1.1.

Spectral Control

Spectral control refers to the employed techniques that increase the spectral efficiency by increasing the in-band radiation/photons that reach the PV cell. Spectral control in the TPV system is achieved using an IR emitter. There are two types of emitters: broadband and selective narrower band emitters. A broadband emitter emits a broad spectrum of blackbody radiation, which includes the undesired sub-bandgap photons. The sub-bandgap photons are reflected back into the cell absorber using either a back-surface reflector (BSR) (silver (Ag), gold (Au), aluminum (Al),¹⁹ etc.) or a front-surface filter (FSF) to enhance photon recycling in the PV cell, a common strategy to increase power efficiency of PV cells.²⁰ The sub-bandgap photons’ reflection transfers the sub-bandgap light energy and prevents the PV cell from heating, which increases spectral efficiency and thus ${\eta }_{\mathrm{TPV}}$[Eq. (1)]. Instead of using a BSR or an FSF, the emitter itself can be modified (called a selective emitter) using rare earth metals/oxides²¹ to radiate only the valuable part of the spectrum. Selective emitter allows using a low-temperature emitter (400 to 1400 K), lower thermal stresses, a wide range of available materials, and improved material stability.^22,23 Selective emitters help reduce thermalization in PV cells but reduce the in-band power density.²⁴ The broadband emitters have higher in-band power density but reduce the overall efficiency; thus, both the broadband and selective emitters have tradeoffs, and a suitable emitter is chosen based on the application.

1.2.

TPV Advantages

TPV is increasingly becoming popular as an energy conversion pathway due to its numerous applications, some of which include energy storage, combined heat and power²⁵ (CHP), waste energy recovery,^17,26 and in-space programs.^12,27 It can be used for CHP applications as it provides electricity and heat (it can also store heat due to its compatibility with storage applications). Due to its higher power density¹² ($>2.5\mathrm{W}/{\mathrm{cm}}^2$) and reduced cost, there has been an increasing focus on energy storage using TPV, called thermal energy electrical storage (TEES) or thermal energy grid storage (TEGS) that is competitive with electrochemical batteries.^12,28 It also provides modular and silent power generation,²⁵ is compatible with a variety of fuels/heat sources (including waste heat), and has no moving parts (thus low maintenance costs). TPV is often compared with the most widespread method of power generation nowadays, power cycles using turbines. It reaches full power in less time as compared to turbines (starting time in order of seconds as compared with tens of minutes to an hour), operates at high temperatures²⁹ (due to its contact-less nature),³⁰ and is suitable for long-duration energy storage applications.^12,25 Due to material and technological constraints, turbines have an upper limit on the operating temperature, which is $\sim 1500°\mathrm{C}$ for the Brayton cycle and 700°C for the Rankine cycle. The efficiency upper limit is closely tied to this temperature limitation, around 38% for the Brayton cycle and 23% for the Rankine cycle.²⁷ TPV can operate at much higher temperatures (around 1700°C) and has an efficiency approaching 40%.²⁸ New TPV thermal energy storage technologies have the potential for commercialization and deployment at a large scale.²⁵ At the same time, turbine-based heat engines are high-risk applications due to their low efficiencies and thus require a significant capital investment.²⁹ The literature has several new studies related to the spectral control, prototyping, modeling, economic analysis, and energy storage applications of TPV systems.^31,32

1.3.

TPV Prototype and Modeling

There are a few models in the literature to predict experimental results from TPV technology and help it scale up and build a practical design for a prototype. Woolf et al.³³ modeled a TPV system consisting of a selective emitter, a dielectric filter, and a PV cell. They predicted accurate photovoltaic conversion efficiency with the model. Hassan et al.³⁴ modeled the optical (emitter-side spectral and spatial subsystem) and photovoltaic subsystems for a TPV system and observed the effects of emitter features on the optimum bandgap and overall efficiency. A recent innovative TPV study used machine learning to automatically model and optimize multilayer thin film structures to design an ideal spectral response.³⁵ Their deep learning-based model is efficient and accurate (to predict target spectra) and reduces resource consumption compared with complex numerical models.

1.4.

