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Market analysis for the integration of new power technologies: A case study of the deployment of hybrid fossil-based generator plus energy storage (ES-FE)
This study examines the national landscape of hybridized fossil energy (FE) power plants with energy storage (ES) technologies (“ES-FE”) and presents the compilation of an ES-FE dataset, which includes over 65 ES-FE projects and concepts in the United States, comprising approximately 500 MWh of co-located ES capacity with FE power plants. This study also estimates the economic feasibility of adding ES to existing FE power plants by characterizing the potential revenues that can be generated by the ES component through flexibility and capacity value. The analysis focuses on ES technologies with 2- to 10-h. durations located in four U.S. independent system operators (ISOs): Midcontinent ISO (MISO), Electric Reliability Council of Texas (ERCOT), PJM Interconnection (PJM), and California ISO (CAISO), which have +70,000 MW of combined FE power capacity that could add ES. Annual revenues are estimated for the ES component using a what-if-analysis approach, for capacity value, price arbitrage, or ancillary services provision. The results show that annual revenues depend on the end-use storage service, wholesale electricity and capacity market prices, and ES technology operation parameters such as discharging duration and cycling frequency. When performing a sensitivity analysis, ES accrues $7–178/kW-yr. via price arbitrage and ancillary services provision in the four ISOs, and $13–92/kW-yr. when providing capacity value only in MISO and PJM. A cash flow analysis is performed to estimate the net present value (NPV) of the ES addition using a range of ES costs. The study finds that for most ES technologies considered, these revenues alone are insufficient to achieve economic feasibility. In conclusion, of the 1645 total runs analyzed, 115 had positive NPVs (7%). Therefore, other revenue streams or monetizable benefits are necessary to achieve the break-even point.
Assessment of the impacts of renewable energy variability in long-term decarbonization strategies
To meet the nationally determined contributions proposed by the countries that signed the Paris Agreement, investments must be made in renewable generation technologies such as solar and wind. However, due to their high variability, these technologies pose challenges in terms of meeting demand or generating excess electricity. For this reason, energy system models are designed to capture this variability by considering flexibility technologies. Nevertheless, it is important to note that some energy system models lack integration with other sectors. Therefore, integrated assessment models have been employed to evaluate mitigation strategies, as they endogenously consider the linkages between energy and non-energy sectors. In addition, due to their complexity, these models do not account for the variability of renewable resources. Hence, this research aims to address this issue. Here, this work represents the first attempt to evaluate how the introduction of hourly resolution affects the outcomes of integrated assessment models, specifically focusing on the Global Change Analysis Model (GCAM). We employ a soft-linking approach between the GCAM and the Highway to Renewable Energy Systems model (H2RES, an hourly level energy system model) to accomplish this. The proposed approach is tested using Chile’s Nationally Determined Contributions under different hydrological profiles in the power sector. The results show that it is possible to use the capacity obtained from the Global Change Analysis Model and implement it on an hourly scale. However, the feasibility of implementation depends on high levels of flexibility technologies, such as battery energy storage. When given the choice of investments in renewable sources and flexible technologies, the optimal dispatch of the H2RES model show small differences than those obtained by GCAM-Chile. H2RES differs from GCAM-Chile in approximately 5% for wind and 3% for solar electricity generation in the year 2050. However, feasible integration of significant renewable sources is obtained with relatively high Critical Excess Electricity Production levels, reaching 20% in 2050. This excess electricity is attributed to the necessity for flexible technologies to manage the intermittency of renewables sources when hourly profiles of such sources are considered.
