Modeling of a hybrid power system integrating solar radiation and syngas combustion energy

This study aims to model a hybrid power system that can continuously generate power by switching between two possible thermal sources: solar radiation and combustion energy from synthesis gases. The system comprised a hybrid energy receiver, solar dish, Stirling generator, fluidized‐bed gasifier, boiler, and water tank. The solar dish was a dual‐reflection solar collector that used two mirrors, namely the main and subordinate concentrators, to concentrate a broad expanse of solar radiation onto a hybrid energy receiver. The fluidized‐bed gasifier was employed for the production of synthesis gases. The synthesis gases were combusted to provide an auxiliary heat source for the Stirling generator when solar radiation was insufficient. Solar radiation or combustion energy was alternatively introduced into the hybrid energy receiver and converted to power by a 1‐kW‐scale beta‐type Stirling engine. In this manner, the Stirling generator could serve as a base‐load power plant regardless of solar conditions. In this study, a complete quantitative model was developed for a demonstration plant by incorporating thermodynamic and dynamic models of the beta‐type Stirling engine, a ray‐tracing model for the dual‐reflection solar dish, an energy model of the hybrid energy receiver, and experimental data for the fluidized‐bed gasifier. The performance response of the system during switching between solar radiation and combustion energy was predicted. The modeling results indicated that switching can result in a continuous power output ranging from 600 to 1200 W. With synthesis gas combustion as the auxiliary heat source, the hybrid Stirling power system can be operated continuously, and the overall power output is increased by 109.82% compared to a conventional concentrated solar power system that only uses solar radiation.


| INTRODUCTION
In recent years, researchers in the energy and environmental sectors have endeavored to pave the way for an effective response to the global challenge of climate change.Their attention has always focused on renewable energy.According to a report by the International Energy Agency (IEA), 1 by 2050, nearly 90% of the total electricity generation will be derived from solar, wind, bio, geothermal, and hydro energies.Among these, solar energy is expected to be the largest because it is considered an eternal zero-emission energy source.Concentrated solar power (CSP) systems that employ parabolic solar troughs, linear Fresnel reflectors, parabolic solar dishes, or central towers are promising technologies for the near future.3][4] This system can be a small-to medium-scale power system applicable to residential buildings. 3Parabolic solar trough power plants are also of great interest to researchers such as Mahlangu and Thopil. 5he combination of a Stirling engine and a parabolic solar dish is one of the most efficient solutions for solar power generation.The first prototype system, a 25-kW vanguard system, was constructed by ADVANCO in Southern California. 4 This system comprised a doubleacting kinematic Stirling engine, a 10.5-m diameter glassfaced dish, and a direct insolation receiver.Its net conversion efficiency was recorded as 29.4%.Two 50 kW solar dish Stirling systems (SDSSs) were installed in Riyadh, Saudi Arabia, and consisted of a 17-m diameter stretched-membrane concentrator, a direct tube receiver, and a kinematic Stirling engine. 6Lopez and Stone 7 described a dish-Stirling system built by McDonnell Douglas Aerospace Corporation and Southern California Edison.This was the first system specifically designed for commercial applications.Reinalter et al. 8 measured the best performance with a measured peak electrical output power of 11 kW in a Eurodish system.The optical, Stirling-engine, and overall efficiencies for the conversion of solar energy to electrical energy were 74.4%, 39.4%, and 22.5%, respectively.