TPV Economic Analyses

Some researchers have worked on evaluating the economic feasibility of TPV systems; however, it is still in its developing stages. Bianchi et al. (2012)^21,36 established an energy and economic evaluation framework for a TPV system for combined heat and power (CHP) application in a residential building. They calculate parameters such as primary and electrical energy consumption, primary energy savings, cost of electricity, and money savings. They conclude that the TPV system has immense potential as it reduces purchased grid electricity and increases monetary savings. Fraas et al.³⁷ performed a preliminary techno-economic analysis (TEA) for a TPV furnace-generator system suitable for CHP applications. It consisted of a silicon carbide (SiC) radiant tube burner surrounded by a cylindrical silicon (Si)/gallium antimonide (GaSb) PV converter array, along with an antireflection-coated tungsten foil and an infrared filter over the cells to reduce out-of-band absorption. The system’s electrical efficiency with a Si array and a standard furnace (without any furnace modifications) was found as 1.5% (and a power density of $0.3{\mathrm{Wcm}}^{-2}$), and for a system with the low-bandgap GaSab cells, it was found as 15% (higher due to better spectral control, power density = $1{\mathrm{Wcm}}^{-2}$). Their proposed TPV CHP unit would be economically feasible for integration into homes when the GaSb cells and arrays reach the desired low production cost. Their fuel-powered TPV system is suitable for distributed CHP applications and can be installed in homes for Winter, and renewable energy sources can be utilized in summer. Durisch and Bitnar propose a novel design of a self-powered residential electric heating system based on TPV technology.³⁸ Their system consists of a ytterbium oxide (Yb₂O₃) selective emitter and thin film solar cell materials (such as Si) or copper indium gallium selenide (Cu(In,Ga)Se₂) (CIGS). Thin film cells are typically 100 to 1000 times thinner than the conventional crystalline Si solar cells, thus saving extensive material and fabrication costs. Yb₂O₃ produces a selective emission spectrum and has a suitable bandgap to be used with Si or CIGS photocells. Their novel TPV system requires a production cost reduction to be feasible. However, it has the potential to be a basis for next-generation TPV technology to power off-grid homes and large-scale industries. The following section focuses on previous efforts in the literature on integrating energy storage and TPV and its economic feasibility.

1.5.

Energy Storage Using TPV

Renewable energy sources such as solar PV and wind have the disadvantage of intermittency: they are only sometimes available throughout the day, which creates an imbalance between the load and energy generation (especially during peak hours). Energy storage technologies help tackle this problem by storing excess renewable energy that can be used when the energy required by the load is higher than the energy generated and thus would be an integral part of future grid networks to help increase power system flexibility and stability and ensure a smooth transition for decarbonization.^39,40 Electrochemical batteries (such as Li-ion) offer a cheap solution for energy storage due to the abundance of Li and other metals like cobalt and nickel used in electric vehicles and electricity storage batteries.⁴¹ Low prices are due to excess supply and low demand, which did not meet the high demand expectations after the coronavirus disease (COVID-19) pandemic in 2020. Low demand might not encourage their mining in the future, but the demand is expected to go up; thus, there are high chances of high prices of these metals (and batteries). In this paper, we consider storing renewable and grid electricity as an emerging alternative to electrochemical batteries.