Demonstration of a multi-channel fluidized bed particle–supercritical carbon dioxide heat exchanger for concentrating solar applications
High-temperature thermal energy storage in oxide particles at temperatures above 600°C can couple concentrated solar energy with high-efficiency thermal power cycles to provide dispatchable solar-driven electricity. Challenges remain in developing cost-effective primary heat exchangers, which require expensive alloys, to extract the high-temperature thermal energy from the particles to power cycle fluids, such as supercritical CO 2 (sCO 2 ) in recuperated Brayton cycles. To explore one pathway for cost-effective, high-temperature particle heat exchangers, the current study demonstrates a shell-and-plate, particle–sCO 2 heat exchanger with narrow- channel fluidized beds coupled with micro-channel sCO 2 flows in the heat exchanger walls. This study evaluates the feasibility of multiple parallel, narrow-channel fluidized beds in shell-and-plate particle–sCO 2 HXs, to achieve high bed-wall heat fluxes at elevated temperatures. A reduced-order model simulates the narrow- channel, fluidized-bed particle–sCO 2 heat exchanger to design the fluidized bed geometry, in terms of depth, height, and number of channels,for a nominal 40-kWth heat exchanger at particle and sCO 2 inlet temperatures up to 600 °C and 400 °C respectively. The resulting shell-and-plate heat exchanger design operates with bubbling fluidization of the downward-flowing oxide particles to enhance bed-wall heat transfer. The heat exchanger core is fabricated with etched sCO 2 micro-channels in thin wall plates that are diffusion bonded to spacer frames to form the shell-and-plate structure with 12 parallel, fluidized bed channels, 10.4 mm deep. The heat exchanger is tested at the National Solar Thermal Test Facility at Sandia National Laboratories with CARBOBEAD HSP particles at design particle flow rates of 0.20 kg s –1 and inlet temperatures up to 525 °C. Results show that fluidization across multiple parallel channel beds can maintain uniform particle inventory with a common freeboard zone above the heat exchanger core. Bubbling fluidization improves particle–wall heat transfer coefficients but also increases axial dispersion of particle thermal energy, which lowers the log- mean temperature difference such that total heat transfer remains relatively constant to within ±10% over a broad range of fluidization gas velocities. The axial dispersion required particle and sCO 2 flow rates to be increased by 25% over model-designed conditions to achieve the targeted 40 kWth, which indicates the importance of incorporating axial dispersion into heat exchanger design models and of deploying bed structures to suppress it. Furthermore, this study demonstrates the feasibility and preferred fluidizing gas conditions for particle heat exchangers for releasing high-temperature thermal energy storage systems.
Feedstock and Catalyst Impact on Bio-Oil Production and FCC Co-Processing to Fuels
NREL's thermochemical biomass conversion research is focused on ex-situ upgrading of biomass fast-pyrolysis (FP) vapors as an efficient route to completely biogenic pyrolysis-based fuel precursors, fuels, and value-added chemicals depending on catalyst and process conditions. A near term pathway being developed uses these liquids for co-processing with petroleum feedstocks to assess biogenic carbon incorporation in hydrocarbon fuel feedstocks for potential refinery use. In this work, the impact of feedstock and catalyst on catalytic fast pyrolysis oil (CFPO) composition was determined with the oils then assessed for biogenic fuel production via FCC (fluidized catalytic cracking) co-processing. Biomass vapors were generated via fast pyrolysis with destabilizing vapor components (char, inorganics, tar aerosols) removed by hot gas filtration to produce clean vapors more responsive to catalytic upgrading. A Davison Circulating Riser (DCR), a petroleum industry standard for fluidized catalytic cracking (FCC) catalyst evaluation, was coupled to a custom pyrolyzer system designed to produce consistent-composition pyrolysis vapors as feed to the DCR. Pyrolysis vapors, derived from pure hardwood and softwood, were upgraded using commercially available modified zeolite-based catalysts to produce CFPOs. These upgraded oils were analyzed via 31P and 13C NMR spectroscopy, GCxGC-TOF/MS, carbonyl and ultimate analysis (CHNO), and simulated distillation (SIMDIS) to assess both oil chemistry and distillation behavior as they relate to catalyst and feedstock type for producing fungible hydrocarbon product liquids. These exploratory vapor-phase-upgrading results demonstrated the feasibility of producing refinery-compatible hydrocarbon fuel intermediates entirely from biomass-derived fast-pyrolysis vapors using an industry-accepted DCR system for catalytic upgrading. The FCC co-processing results demonstrated the feasibility of using CFPOs with VGO feeds in FCC refinery operations to produce biogenic carbon containing fuels.