Regarding the modeling and simulation of SDSSs, Fraster 9 presented a prediction model for the performance of Stirling dish systems.Reddy and Veershetty 10 performed a viability analysis for a 5-MW solar parabolic-dish concentrator field in India.They investigated the effects of shading on the performance of a solar parabolic-dish collector and performed an economic analysis of parabolic-dish plants.Ahmadi et al. 11 performed a multiobjective optimization of an SDSS.This study provided an optimal solution for the system parameters through the design process.Hafez et al. 12 developed a model to design and evaluate SDSS performance.The authors compared the relative performance of reflectors made from different materials (polymeric film, nonmetal, polished stainless steel, and anodized aluminum).Gholamalizadeh and Chung 13 presented a thermal model for estimating a 1-kW-scale SDSS.This model accounted for conduction, convection, and radiation heat losses through the aperture of the receiver.A maximum receiver efficiency of approximately 60% and a maximum power output of 850 W were obtained.Aksoy et al. 14 established a solar simulator to investigate a beta-type Stirling engine.The experimental results revealed that the 1000-W halogen lamp had a maximum power output of 127.17 W and a thermal efficiency of 12.85%.Caballero et al. 15 presented a multiobjective optimization model for a solar-dish Stirling engine in Itajubá, Brazil.The NSGA-II algorithm was employed to optimize the power and efficiency of the system.The optimal power output was 11.1 kW with an overall efficiency of 21%.Shabanpour et al. 16 performed energy, environmental, and economic analyses of a solar-dish Stirling micro-combined heat and power (micro-CHP) system in a residential building.The payback periods for five different locations were estimated.Kadri and Abdallah 17 proposed a model for a standalone solar dish Stirling generator power plant in Tunisia.The model included different meteorological conditions and uncontrollable power loads.Yaqi et al. 18 developed a theoretical model that incorporated the effects of the absorber temperature and concentration ratio.The results showed that when the temperature of the absorber was maintained at 1100K with a concentration ratio of 1300, the thermal efficiency under optimized conditions was 34%.Zayed et al. 19 established a mathematical model for simulating an SDSS.The system produced 28.748 MWh per year with an annual efficiency of 19.55%.Castellanos et al. 20 performed a numerical simulation of an SDSS.According to the simulation, the theoretical temperature in the receiver cavity was 1596K, and the efficiency was 68% for a 10.5-m diameter concentrator.
However, the instability of solar irradiation owing to cloudy weather and the absence of solar irradiation at night are inherent flaws of solar energy.Cardozo et al. 21ntegrated a 1-kW Stirling engine with a 20-kW wood pellet burner to improve the instability of solar irradiation.The heating temperature of a Stirling engine combined with a burner was discussed previously.The experimental data showed that the overall efficiency of the system for producing both heat and power was greater than 72%.Thiers et al. 22 presented a numerical model to characterize the dynamic behavior of a wood-pellet micro-CHP unit.A complete model, including a stratified storage tank and a micro-CHP unit, was developed.Nishiyama et al. 23 developed a demonstration plant consisting of a Stirling engine CHP system and a simplified biomass combustor.The calculations were performed with a 55-kW Stirling engine in mind.In addition, Lombardi et al. 24 investigated the advantages of installing the heater head of a Stirling engine within a fluidized-bed combustor.This design had a positive effect on the thermal efficiency of the Stirling engine because of the enhancement of the heat transfer coefficient and the reduction in dead space.However, the dynamic model was simplified, and mechanical loss was not accounted for in the mathematical model.The model overestimated the predicted performance of the Stirling engine.Mehrpooya et al. 25 quantitatively investigated a power system composed of an SDSS and a thermoelectric device.By conducting multiobjective optimization for the hybrid energy system, the electric power output and overall efficiency could be increased to 26.21 kW and 39.17%, respectively.Angrisani et al. 26 proposed a CHP system that used direct solar energy and biomass.They used a fluidized bed as a receiver with a Scheffer-type mirror and a Stirling engine to convert heat to power using a simple model.The authors presented a hybrid solar biomass system and discussed the disadvantages of Scheffer mirror concentrators.Seasonal adjustments were required to refit the Scheffer mirror to efficiently concentrate solar radiation on the target area.In addition, Sareriya et al. 27 conducted a comprehensive review of Scheffler concentrators.The authors found several limitations to the Scheffler concentrator technology.These included vast space requirements, high cosine losses, difficulty attaining temperatures higher than 300°C, single-axis tracking, and high maintenance costs.Lower operating temperatures resulted in reduced performance for Stirling engines.
Inspired by the existing reports, [21][22][23][24][25][26][27] this study aims to build a hybrid power system by integrating a hybrid energy receiver, a two-axis concentrating solar dish, a Stirling generator, a fluidized-bed gasifier, and a boiler with a water tank to overcome the inconsistent solar irradiation and the complexity of seasonal adjustment for the Scheffer-type mirror 27 with one-axis tracking and to continuously generate renewable energy under any circumstances.The hybrid energy receiver was designed to ensure that both the solar radiation and combustion energy of the synthesis gases produced by the fluidizedbed gasifier were alternatively introduced into the hybrid energy receiver for power generation using the Stirling engine.In this manner, the Stirling generator could be operated continuously and function as a base-load power plant even when solar irradiation was insufficient.