Storing electricity as heat, sometimes called electrothermal energy storage (ETES), is a possible solution to decarbonize industrial heating systems and can reduce up to 40% of 2022 global natural gas use and 14% of global energy greenhouse gas (GHG) emissions.⁴² Many commercially available technologies for storing energy as sensible heat for industrial processes require high temperatures. Rondo Energy has designed a way to store excess renewable energy as high-temperature heat in insulated material at more than 1200°C for industrial applications.⁴³ Using renewable energy for industrial processes would help reduce its significant GHG emissions, especially from the two processes that release most emissions—the iron and steel industry⁴⁴ (ISI) and cement manufacturing.⁴⁵ The automotive and clean energy company Tesla mentions in its master plan for sustainable energy that thermal batteries (with an annual energy capacity of 41 TWh) can meet global electricity and transportation storage demand, along with renewables and other batteries.⁴⁶ Octopus energy uses artificial intelligence, machine learning, and its software system, Kraken, to balance power demand and supply using renewable energy storage technologies.⁴⁷ PV cell thermal energy storage technologies have the potential for commercialization and deployment at a large scale. In literature, there has been a focus on a few storage mediums, such as Si/Si alloys (phase-change materials, PCMs having high-energy densities $>1\mathrm{MWh}/{\mathrm{m}}^3$ and low cost $<4€/\mathrm{kWh}=4.31\$/\mathrm{kWh}$,^25,48 graphite,⁴⁹ Fe-Si-B alloy,^25,50 alumina fiber board.⁵¹ For long-duration energy storage systems (10 to 100 h), it is essential to reduce the cost per unit energy (CPE) more than the cost per unit power (CPP) and round trip efficiency (RTE).²⁵ Datas et al. analyzed a storage-integrated solar thermophotovoltaic (SISTPV) system, combining the TPV and PCMs.⁵² They perform a steady-state analysis for a system using PCM to store incoming heat as latent heat, which is then used to produce electricity via the TPV system. Sensible heating systems need temperatures of more than 1500°C to operate, thus more challenging insulation requirements, but not latent heat units, as they operate at a constant discharge temperature. In a subsequent paper, they performed a transient analysis for the same SISTPV system.⁵³ They obtained promising results but mentioned that future technological improvements must be made to the model to perform an in-depth analysis. Datas et al.³⁰ designed a thermal energy storage system using phase change materials (PCMs) that convert electricity to latent heat (stored in PCM), which is then converted to electrical energy via TPV cells. Electricity is stored as heat in the PCM, which is inefficient, but it is economical to store heat that need not be converted to electricity due to heating loads.^25,49 As opposed to sensible heating storage mediums, latent heat provides the benefit of almost constant discharge temperature, which ensures the decoupling of energy storage and power generation capacity and operation at lower temperatures. They considered ideal TPV cells with 100% internal luminescent efficiency ${\eta }_{\mathrm{int}}$ (the fraction of electron-hole pairs that recombine radiatively within the semiconductor), a bandgap of 0.5 eV and BSR reflectivity of 80% and 100% (which denote the practical and ideal values, respectively). They obtained a maximum total energy density (thermal + electrical) of 1 MWh/m³ and electrical energy densities of 200 to $600\mathrm{kWh}/{\mathrm{m}}^3$, comparable to the state-of-the-art lithium-ion (Li-ion) batteries. Datas et al.²⁵ estimate the levelized cost of electricity (LCOE), CPE, and CPP for a latent heat TPV (LHTPV) system. Their latent heat TPV (LHTPV) system stores the incoming power as heat with the help of a PCM (Si or FeSiB). First, the incoming power (from the grid or solar panels) is converted to heat via a heater (ohmic/induction/microwave/arc system) using an electric switch. The heat then melts the PCM (initially a solid), and the power is stored as latent heat in it. When the TPV cells are introduced into the system, the heat is transferred to the emitter of the TPV arrangement, and the PCM starts to solidify. For a detailed system embodiment, readers are referred to the original paper.²⁵ The PCM then converts heat to electricity as and when required with the help of a TPV cell. Amy et al.²⁹ presented a TEGS unit consisting of integrating energy storage with multi-junction PV (MPV) cells. In their proposed system, they first convert electricity to heat via joule heating of liquid Si. The heat is stored at 2400°C in a storage tank, then converted back to electricity on demand via MPV cells. They introduce a framework to evaluate economic feasibility using cost per unit energy (CPE), power (CPP), and the RTE.²⁹ They conclude that their TEGS system using MPV cells has the potential to be economically feasible and can enable high renewable energy penetration in the grid. Kelsall et al. modified the TEGS system presented by Amy et al. to include a multi-junction TPV cell, a solid graphite storage tank, and tin (Sn) as a heat-transfer fluid instead of liquid Si tanks.¹⁹ This replacement by graphite and Sn is because of their advantages of low melting point and low solubility of Sn in graphite. Their TEA concludes that the CPE for their system can be below the target value of ${€20/\mathrm{kWh}}_e$⁵⁴ (= $\$21.55{/\mathrm{kWh}}_e$) after the production capacity reaches a 100 MW target. A bottom-up TEA for highly concentrated PV modules suggests that the present PV cell cost can be reduced from a present value of ${€2/\mathrm{cm}}^2$ to $€0.{2/\mathrm{cm}}^2$ by reusing the substrate and reducing metallization costs, among other improvements.⁵⁵ Thus, there is an immense potential in energy storage using TPV, as seen from literature studies. Section 2 describes our methodology to obtain our economic analysis and uncertainty assessment results.