Effect of ash in paper sludge on enzymatic hydrolysis
The valorization of paper sludge is a high-potential process to develop renewable fuels and chemicals, which can be integrated with pulp and paper mills. Calcium carbonate is the main ash component in sludge, which plays a role in buffering pH and potentially lowering the conversion during enzymatic hydrolysis. Therefore, it is important to investigate the effect of ash on sugar yields and examine pH change to introduce efficient and economical enzymatic hydrolysis of sludge. Carbohydrate conversion was enhanced when the ash was removed by fractionation. On the other hand, the highest sugar recovery was obtained when the sludge contained 20% ash content. The pH change during enzymatic hydrolysis was influenced by ash and explained why sludge-derived hydrolysate showed lower carbohydrate conversion. Therefore, a high shear process with the increased acid amount is suggested to prohibit the negative effect of ash and enhance the accessibility of cellulase to fibers. Finally, this study highlights the feasibility of using wet waste streams generated by the paper industry.
Techno-economic analysis of biomass value-added processing informed by pilot scale de-ashing of paper sludge feedstock
Paper sludge biomass represents an underutilized feedstock rich in pulped and processed cellulose which is currently a waste stream with significant disposal cost to industry for landfilling services. Effective fractionation of the cellulose from paper sludge presents an opportunity to yield cellulose as feedstock for value-added processes. A novel approach to cellulose fractionation is the sidehill screening system, herein studied at the pilot-plant scale. Composition analysis determined ash removal and carbohydrate retention of both sidehill and high-performance benchtop screening systems. Sidehill screening resulted in greater carbohydrates retention relative to benchtop screening (90% vs 66%) and similar ash removal (95% vs 98%). Techno-economic analysis for production of sugar syrup yielded a minimum selling price of $331/metric ton of sugar syrup including disposal savings, significantly less than a commercial sugar syrup without fractionation. Furthermore, sensitivity analysis showed that screening conditions played a significant role in economic feasibility for cellulosic yield and downstream processes.
Influence of extreme temperature conditions on CO 2 direct air capture using amino-acid solutions
Geological features play a pivotal role in determining the feasibility of deploying CO₂ direct air capture (DAC) technologies, primarily because they influence the availability of cost-effective energy sources, such as natural gas and geothermal energy, and also due to the potential for CO₂ sequestration. Many regions face challenges due to variable weather conditions including seasonal temperature fluctuations, high or low humidity, and sub-ambient temperatures. These extremes can reduce DAC performance or even lead to catastrophic events. Aqueous solvents considered for DAC systems are particularly vulnerable to seasonal variations in colder climates, where the solvent may underperform or freeze. It is therefore essential to investigate the CO₂ capture efficiency of aqueous solvents across a broad range of environmental temperatures, spanning sub-zero to hot conditions (>30 °C). In this study, DAC operation is examined using a high-flux solvent–air crossflow contactor under two major weather scenarios: (i) cold conditions below 0 °C and (ii) hot conditions above 30 °C. A parametric study is conducted to investigate the contactor performance regarding CO₂ removal efficiency, uptake capacity, and reaction kinetics versus temperature when the air velocity through the contactor exceeds 1 m/s. The efficacy of the contactor is systematically investigated using various anti-freeze amino-acid solvent formulations. A mass-transfer mechanistic model is developed to assess the process performance over a wide temperature range and propose scalable design guidelines. Machine learning is also employed to identify key parameters affecting the CO₂ capture efficiency. It is shown that air velocity and temperature are the primary factors influencing CO₂ uptake. Based on performance data obtained under subfreezing temperatures, a technoeconomic analysis is conducted to evaluate the feasibility of using aqueous solvents in seasonal cold regions. In conclusion, the findings of this study provide valuable insights into siting considerations for deploying solvent-based DAC, thereby contributing to the advancement of sustainable carbon removal solutions.
