Power spectrum with k6k^6 growth for primordial black holes

The decrease of both the rolling speed of the inflaton and the sound speed of the curvature perturbations can amplify the curvature perturbations during inflation so as to generate a sizable amount of primordial black holes. In the ultraslow-roll inflation scenario, it has been found that the power spectrum of curvature perturbations has a $k^4$ growth. In this paper, we find that when the speed of sound decreases suddenly, the curvature perturbations becomes scale dependent in the infrared limit and the power spectrum of the curvature perturbation only has a $k^2$ growth. Furthermore, by studying the evolution of the power spectrum in the inflation model, in which both the sound speed of the curvature perturbations and the rolling speed of the inflaton are reduced, we find that the power spectrum is nearly scale invariant at the large scales to satisfy the constraint from the cosmic microwave background radiation observations, and at the same time can be enhanced at the small scales to result in an abundant formation of primordial black holes. In the cases of the simultaneous changes of the sound speed and the slow-roll parameter $\eta$ and the change of the sound speed preceding that of the slow-roll parameter $\eta$, the power spectrum can possess a $k^6$ growth under certain conditions, which is the steepest growth of the power spectrum reported so far.Comment: 29 pages, 14 figures, to appear in PR

Growth of power spectrum due to decrease of sound speed during inflation

We study the amplification of the curvature perturbations due to a small sound speed and find that its origin is different completely from that due to the ultraslow-roll inflation. This is because when the sound speed is very small the enhancement of the power spectrum comes from the fact that the curvature perturbations at the scales smaller than the cosmic microwave background (CMB) scale becomes scale-variant, rather than growing that leads to the amplification of the curvature perturbations during the ultraslow-roll inflation. At large scales the power spectrum of the curvature perturbations remains to be scale invariant, which is consistent with the CMB observations, and then it will have a transient $k^2$ growth and finally approach a $k^4$ growth as the scale becomes smaller and smaller. Thus the power spectrum can be enhanced to generate a sizable amount of primordial black holes. Furthermore, when the high order correction in the dispersion relation of the curvature perturbations is considered the growth of the power spectrum of the curvature perturbations has the same origin as that in the case without this correction.Comment: 11 pages, 1 figure. three references adde

The Optimization of Power Dispatch for Hydro-thermal Power Systems

AbstractA model in power market for hydro-thermal-nuclear power system has been proposed in this paper. Nuclear units, hydropower units and coal-fired power units are considered to have the renewable energy best used. The model contains two sub-models: Model1 and Model2. Model1 is used to solve the problem of allocating hydro loads and thermal loads, while Model2 is used to solve the problem of optimal power dispatch within hydro units and coal-fired units. Simulation and sensitivity analysis have been done in a case study. The results reveil that the proposed model is correct and the solution approach is effective

Thermal performance of different integration schemes for a solar tower aided coal-fired power system

A Solar Tower Aided Coal-fired Power (STACP) system utilizes a solar tower coupled to a conventional coal-fired power system to reduce pollutants, greenhouse gas emissions and the investment of solar energy facilities. This paper examines three different schemes for integrating solar energy into a conventional boiler. For each scheme, an energy and exergy analysis of a 600 MWe supercritical coal-fired power system is combined with 53 MWth of solar energy in both a fuel saving mode and a power boosting mode. The results show that, for all these integration schemes, the boiler’s efficiency and system’s efficiency are reduced. However, the standard coal consumption rate is lower in comparison to conventional power plants and the standard coal consumption rate in the fuel saving mode is lower than that in the power boosting mode for all three schemes. Comprehensively considering both the standard coal consumption rate and efficiency, the scheme that uses solar energy to heat superheat steam and subcooled feed-water is the best integration option. Compared with a coal-fired only system, the saved standard coal consumption rate of the above mentioned scheme in fuel saving mode and power boosting mode can reach up to 11.15 g/kWh and 11.11 g/kWh, respectively. Exergy analysis shows, for STACP system, exergy losses of boiler and solar field contribute over 88% of whole system’s exergy loss