This study performs a techno-economic analysis and uncertainty assessment (using Monte Carlo simulations) and calculates the CO₂eq. emissions of energy storage using TPV. We are not aware of any literature studies performing Monte Carlo simulations for the TEA and CO₂eq. emissions of a TPV system. However, Monte Carlo simulations are essential for evaluating the uncertainty in input parameters, which is essential for evaluating the robustness of emerging TPV systems. The findings from this study could inform performance improvement targets and metrics for various grid resilience applications.

3.1.

Scenario Analysis Results

The results for scenario 1, W₂I₄C_32,323,970, are displayed in Table 4 based on the inputs listed in Tables 1, 2, and 3. We obtain the minimum base-case LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ as $0.046/kWh and $0.17/kWh, respectively.

Table 4

Base-case and optimized inputs and results for scenario 1 (W2I4C32,323,970).

From Table 4, for the base-case scenario, the power obtained from the grid = 5.13 MW (= 55% of the total power demand), from solar PV = 3.93 MW (= 43% of the total power demand), and from the PGU (by stored energy in HTES) = 0.18 MWh (= 2% of the total power demand). These three sources satisfy entirely the power demand of 9.24 MW. HTES energy losses constitute 79% of the incoming solar PV energy into HTES (=3.59 MW), and the rest is mainly passed to the PGU (20%) or stored in HTES at the end of the year (less than 1%). These numbers change for the optimized case, represented in the fourth column of Table 4. HTES energy losses decrease to 66%, and the heat passed to the PGU increases to 33%. Less than 1% of the energy is stored in HTES at the end of the year, as most of it is passed to the PGU to satisfy the electrical load. LTES supplies only 0.96% of the heating demand due to the algorithm’s priority of HTES for energy storage over LTES (as defined in the reference study⁵⁶). LTES stores energy only when it is not fully charged, and the HTES is either almost entirely ($>99\%$) or fully charged. The external boiler supplies the rest (99%) of the heating demand. These numbers improve modestly after optimizing LCOE, and the LTES supplies 1.5% of heating demand, and the external boiler supplies less energy = 98.5%. Thus, optimizing the system or searching for the least LCOE increases the energy supply from both the energy storages. Using the energy management algorithm is beneficial as it reduces the LCOE and increases solar PV’s self-consumption ratio (SCR) from 57.2% to 61.7%. Less PV energy is lost, and the consumer utilizes more.

The SCR [defined in Eq. (2)] represents the amount of PV energy generated being utilized by the load either directly as electricity or indirectly as stored energy in HTES or LTES.

The optimal system configuration is nominal PV capacity $(P_{\text{nom}})=5{\mathrm{kW}}_{\mathrm{el}}$, HTES maximum capacity $({\mathrm{HTES}}_{\text{max}})=15{\mathrm{kWh}}_{\mathrm{th}}$, and PGU maximum capacity $({\mathrm{PGU}}_{\text{max}})=0.504{\mathrm{kW}}_{\mathrm{el}}$. The base-case system configuration ($P_{\text{nom}}=9.5{\mathrm{kW}}_{\mathrm{el}}$, ${\mathrm{HTES}}_{\text{max}}=40{\mathrm{kWh}}_{\mathrm{th}}$, and ${\mathrm{PGU}}_{\text{max}}=1.0\mathrm{kW}$) converges to the minimum bounds for two optimized variables and is very close to the minimum for the third one, as seen in Table 5.

Table 5

Scenario analysis results showing optimized system size (nominal PV capacity, HTES max. Capacity, and PGU max. generation capacity) and optimum LCOE and LCOEel values.

We observe that the optimal solution for the economically favorable scenarios (having lower ${\mathrm{WACC}}_{\text{nom}}$ and CAPEX values) converges to a somewhat larger PGU system, with its size being $0.504{\mathrm{kW}}_{\mathrm{el}}$ for scenario 1 (${\mathrm{W}}_2{\mathrm{I}}_4{\mathrm{C}}_{\mathrm{32,323,970}}$). It obtains a lower $P_{\text{grid}}(=4.99\mathrm{MWh})$, whereas small systems (nominal PV capacity = $5{\mathrm{kW}}_{\mathrm{el}}$, HTES max. capacity = $15{\mathrm{kWh}}_{\mathrm{th}}$, and PGU max. generation capacity = $0.5{\mathrm{kW}}_{\mathrm{el}}$) are obtained for unfavorable economic conditions, including high WACC_nom and high capital cost of HTES, PGU, and PV systems (their values mentioned in Table 5, column 1). Table 5 presents the scenario analysis results—the optimum system size (HTES, PGU, and nominal PV capacity) and the optimum LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ values. The base case and optimum LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ values are also shown in Fig. 3.