Spectroscopic investigations on structural incorporation pathways of FeIII into zeolite frameworks in cement-relevant environments
Fe{sup III}-containing aluminosilicate zeolites are present in cement-relevant and natural environments. Although Fe{sup III} is known to occur in framework tetrahedral sites where it substitutes isomorphically Al{sup III}O{sub 4} or in extra-framework octahedral sites as free Fe(H{sub 2}O){sub 6}{sup 3+}, the structural incorporation process of Fe{sup III} into different sites is little known. We aim to discern feasible pathways of Fe{sup III} incorporation using hydrothermal synthesis methods and synchrotron-based spectroscopic analyses. Results showed that introducing either Fe{sup 3+} or Fe{sub 2}O{sub 3}·xH{sub 2}O initially during zeolite nucleation did not lead to Fe{sup III} incorporation into the zeolites but only Fe{sub 2}O{sub 3}·xH{sub 2}O prevailed in both cases. However, Fe(NO{sub 3}){sub 3}, FeCl{sub 3}, and Fe{sub 2}O{sub 3}·xH{sub 2}O affected the kind of zeolite formed. A feasible pathway to incorporate tetrahedral Fe{sup III} in the zeolite framework was to introduce firstly Fe{sup III} in the cage of faujasite-Y followed by a phase transformation to chabazite. This study facilitates understanding of Fe{sup III} uptake in zeolites and of Fe{sup III} functional sites that can contribute to immobilization of contaminants.
A comparative TEA of a two-step process using chemical solvents for producing an ultra-sweet natural gas
Here, a comprehensive Techno-Economic Analysis (TEA) was performed to evaluate the economic feasibility of a novel two-step process (TSP) developed in Aspen Plus V12.1 to desulfurize and decarbonize a raw natural gas containing (2 mol% H 2 S and 5 mol% CO 2 ) into an ultra-sweet natural gas containing (1.72 ppmv H 2 S and 4.19 ppmv CO 2 ). The raw natural gas flow rate used in the TSP was 117.74 kg/s at 60 °C and 50 bar. The TSP combines an H 2 S desulfurization step using potassium carbonate (K 2 CO 3 ) and a CO 2 capture step using 3 different chemical solvents, monoethanolamine (MEA), sodium glycinate (SGS), and potassium glycinate (PGS). Both steps employ fixed-bed absorbers packed with Mellapak 250Y structured packing. The hydraulics and mass transfer characteristics for the TSP were calculated, indicating normal operation with higher gas-side (k G ) than liquid-side (k L ) mass transfer coefficients. The TEA of TSP indicated that PGS had the most promising economic feasibility among the 3 solvents as it exhibited the lowest Levelized Cost of CO 2 capture (LCOC) of $\$$47.54/ton.CO 2 at a Capital Expenditure (CAPEX) of $\$$24.98 million, and an Operating Expenditure (OPEX) of $\$$12.20 million/year. Also, the TSP could produce one MMSCF of ultra-sweet natural gas at a total cost of $\$$339.55.
The latent variable proximal point algorithm for variational problems with inequality constraints
The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.
Development of novel dynamic machine learning-based optimization of a coal-fired power plant
The increasing fraction of intermittent renewable energy in the electrical grid is resulting in coal-fired boilers now routinely ramp up and down. The current state-of-the-art operation for such boilers is to apply steady-state, neural network-based optimization to make control decisions in real-time, and this report demonstrates the feasibility of extending this to dynamic, neural network-based optimization using a long short-term memory neural network. A simplified numerical simulation of a t-fired coal boiler and supporting equipment is used to represent a real plant subjected to both steady-state, neural network-based optimization and dynamic, neural network-based optimization. Using the same intervals and a particle swarm optimization algorithm, the dynamic optimization outperforms the steady-state optimization and realizes up to 4.58% improvement in thermal efficiency. Dynamic optimization with a long short-term memory neural network is shown to both be feasible and beneficial for operation of a coal-fired boiler under changing load.