Thermal performance of different integration schemes for a solar tower aided coal-fired power system

A Solar Tower Aided Coal-fired Power (STACP) system utilizes a solar tower coupled to a conventional coal-fired power system to reduce pollutants, greenhouse gas emissions and the investment of solar energy facilities. This paper examines three different schemes for integrating solar energy into a conventional boiler. For each scheme, an energy and exergy analysis of a 600 MWe supercritical coal-fired power system is combined with 53 MWth of solar energy in both a fuel saving mode and a power boosting mode. The results show that, for all these integration schemes, the boiler’s efficiency and system’s efficiency are reduced. However, the standard coal consumption rate is lower in comparison to conventional power plants and the standard coal consumption rate in the fuel saving mode is lower than that in the power boosting mode for all three schemes. Comprehensively considering both the standard coal consumption rate and efficiency, the scheme that uses solar energy to heat superheat steam and subcooled feed-water is the best integration option. Compared with a coal-fired only system, the saved standard coal consumption rate of the above mentioned scheme in fuel saving mode and power boosting mode can reach up to 11.15 g/kWh and 11.11 g/kWh, respectively. Exergy analysis shows, for STACP system, exergy losses of boiler and solar field contribute over 88% of whole system’s exergy loss

Annual performance analysis and optimization of a solar tower aided coal-fired power plant

The integration of solar energy into coal-fired power plants has been proven as a potential approach in the utilization of solar energy to reduce coal consumption. Moreover, solar augmentation offers low cost and low risk alternatives to stand-alone solar thermal power plants. In this study, the annual performance of a solar tower aided coal-fired power (STACP) system is investigated, and the influence of thermal storage system capacity on the annual solar generating power and annual solar-to-electricity efficiency is explored. The thermal storage system capacity is optimized to obtain the lowest levelized cost of electricity (LCOE). At the same time, the influence and sensitivity of several important economic factors are explored and assessed. Results demonstrate that compared to a coal-fired power system, the reduction in the annual average coal consumption rate of the STACP system with high direct normal irradiance (DNI), medium DNI, and low DNI are 5.79, 4.52, and 3.22 g/kWh, respectively. At a minimum, the annual coal consumption can be reduced by 14,000 t in a 600 MWe power generation unit. Because the same solar field is considered under different DNI conditions, the LCOE in the high DNI, medium DNI, and low DNI scenarios are all fairly similar (6.37, 6.40, and 6.41 ¢/kWh, respectively). When the solar multiple is 3.0, the optimal thermal storage capacity of the STACP system, with high, medium, and low DNIs are 6.73, 4.42, and 2.21 h, respectively. The sensitivity analysis shows that the change in economic parameters exerts more influence on the STACP system with the high DNI compared with the other two scenarios

Off-design thermodynamic performances of a solar tower aided coal-fired power plant for different solar multiples with thermal energy storage

Solar aided coal-fired power system has been proven to be a promising way to utilise solar energy in large scale. In this paper, the performances of the solar tower aided coal-fired power (STACP) system at 100% load, 75% load, and 50% load for different days are investigated and the maximum solar power that the boiler can absorb under different plant loads are explored. Then, the effects of solar multiple (SM) and the thermal energy storage (TES) hour on the daily performance of STACP system are investigated. Results show that the maximum solar power that a 600 MWe boiler can absorb at 100% load, 75% load and 50% load are 76.4 MWth, 54.2 MWth and 23.0 MWth, respectively. Due to the augmented energy from the solar field, the maximum standard coal consumption rate is reduced by 13.53 g/kWh, 12.81 g/kWh and 8.22 g/kWh at 100% load, 75% load and 50% load, respectively. With an increase of solar power input, the boiler efficiency, overall system efficiency and solar thermal-to-electricity efficiency show a downward trend. In addition, the daily coal consumption of summer solstice is the lowest while the winter solstice is the highest for a particular SM and TES hour