Fig. 3

Base-case and optimum (a) LCOE and (b) LCOE_el variation with scenarios.

Unfavorable economic conditions produce a high optimum $P_{\text{grid}}$ (=5 MWh for scenario 4:${\mathrm{W}}_3{\mathrm{I}}_2{\mathrm{C}}_{\mathrm{215,2155,1293}}$). As economic conditions become favorable (low ${\mathrm{WACC}}_{\text{nom}}$ and low capital cost), we obtain a large PGU system, which becomes favorable to accommodate a large system (a large system is needed to store the produced PV energy). The same is true for LCOE_el minimization—scenario 1: ${\mathrm{W}}_2{\mathrm{I}}_4{\mathrm{C}}_{\mathrm{32,323,970}}$ (having the least ${\mathrm{WACC}}_{\text{nom}}$ and CAPEX) produces a system with PGU size = $0.519{\mathrm{kW}}_{\mathrm{el}}$. In comparison, all the rest scenarios converge on the lower bounds and give the result as nominal PV capacity = $5{\mathrm{kW}}_{\mathrm{el}}$, HTES max. capacity = $15{\mathrm{kWh}}_{\mathrm{th}}$, and PGU max. generation capacity = $0.5{\mathrm{kW}}_{\mathrm{el}}$ (a small system). This phenomenon is illustrated in Appendix D, and an explanation is provided in Table 6.

Table 6

Mean parameter values, as obtained from the Monte Carlo simulation fitted probability distributions.

The optimized LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ values mentioned in Table 5 seem counterintuitive: their values for the favorable scenario are higher than some unfavorable ones. This is due to the higher value of ${\mathrm{Infl}}_{\text{fuel}}$ and ${\mathrm{Infl}}_e$_l for favorable cases, as assumed in the reference study. The LCOE equation [Eq. (3)] has two terms involving inflation rates, and ${\mathrm{LCOE}}_{\mathrm{el}}$ [Eq. (4)] just has one. This is why the effect is less pronounced for the ${\mathrm{LCOE}}_{\mathrm{el}}$ optimization case and more for LCOE. Scenario 3 (${\mathrm{W}}_3{\mathrm{I}}_2{\mathrm{C}}_{\mathrm{108,1077,1293}}$) produces the least optimized LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$, as it has the right tradeoff between ${\mathrm{WACC}}_{\text{nom}}$ and inflation rates.

3.2.

Sensitivity Analysis and Monte Carlo Risk Assessment Results

Based on historical data from the literature, the fitted distribution for the non-triangular distributed parameters—natural gas price is a general extreme value, ${\mathrm{Infl}}_{\mathrm{el}}$ and ${\mathrm{Infl}}_{\text{fuel}}$ is t; ${\mathrm{CAPEX}}_{\mathrm{PV}}$⁷⁰ is a general extreme value; and electricity price is Weibull distribution, as shown in Fig. 4, along with their 10 and 90% confidence interval limits.

Fig. 4

Fitted probability distributions and 90% confidence limits for Monte Carlo parameters. Their distributions, mean, and standard deviation are as follows: (a) Lifetime (triangular distribution: 24.34 years, 2.47 years), (b) ${\mathrm{WACC}}_{\text{nom}}$ (triangular distribution: 2.17%, 0.31%), (c) PGU efficiency (triangular distribution: 27.45%, 5.08%), (d) electricity price (Weibull distribution: $0.124/kWh, $0.015/kWh), (e) CAPEX_PGU (triangular distribution: $1184.66/kW, $373.18/kW), (f) CAPEX_PV (general extreme value distribution: $914.98/kW, $145.41/kW), (g) ${\mathrm{CAPEX}}_{\text{HTES}}$ (triangular distribution: $118.40/kWh, $37.60/kWh), (h) inflation rates—${\mathrm{Infl}}_{\text{fuel}}$ and ${\mathrm{Infl}}_{\mathrm{el}}$ (t distribution: 2.31%, 2.11%), and (i) natural gas price (general extreme value distribution: $0.015/kWh, $0.011/kWh).

