources. The smart networks shall allow for the integration of solar power plants (SPP) into the power engineering sector specified by a wide range of both installed capacity values (from several kW to tens of MW), and energy production during the day, while ensuring their operation in a centralized system or in an isolated mode [1–2].
At present, the solar cells (SC) with several (3–6) active p-n junctions and a total spectral range of spectral response of 380–1850 nm are already available or in the final stages of development [3–6]. They absorb the solar spectrum in terms of its energy content almost completely, unlike the silicon SCs operating in the spectral range of 350–1100 nm, and other SCs with an even narrower range of spectral response. Although the efficiency of SCs only partly depends on the spectral response range, the multijunction SCs have the highest efficiency (40% and higher), the works are being carried out for its further increase. The modules based on such multi-junction SCs, shall be further called the full-spectrum modules (FSM) by using this attribute as a determinant one.
The problem of using the FSM-based solar power plants in the solar power engineering to implement the advantages of their high efficiency is of not only practical but also scientific interest, since the FSMs have significant differences from silicon and other solar cell batteries. Moreover, the market entry of the FSM-based solar power plants shall be different, at least since its stall shall be “conquered” due to its competitive advantages.
The peculiarity of the FSM-based solar power systems is that they almost always include optical concentration of solar radiation and the Sun position tracking. The specificity is demonstrated both due to the concentration and tracking processes that occur simultaneously with the power generation, and due to the availability of the relevant structural elements (see the figure).
Tracking is necessary as a result of the direct solar radiation concentration on the surface of multijunction solar cells, and concentration is required due to the small size of such solar cells and due to the increased conversion efficiency in the case of radiation concentration. It should be noted that the solar power plants based on other solar cells almost never use the solar radiation concentration. However, the Sun tracking (often uniaxial process) can take place: to increase the daily power generation.
Another feature of such solar power plants is that the FSM development is complicated by the extensive variability of design parameters by the type and dimensions of its components: a concentrator, a solar cell, a tracking support. As a consequence of this variability, a scientific mission is determined to create a special FSM evaluation criterion with due regard to both the design properties and possible integration of the solar power plants based on them into the distributed power generation industry.
Relative LCOE as a criterion for developing the FSM-based solar power plants
At present, the main criterion in the development of solar modules is conventionally the standardized efficiency for the solar cell and for the module (ASTM G 173-03). Focusing on this criterion makes it possible to conduct research aimed at reducing the transmission losses during the radiation concentration process, and increasing the photovoltaic conversion efficiency. If the additional criterion is the Sun tracking accuracy, then, upon ensuring its acceptable value, a tracking support with the highest efficiency modules shall represent completion of the SPP prototyping stage. The next stage of the SPP project involves calculation of the plant capacity factor at the SPP location and calculation of the aggregated economic indicators in the well-known market conditions to justify the project feasibility. For example, the following indicator is widely used to compare the power engineering technologies: LCOE (Levelised Cost of Energy).
However, the module improvement process based on the efficiency criterion may imply reaching the maximum value to the detriment of economic factor: the increase in the cost of components and technological processes may have a predominant contribution to the LCOE value, not covered by the increased energy yield.
In addition, in the case of full-spectrum conversion, the dependence of energy yield on the spectral composition of solar radiation during the year is demonstrated to a greater extent [9]. It shall have impact on the plant capacity factor value, but not the nominal efficiency, since the latter as a development evaluation criterion includes information only about the module operation in a spectrum of AM1.5 according to ASTM G 173-03.
Finally, the efficiency maximization of solar cells and FSMs as the main criterion does not solve the optimal design issue in terms of the component type and dimensions, since the maximum efficiency shall result from improving the production technology of a design option selected once at the earliest design stage that makes it impossible to develop with due regard to the current or expected market conditions.
In our opinion, the above tasks can be solved by taking into account the future SPP competitiveness already at the initial stage of its design development. One of the main optimization criteria can be the LCOE (RUB/kWh). The LCOE value in absolute terms depends on the market conditions at the economic project justification stage and on the results of its forecasting, as well as, just as much, on the insolation conditions of the solar power plant location. The time lag from the start of development to the economic project justification and the lack of information about where the solar power plant will be located make it impossible to determine the LCOE value in absolute terms at the initial stage.
In this regard, it is proposed to evaluate the LCOE of the FSM-based SPPs in relation to the LCOE of one of the commercially successful SPPs, thereby solving the competitiveness evaluation issue in the same and well-known conditions that have similar predictive potential, manifested under the similar atmospheric conditions affecting the insolation process.