Figure 1 depicts an image of the complete integrated system.The solar dish was a two-axis active solar tracker that used a sun-tracking control system to track the trajectory of the sun to maximize the absorption of solar radiation.The solar dish was a dual-reflection solar collector that utilized two mirrors, namely, the main concentrator and the subordinate concentrator, to concentrate solar irradiation onto a small area.A fluidized-bed gasifier was employed to produce synthesis gases such as H 2 , CH 4 , and CO from wood pellets.The synthesis gases were then combusted to provide an auxiliary heat source for the Stirling generator when solar radiation was insufficient.The hybrid energy receiver was placed at the focal point of the solar dish to capture solar energy.Meanwhile, the synthesis gases were burned in the combustor, and the burned mixture was emitted from the combustor via a pipeline to the hybrid energy receiver.In this manner, the Stirling generator could serve as a baseload power plant regardless of the solar conditions.The waste heat emitted by the Stirling generator and combustor was channeled into the boiler for domestic water heating.
In this study, we investigated the system response in terms of power and temperature during the switching F I G U R E 1 Photograph of the whole hybrid power system.
between solar radiation and combustion energy to minimize system performance stability.To achieve this, the modeling of a hybrid power system was attempted for a newly built demonstration plant.The model was developed by incorporating the thermodynamic and dynamic models of the beta-type Stirling engine, a raytracing model for the solar dish, an energy model of the hybrid energy receiver, and combustion energy predictions.Switching is a major concern because the transition time, power variation, and temperature variation from one energy source to another have subtle effects on the power output stability of the system.

| Hybrid energy receiver
The detailed design of the hybrid energy receiver is depicted in Figure 2. The hybrid energy receiver was insulated to minimize thermal loss.The heating tubes of a beta-type Stirling engine were inserted into the chamber of the hybrid energy receiver to receive energy.The solar energy entering the chamber through an aperture was protected by quartz glass and concentrated on the heating tubes of the Stirling engine.A flue tube is installed around the heating tubes of the Stirling engine.As the hot flue gases flow through the flue tube, they could heat the surface of the heater tube of the Stirling engine.Therefore, the heating tube of a Stirling engine receives combustion energy from the flue tube.A series of annular fins was installed on the external surface of the flue tube to improve heat transfer.When solar radiation was insufficient, the high-temperature flue gases emitted by the combustor were channeled through a heating coil to provide combustion energy for the Stirling engine.
In the theoretical model, the heating tubes of the Stirling engine were regarded as the control volume for which the energy equation was formulated and solved.The Stirling engine received either solar radiation or combustion energy during operation; therefore, in the energy analysis of the Stirling engine, the solar radiation energy, combustion energy, energy absorbed by the beta-type Stirling engine, and thermal losses via convection were all considered.In addition, the chamber was well isolated using insulation materials that aid in minimizing heat loss from the hybrid energy receiver.Energy conservation with the heating tubes of the Stirling engine was expressed as follows: where T hw represents the temperature of the heating tubes of the Stirling engine and Q h denotes the energy absorbed by the working gas in the Stirling engine for power generation.
For the solar radiation mode, Q in represents the net energy input, which is equal to the difference between the energy received from solar irradiation Q ir and the thermal losses in the receiver.Thus, Q in is expressed as follows: The first term on the right-hand side of Equation (2a) shows the solar irradiation Q ir entering the hybrid energy receiver.
For the gas combustion mode, Q in is determined as follows: The first term on the right-hand side represents the combustion energy Q com that is provided by the flue tube.
The solar irradiation is calculated with the following equation: where I ¯, φ, ρ, A m , and A s represent hourly average values for solar irradiation, interception factor, concentrator reflectance, area of the main concentrator, and area of the subordinate concentrator, respectively.In contrast, the combustion energy Q com is calculated in terms of the mass flow rate of the exhaust gas, its chemical composition, and the heating values of the synthesis gases.
The radiation reflected from the hybrid energy receiver is determined by Barreto and Canhoto 3 : where α eff represents the effective absorptivity of the hybrid energy, defined by Duffie and Beckman 28 as follows: where α is the absorptivity of the inner surface of the hybrid energy receiver, A ap denotes the area of the aperture of the hybrid energy receiver, and A rec indicates the area of the inner surface of the hybrid energy receiver.