Now, we mention the results from the scenario analysis we used for our study. First, the base-case and optimized LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ for a mean scenario are illustrated in Fig. 5. For this scenario, we chose the mean parameter values (listed in Table 6 and Fig. 4) from the fitted Monte Carlo distributions. The values in Table 6 differ from the ones used in the four scenario analyses previously as those values were obtained from the reference study,⁵⁶ and these updated values are obtained from the fitted probability distributions.

Fig. 5

Mean scenario (obtained from Monte Carlo results) analysis results for this study. The number on top of the bar denotes the total ${\mathrm{LCOE}}_{\mathrm{el}}/\mathrm{LCOE}$, and the one below denotes the capital cost. (a) Base-case ${\mathrm{LCOE}}_{\mathrm{el}}=\$0.165/\mathrm{kWh}$. (b) Optimized ${\mathrm{LCOE}}_{\mathrm{el}}=\$0.129/\mathrm{kWh}$. (c) Base-case LCOE = $0.045/kWh. (d) Optimized LCOE = $0.038/kWh.

LCOE and LCOE_el are defined in Eqs. (3) and (4). LCOE represents the cost of supplying both heat and electricity; however, ${\mathrm{LCOE}}_{\mathrm{el}}$ only takes into account electricity costs. ${\mathrm{LCOE}}_{\mathrm{el}}$ was defined in the reference study as an alternative to LCOE to lower the payback period (LCOE minimization converges to a larger system, thus high investment and longer payback period) at the cost of obtaining a higher value for ${\mathrm{LCOE}}_{\mathrm{el}}$. For our study, Fig. 5 shows the base-case ${\mathrm{LCOE}}_{\mathrm{el}}$ is $0.165/kWh, which is reduced by 22% to $0.129/kWh on optimization. The optimized value is very close to the average price of electricity obtained in Monte Carlo simulations (Fig. 4) = $0.124/kWh. Energy storage using TPV can thus be profitable in the future. To assess future scenarios, we performed a sensitivity analysis and Monte Carlo simulations on the optimized system, which reduced LCOE and LCOE_el, and the results are mentioned in the next section.

LCOE has a much smaller value of $0.045/kWh and optimizes to $0.038/kWh. For both LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$, the optimum system converges to the smallest system size: nominal PV capacity = 5 kW_el, HTES max. capacity = $15{\mathrm{kWh}}_{\mathrm{th}}$, and PGU max. generation capacity ${\mathrm{kW}}_{el}=0.5\mathrm{kW}$. Based on this optimized system, we perform a sensitivity analysis based on the same parameters we considered for the uncertainty assessment. The results are displayed in Fig. 6 for parameters with values $\pm 25\%$ from the mean values listed in Table 6. The parameters having the most significant impact on LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ are ${\mathrm{Infl}}_{\text{fuel}}$ and ${\mathrm{Infl}}_{el}$, electricity price, ${\mathrm{CAPEX}}_{\mathrm{PV}}$, lifetime, and natural gas price (only for LCOE), with a potential cost reduction of around 10% by the most dominant parameter (natural gas price for LCOE and Infl_fuel and Infl_el for ${\mathrm{LCOE}}_{\mathrm{el}}$). ${\mathrm{LCOE}}_{el}$ does not change with natural gas prices because it only considers electricity, not heating requirements.

Fig. 6

Sensitivity analysis results for (a) LCOE and (b) LCOE_el with parameter values $\pm 25\%$ from the mean values listed in Table 6.

Figure 7 shows the Monte Carlo uncertainty assessment results for LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ (for an optimized system: nominal PV capacity = $5{\mathrm{kW}}_{\mathrm{el}}$, HTES max. capacity = $15{\mathrm{kWh}}_{\mathrm{th}}$, PGU max. generation capacity ${\mathrm{kW}}_{el}=0.5\mathrm{kW}$). We depict the confidence intervals for our large sample analysis and do not rely on the p-values as they offer little insight for large samples.⁷¹ The fitted distribution for LCOE is a general extreme value distribution, with a mean of $0.035/kWh and a standard deviation of $0.009/kWh, and that for ${\mathrm{LCOE}}_{\mathrm{el}}$ is a t distribution, with a mean of $0.132/kWh and a standard deviation of $0.016/kWh. The previously obtained optimized LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$ values listed in Table 5 (scenario analysis results) are within the 10% and 90% confidence limits. Thus, we obtained similar cost numbers to those in reference study⁵⁶ even after updating the assumptions and input values. The optimized LCOE from Fig. 6 is $0.033/kWh, close to the mean ($0.035/kWh) and median ($0.039/kWh) values obtained here, and is much less than the electricity price mean ($0.124/kWh), but is higher than the natural gas price mean ($0.015/kWh). LCOE represents the cost of consumed energy (heat and electricity) and thus is compared with both mean values. Adding storage units and PV energy sources increases the price of the supplied energy, but it can be reduced, as shown in sensitivity analysis and uncertainty assessment results.