The LCOE indicator (RUB/kWh) shall consider the costs of power production, distributed throughout the life cycle of the solar power plant, and represent the average estimated manufacturing costs of a unit of electric energy with due regard to the investment conditions.
LCOE = Σ Σ , (1)
where the costs during the year t shall be of the following types: CAPEXt – specific capital outlays, RUB/kW; OPEXt – specific operating costs, RUB/kW; E1 – specific power generation during the first year of power plant operation, kWh/kW; r – discount rate, % per year; n – number of operating years; d – power plant degradation factor, % per year [10]. The capital costs shall be one-time: CAPEX1 = CAPEX, CAPEX2 = CAPEX3 = …= CAPEXt = 0, the operating costs for each year can be taken to be the same: for t = 1 .. n OPEXt = OPEX. Then formula (1) shall be as follows:
LCOE = · +
+ · = RCAPEX + ROPEX, (2)
where RCAPEX is the capital component of the power cost, and RОPEX is the semi-constant component of the cost.
The competitiveness condition of any new and reference solar power plant design shall be as follows:
LCOE ≤ LCOEref или RCAPEX ≤ Rref CAPEX − (ROPEX − RrefOPEX). (3)
That is, the capital component of the power cost of the developed SPP shall not be greater than the similar parameter of the reference SPP minus the difference between the semi-constant cost components of the new and reference technologies. The operating expenses (OPEX) for the SPP with the tracking function are definitely higher. It is expected that ROPEX shall be greater than RrefOPEX, but it may also be the other way around if the power production during the first operating year of the new technology Е1 shall significantly exceed the similar parameter of the reference technology. In the latter case, the competitiveness condition (3) of the new technology shall be softened.
The feature of SPP technologies is such that the operating costs are much lower than the capital costs. Therefore, without restricting the generality, the ratio of the capital power cost components of new and reference technologies (4) can be used as a competitiveness condition.
RCAPEX ≤ RrefCAPEX (4)
The competitiveness condition of new technology under the equal financial conditions (r), degradation factors (d) of the estimated service life (n) shall be as follows:
CAPEX ≤ CAPEX ref · E1Eref1 (5)
To be competitive, the specific capital costs of a technologically new solar power plant shall not exceed the specific capital costs of a reference solar power plant multiplied by the coefficient СЕ = E1 / Eref1 that indicates the increase (СЕ > 1) or shortfall (СЕ < 1) of annual power production using the new technology.
The specific (per unit of installed capacity) annual power production E1 is related to the plant capacity factor: Е1 = plant capacity factor · 365 · 24 h · 1 kW.
The installed capacity is determined for a solar radiation flux density of 1 kW/m2. Since a unit of installed capacity is considered, the effect of efficiency difference of the solar power plant and other technical parameters of the compared solar power plants is demonstrated by the difference in the total area of module apertures that is required to generate 1 kW when absorbing radiation with a power density of 1 kW/m2. For a preliminary evaluation, it can be assumed that the actual power generation is changed with a natural change in the power density of incoming radiation linearly with a proportionality coefficient of one. Then the coefficient СЕ is equal to the ratio of the solar energy actually received per year, P and Pref, kWh/m2 per unit of installed capacity of the compared solar power plants.
СЕ = E1 / Eref1 = plant capacity factor / plant capacity factorref =
= P / Pref, (6)
For greater accuracy in determining СЕ, it is recommended to estimate the specific power generation during the first operating year of power plants E1 and Eref1.
The formulas (3–6) are suitable for estimating the costs of changing the location of a well-known solar power plant or for determining the feasibility of installing the well-known solar modules (usually of static type) on the tracking systems. In this case, P is the energy of incident solar radiation on a solar power plant with a tracking device, falling on a site perpendicular to the rays, and Pref is the energy of solar radiation falling on a statically fixed surface.
To express the capital expenses (CAPEX) per 1 m2 of SPP aperture, it shall be assumed that CAPEX per 1 kW of installed capacity is greater than CAPEX per 1 m2 of apertures by the same number of times as the area of apertures in m2 that isrequired to generate 1 kW of installed capacity.