The heat losses from the aperture owing to convective heat transfer Q ap include natural convection and forced convection losses.Convective heat losses are affected by the ambient air temperature, wind speed, and size of the aperture and the hybrid energy receiver.The heat loss by natural convection from the aperture can be estimated using the Stine-McDonald correlation described in Reinalter et al. 8 as follows: where  T represents ambient temperature; θ denotes the tilt angle of the hybrid energy receiver; and D ap indicates the aperture diameter of the hybrid energy receiver.According to Beltran et al., 2 the temperature at the inner wall of a cavity can be considered approximately equal to the absorber temperature within the cavity.In this study, the absorber temperature inside the cavity was assumed to be equal to the temperature of the heating tubes of the Stirling engine.Therefore, in Equation ( 6), T hw is in use.In addition, exponent s is determined as follows: ap rec (7)   where θ = 0°for horizontal hybrid energy receiver and 90°v ertical.The natural convection heat transfer coefficient is then calculated as follows: nat nat rec rec (8)   Meanwhile, the forced convection heat transfer coefficient can be expressed in terms of the wind speed and tilt angle 2 as follows: where v wind is the wind speed; and f θ ( ) is calculated as follows: ( The overall heat transfer coefficient is the sum of the natural and forced convection heat transfer coefficients: ap nat wind (11)   It is important to mention that when quartz glass is placed over an aperture, the conduction and convection resistances are in series and can be summed.Therefore, the heat loss from the aperture Q ap is calculated as follows: where k g , l g , and A g are the thermal conductivity, thickness, and cross-sectional area of the quartz glass, respectively.Subsequently, the heat loss from the external surface of the hybrid energy, Q rec is evaluated.As the external surface of the hybrid energy receiver is insulated, the resistance to heat flow is associated with conduction through the insulation layer and convection at the outer surface.Therefore, the heat loss from the external surface of the hybrid energy receiver is calculated as follows: where k i and l i represent the thermal conductivity and thickness of the insulation, respectively, and A rec denotes the surface of the hybrid energy receiver.The heat transfer coefficient at the external surface of the cylindrical hybrid energy receiver was determined using the relationship presented by Morgan 29 : CHENG and HUANG where  k is the thermal conductivity of the ambient air.In addition, the radiation loss, Q rec rad .because of the net radiative flux leaving the aperture was calculated.The relation given by Incropera et al. 30 is expressed as follows:

| Beta-type Stirling engine
Stirling engines are external combustion engines that are compatible with a variety of thermal energy sources, such as solar radiation or synthesis gas combustion energy.Therefore, these two energy sources can be alternatively introduced into the hybrid energy receiver to power the Stirling engine for power generation.In this study, a 1-kWscale beta-type Stirling engine was used.Figure 3 shows a photograph of the Stirling engine connected to the hybrid energy receiver.As mentioned in the previous section, the heating tubes of the beta-type Stirling engine are inserted into the chamber of the hybrid energy receiver for heating.
A typical beta-type Stirling engine has two major components: a displacer and a piston.During operation, the two moving parts traverse back and forth coaxially within the cylinder, causing the working gas to be periodically moved between the heating and cooling components.In addition, the rhombic-drive mechanism was selected because a beta-type Stirling engine with a rhombic drive has a higher power density and a compact structure, as described by Cheng and Yang. 31Meanwhile, helium was used as the working gas.The model in the present study was based on the model proposed by Yang and Cheng 32 for a beta-type Stirling engine with a rhombic drive and additional modifications.In this model, the engine cylinder is divided into five working spaces: expansion space, heater, regenerator, cooler, and compression space.Each working space has its own volume (V), temperature (T), absolute pressure (p), and gas mass (m).Herein, the model is only briefly described to save space; detailed information can be found in Yang et al. 32 The volumes of the expansion and compression spaces were determined from the geometric variables of the engine as follows: where  16) and ( 17), one can determine the volume of each working space at present (i-th) time step and consecutive (i + 1-th) time step.