Formation and reconfiguration of tight multi-lane platoons
Advances in vehicular communication technologies are expected to facilitate cooperative driving in the future. Connected and Automated Vehicles (CAVs) are able to collaboratively plan and execute driving maneuvers by sharing their perceptual knowledge and future plans. In this paper, an architecture for autonomous navigation of tight multi-lane platoons traveling on public roads is presented. Using the proposed approach, CAVs are able to form single or multi-lane platoons of various geometrical configurations. They are able to reshape and adjust their configurations according to changes in the environment. The proposed architecture consists of two main components: an offline motion planner system and an online hierarchical control system. The motion planner uses an optimization-based approach for cooperative formation and reconfiguration in tight spaces. A constrained optimization scheme is used to plan smooth, dynamically feasible and collision-free trajectories for all the vehicles within the platoon. The paper addresses online computation limitations by employing a family of maneuvers precomputed offline and stored on a look-up table on the vehicles. The online hierarchical control system is composed of three levels: a traffic operation system (TOS), a decision-maker, and a path-follower. The TOS determines the desired platoon reconfiguration. The decision-maker checks the feasibility of the reconfiguration plan based on real-time information about the surrounding traffic. The reconfiguration maneuver is executed by a low-level path-following feedback controller in real-time. The effectiveness of the approach is demonstrated through simulations of three case studies: (1) formation reconfiguration (2) obstacle avoidance, and (3) benchmarking against behavior-based planning in which the desired formation is achieved using a sequence of motion primitives.
Moving-horizon false data injection attack design against cyber–physical systems
Systematic attack design is essential to understanding the vulnerabilities of cyber–physical systems (CPSs), to better design for resiliency. In particular, false data injection attacks (FDIAs) are well-known and have been shown to be capable of bypassing bad data detection (BDD) while causing targeted biases in resulting state estimates. However, their effectiveness against moving horizon estimators (MHE) is not well understood. In fact, this paper shows that conventional FDIAs are generally ineffective against MHE. One of the main reasons is that the moving window renders the static FDIA recursively infeasible. Here, this paper proposes a new attack methodology, moving-horizon FDIA (MH-FDIA), by considering both the performance of historical attacks and the current system’s status. Theoretical guarantees for successful attack generation and recursive feasibility are given. Numerical simulations on the IEEE-14 bus system further validate the theoretical claims and show that the proposed MH-FDIA outperforms state-of-the-art counterparts in both stealthiness and effectiveness. In addition, an experiment on a path-tracking control system of an autonomous vehicle shows the feasibility of the MH-FDIA in real-world nonlinear systems.
Analytical population dynamics underlying harmful algal blooms triggered by prey avoidance
A modified version of the NPZD ecosystem model is used to analytically examine the effects of predation avoidance, a possible mechanism for triggering harmful algal blooms (HAB). To resolve HAB development caused by predation avoidance, an additional phytoplankton functional group is considered, one that has slower nutrient uptake and better predation avoidance characteristics than the non-harmful phytoplankton group used in traditional NPZD models. Because the two phytoplankton groups (one non-harmful and one HAB) compete for only one resource within the same system, steady state (equilibrium) conditions cannot occur without the presence of zooplankton; only the non-harmful phytoplankton group, which defeats the HAB group in the resource competition, can survive in the equilibrium. The presence of sufficient zooplankton effectively acts to replenish the nutrient pool by consuming the non-harmful phytoplankton. When this occurs, two equilibrium states are found: one with both phytoplankton groups coexisting, and one that only includes the HAB group. Further, the condition required for equilibrium is that the total nitrogen within the system should be larger than a threshold determined by model coefficients. The threshold and feasibility of the equilibrium are sensitive to the relative HAB predation avoidance coefficient. If the coefficient is larger than the ratio of net growth rates between the HAB and non-harmful phytoplankton group, the threshold becomes infinite, and an equilibrium is not feasible. The time scale for the system to reach an equilibrium state that includes a HAB group is determined asymptotically. The dependence of a threshold condition as a controlling factor may explain the regime shift of dominant species causing HABs. The ecosystem model is fully implemented into the Regional Ocean Modeling System and applied to an idealized coastal embayment (with depths and geometry taken from San Francisco Bay) to show numerically the dominance of prey avoidance dynamics in a natural shallow water environment that includes advection and diffusion. The analytical results improve strategies for HAB modeling and provide guidance for setting model coefficients necessary to resolve a HAB event.