CAPEX / CAPEXm2 =
= 1 kW (installed capacity) /
/ (1 kW/m2 (solar radiation) × η), (7)
where CAPEXm2 – capital costs per unit area of the apertures of photovoltaic modules, η – efficiency of the photovoltaic module. Then, based on the formulas (5) and (6),
CAPEXm2 ≤ CAPEXrefm2 · P / Pref · η / ηref. (8)
When designing the FSM-based solar power plant, it is proposed to focus mainly on its reliability as the ability to maintain the required properties and perform the intended functions during the specific period of time. In the case of a solar power plant, this period is approximately 25 years. Thus, the attention of developers shall be directed to ensuring the installation failure-free operation, maintainability and durability that, unfortunately, cannot be currently determined due to the lack of statistical data confirming the reliability parameters.
The remaining specifications of the solar power plant, namely, annual energy yield and capital costs, including the cost of components and technologies (at the current stage of development), are proposed to be considered as the basic and dependent variables when calculating and minimizing LCOE. The calculated LCOE as a competitiveness criterion of the design of a FSM-based solar power plant shall comply with the inequalities (1–8). The comparison can be made with the solar power plants that have left the development stage and obtained the well-known exact LCOE and CAPEX values, as well as with the solar power plants that are at the development stage, then these parameters shall be of an evaluative nature. The CAPEX value of the FSM-based SPP being developed shall also partially have an evaluative nature in view of its future reduction due to the scale effect during the production concentration.
An example of evaluation using the formula (8) is shown for a location in the Zabaikalskiy region (51N, 108E), where the average direct solar radiation density over several years is 1636 kWh/m2/year, and the average solar radiation density falling on a static area inclined at an optimal angle is 1717 kWh/m2/year [11]. The paper [12] presents a FSM with η = 36% that is lower than the efficiency of solar cell used in this module (42.7%) due to the transmission losses during the solar radiation concentration process. A widely used silicon module with an efficiency of ηref = 18% [1] was used for a comparison. Then, as for the competitiveness in terms of cost factor, it is possible that the capital costs per 1 m2 of the FSM aperture are higher than the capital costs of the compared silicon module by no more than 1.9 times.
For a more accurate assessment of the relative LCOE of the FSM-based SPP, it is necessary to consider the spectral composition of the annual solar radiation, since in the regions with a high atmospheric turbidity index, the FSM efficiency is decreased [9]. Moreover, it is necessary to take into account the temperature changes in the SPP efficiency that is more typical for the silicon modules. The reduction of LCOE value is facilitated by optimizing the SPP design by the types and dimensions of the concentrator-SPP pair and placing the SPP in a location with a high level of direct solar radiation. It should be noted that there are some territories in the world where the annual direct radiation is higher than the annual radiation falling on an optimally inclined static site, unlike the location considered in the Zabaikalskiy region.
CONCLUSION
In order to simplify the market entry of the highly-efficient FSM-based solar power plants, it is proposed to conduct an evaluation of the average weighted cost at which the power shall be generated at the solar power plant already at the development stage and to use its ratio to the average weighted cost of the competitive solar power plant technologies as a criterion when conducting R&D. Application of the relative LCOE as the evaluation criterion for the FSM-based SPPs at the design stage shall ensure a sustainable approach to achieving the goal of the FSM development and implementation.
AUTHORS
Ionova Evgeniya Aleksandrovna, research assosiate at the Ioffe Physical-Technical Institute, Laboratory of Photovoltaic Converters, e-mail: ionova@mail.ioffe.ru; Saint Petersburg, Russia. Region of interest: concentrator photovoltaics.
ORCID: 0000-0003-2886-6706
Ovchinnikov Kirill Andreevich, Master’s student, St. Petersburg Polytechnic University, e-mail: owe4kink@yandex.ru; Saint Petersburg, Russia. Region of interest: innovation economics in power engineering.
ORCID 0009-0006-5774-0925
Malevskiy Dmitry Andreevich, research assistant, Ioffe Physical-Technical Institute, Photovoltaics Laboratory, e-mail: dmalevsky@scell.ioffe.ru; Saint Petersburg, Russia. Region of interest: concentrator power plants.
ORCID: 0000-0002-9337-4137
AUTHOR CONTRIBUTION
Ionova E. A.: concept of the article based on the methods of solving three issues: implementation of a new development in the power engineering sector, evaluation of its energy parameters, assessment of the economic project; Ovchinnikov K. A.: assessment of the economic specifications of an innovative project in the power engineering sector; Malevskiy D. A.: development of a solar energy system with the full-spectrum solar cells.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
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