Fig. 7

Monte-Carlo risk uncertainty assessment results (probability density function, cumulative distribution function, 10% and 90% confidence limits) for (a) LCOE: mean = 0.035, median = 0.039, standard deviation = 0.009, 10% and 90% confidence limits = (0.028,0.064) (all in $/kWh) and (b) LCOE_el: mean = 0.132, median = 0.132, standard deviation = 0.016, 10% and 90% confidence limits = (0.098, 0.165) (all in $/kWh).

The optimized ${\mathrm{LCOE}}_{\mathrm{el}}$, as mentioned in Fig. 5, is $0.129/kWh. The mean value calculated from the uncertainty analysis is close, $0.132/kWh. Figure 7 depicts other statistical parameters such as standard deviation = $0.016/kWh, 10%, and 90% confidence limits = (0.098, 0.165) $/kWh. It also shows the probability density function and the cumulative distribution function for LCOE and LCOE_el.

Box plots in Fig. 8 show the effects of each parameter’s uncertainty on LCOE and ${\mathrm{LCOE}}_{\mathrm{el}}$. The boxes’ left and right edges denote the 0.25 and 0.75 quartiles of the distributions (the width of the box is termed inter-quartile region, IQR), the dotted line inside the box indicates the median, and the whiskers and caps at the ends indicate the region from the box to the outermost data point within 1.5 times the IQR. Figure 8 illustrates that lifetime, CAPEX_PV, inflation rates, natural gas, and electricity prices have the most considerable impact on LCOE (the same parameters for sensitivity analysis). LCOE_el has all the same dominant parameters (except natural gas price). A way to reduce LCOE and LCOE_el would be to improve these parameters, as the boxes primarily lean towards the left (which implies lower cost). Thus, an improvement would lead to favorable economic results. The slightest uncertainty is observed in CAPEX_PGU and PGU efficiency; in other words, their variation does not have much effect on LCOE and LCOE_el.

Fig. 8

(a) LCOE and (b) LCOE_el box plot representing parameter uncertainty.

3.3.

CO₂eq. Emission Results

Based on the results in Fig. 5, we calculate the CO₂eq. emissions from the energy system before and after optimization using emission factors listed in Table 7. Here, we use the emission factors for natural gas, grid electricity, and PV electricity and assume negligible emissions from the HTES, LTES, and PGU/TPV units due to a lack of literature data. The results are shown in Fig. 9. We observe that before using energy storage (using natural gas for heating and grid electricity), natural gas CO₂eq. emissions are the highest (=7.166 tons/year) and reduce modestly for the base case and optimized cases (both use energy storage). The total CO₂eq. emissions for the system with no energy storage are 9.98 tons/year. The total emissions reduce for the base case (b) = 8.824 tons/year due to lesser dependence on natural gas and grid electricity and more utilization of cleaner solar PV energy to supply heat and electricity. The emissions are the lowest for the optimized case (c) (=8.75 tons/year) due to an optimized system with less dependence on grid electricity and an external boiler. Thus, according to our results, utilizing the energy management algorithm for energy storage and optimizing the system reduces CO₂eq. emissions by a modest amount (12%), primarily due to less dependence on grid electricity. Renewable energy integration in future grids would reduce their environmental impact; thus, TPV energy storage inclusion might not significantly reduce emissions. However, a detailed life cycle assessment must be performed to understand the process emissions better.

Table 7

Emission factors for natural gas, grid electricity, and PV electricity.

Fig. 9

CO₂eq. emissions in tons/year for (a) without energy storage (heat and electricity obtained from an external boiler and the grid, respectively), (b) base case, and (c) optimized case. For each column, the numbers represent the emissions from natural gas, grid electricity, and solar PV electricity (going from bottom to top).