Quantum computing approach for building surface sunlit in urban-scale energy modeling
Solar shadow calculations are needed in building energy modeling and performance simulation of PV systems installed on roofs or facades of buildings. We present a quantum computing approach for calculation of building surface sunlit fractions by recasting solar visibility as a binary optimization problem solved by quantum annealing. Each triangulated surface centroid is encoded as a binary qubit indicating sunlit or shaded status. Geometric visibility constraints are derived from the Möller-Trumbore intersection algorithm and converted into a constrained quadratic binary model compatible with contemporary quantum annealers. The coefficients were embedded to D-Wave quantum computer. To demonstrate feasibility, we conducted a case study in San Francisco for a target building with 52 triangles and roughly 2700 nearby triangles within 50 m evaluated at representative winter and summer solar positions. The results demonstrated that quantum annealing can reliably calculate and distinguish sunlit from shaded surfaces. Quantum samples achieved average accuracy exceeding 92.4 %, with the aggregate surface-level agreement approaching 99.9 %. The outputs of quantum computers agreed closely with classical algorithms, indicating practical feasibility and promising scalability. Finally, the hourly sunlit fractions of building surfaces can be obtained for urban energy modelling. This is the first study to apply quantum computing to the solar shadow and building surface sunlit calculation. It introduces a new paradigm that differs fundamentally from traditional approaches.
Thermodynamic analysis and optimization of supercritical carbon dioxide Brayton cycles for use with low-grade geothermal heat sources
The transcritical carbon dioxide Rankine cycle has emerged as an alternative for power generation in low-grade heat applications. However, the low heat rejection temperatures required for condensing the carbon dioxide is almost prohibitive for many locations. A simple solution is the adoption of a supercritical carbon dioxide Brayton cycle which does not need such low temperature heat sinks. This power cycle has been poorly studied previously in low-grade heat applications. Therefore, with the aim of determining the performance and feasibility of the supercritical carbon dioxide Brayton cycle from thermodynamic viewpoint, using a low-grade geothermal heat source, this paper presents a comparative thermodynamic analysis between four different supercritical carbon dioxide Brayton cycles. For this purpose, detailed models were developed and solved by coupling the thermodynamic model with the thermal-hydraulic model of a Printed Circuit Heat Exchanger. Subsequently, simulations of a base case, a parametric analysis, and an optimization using Genetic Algorithms, were carried out. Results show that there is a combination of operating conditions that maximizes the electrical output of the system. Besides, some values of the minimum pressure of the cycles can increase substantially the precooler cooling water pumping power. At the optimum design point, using a 20 kg/s geothermal brine stream at 150 °C as heat source with a minimum allowable reinjection temperature of 70 °C, the Intercooled Recuperated Brayton Cycle achieved the highest electric power output, energy and exergy efficiencies, obtaining values of 779.99 kW, 11.51%, and 52.49%, respectively. The other feasible alternatives were the Recuperated Brayton Cycle, the Simple Brayton Cycle and the Intercooled Brayton Cycle, ranked, in that order.
Solving the duck curve in a smart grid environment using a non-cooperative game theory and dynamic pricing profiles
With the intermittency that comes with electricity generation from renewables, utilizing dynamic pricing will encourage the demand-side to respond in a smart way that would minimize the electricity costs and flatten the net electricity demand curve. Determining the optimal dynamic pricing profile that would leverage distributed storage to flatten the curve is a novel idea that needs to be studied. Moreover, the economic feasibility of utilizing distributed electrical energy storage is still not given in the literature. Therefore, in this paper, a novel way of solving a citywide dynamic model using a bilevel programming algorithm is introduced. The problem is developed as a novel non-cooperative Stackelberg game that utilizes air-conditioning systems and electrical storage through the end-users to determine the optimal dynamic pricing profile. The results show that the combined effect of utilizing demand-side air-conditioning systems and distributed storage together can flatten the curve while employing the optimal dynamic pricing profile. An economic study is performed to determine the economic feasibility of 20 different cases with different battery designs and the level of solar penetration. Three metrics were used to evaluate the economic performance of each case: the levelized cost of storage, the levelized cost of energy, and the simple payback period. Most cases had levelized cost of storage values lower than 0.457 $/kWh, which is the lower bound available in the literature. Seven out of 16 cases have a simple payback period shorter than the lifetime of the system (25 years). The case with a 100 MW PV power plant and a battery storage of size 597 MWh, was found to be the most promising case with a simple payback period of 12.71 years for the photovoltaic plant and 19.86 years for the demand-side investments.