The accompanying variation in volume is the pressure variation, which can be calculated using the equation suggested by Yu et al. 33


where T e h , is the working gas temperature at the interface of the expansion space and heater, and T k c , is the working gas temperature at the interface between the compression space and cooler.The values of T e h , and T k c , depend on the flow direction of the working gas.When m e h , > 0, working gas flows from the expansion space to the heater, and then . When m e h , < 0, then . Similarly, when m k c , > 0, the working gas flows from the cooler to the compression space, and then The temperature change in each working space is predicted by calculating the respective energy equations.The heating tubes of a beta-type Stirling engine absorb energy from the hybrid energy receiver.The temperatures of the working gas in all spaces were updated for each successive time step as follows: where Q in represents the net energy input determined using Equation (2a) or Equation (2b), Note that Q h is the energy transferred to the heating tubes of the betatype Stirling engine from the hybrid energy receiver where T hw i is temperatures on the wall of the heating tubes, T h i represents the temperature of the working gas inside the heater, T rw denotes the temperature of the regenerator matrix, and R e i , R R R R , , , and i indicate the thermal resistances in the respective spaces.
The instantaneous mean pressure of the working gas is calculated from the following equation: where R gas represents the helium gas constant.Equations (1-20) constitute a set of simultaneous equations that are iteratively solved for all time instants.Consequently, the temperature, mean pressure, volume, and mass of all spaces can be obtained.In addition, the pressure decrease ∆p between the expansion and compression spaces can be determined using the friction factor, which is a function of the flow Reynolds number.Next, using the data obtained for the mean pressure and pressure drop, the pressures in the expansion and compression spaces can be obtained as follows: A dynamic model for beta-type Stirling engines containing a rhombic-drive mechanism was developed by Yang and Cheng 32 based on force and moment balances for each link and joint.A dynamic simulation of the engine can be performed under various operating conditions by combining the dynamic model with the abovementioned thermodynamic model.Assuming that all engine parts are rigid bodies and constructing a kinematic and dynamic analysis of the mechanism, we obtain the following equations used in the dynamic simulation: CHENG and HUANG where 1 , , I 01 repre- sents the moment of inertia of the driving gears, τ rf denotes the friction torque generated by the sealing ring with the displacer and piston, and τ sf indicates the friction torque generated by the sealing ring with the driving shaft.The mechanisms of the engine and the joints are illustrated in Figure 4.

| Dual-reflection solar dish
The CSP system proposed in this study consisted of a dualreflection solar dish with a nacelle that housed a hybrid energy receiver and Stirling engine.The nacelle was positioned beneath the dish to ensure that it did not hinder incident sun rays.The quartz glass of the hybrid energy receiver was mounted at the center of the main concentrator.In addition, the nacelle was shielded by the dish to ensure that damage to the hybrid energy receiver and Stirling engine caused by long-term exposure to sunlight could be prevented.The reflective surfaces of concentrators consist of a silver-coated polymer film to reduce the weight and cost of concentrators.The design of the entire structure was proposed by Cheng et al., 34 and a photograph of the solar dish is shown in Figure 5A.In this section, the modeling of the solar dish based on ray-tracing analysis is performed to evaluate the magnitude of solar energy concentrated by the two concentrators and ensure that the solar radiation can be focused and pass through the aperture of the hybrid energy receiver.Therefore, it is essential to determine the aperture size for the hybrid energy receiver.When the size of the aperture is increased, there is a trade-off between increasing the intercepted solar radiation and increasing the radiation loss.The dimensions of the solar dish are illustrated in Figure 5B.
A ray-tracing model of the dual-reflection solar dish was constructed to design the concentrators.The solar dish used a parabolic mirror as the main concentrator and an ellipse mirror as the subordinate concentrator.The profile of the main concentrator is represented in Cartesian coordinates as follows: ( ) In addition, for the present subordinate concentrator, it is as follows: where f m and f s are the focal lengths of the main and subordinate concentrators, respectively.As suggested by Granet, 35 the parameter a g is calculated as follows: where θ E represents the angle between the x-axis and the fringe sunrays on the subordinate concentrator.
The geometrical parameters of the solar dish were established using ray-tracing analysis.Ray tracing is a widely used numerical method for predicting sunlight pathways.Rays are straight lines generated from discrete points on certain surfaces that represent irradiation from the sun and then change direction at the refractive interface or are reflected at the mirror boundary.In this model, it was assumed that no intermediate scattering medium influenced ray travel.Parallel rays of light enter the optical system along the x-axis and are reflected from the surfaces of the main and subordinate concentrators.The number of sunrays simulated in this study was 5000.For each sun ray, the model calculated the intersection point, incident angle, and reflection angle on the surfaces of the concentrators.The concentrator profiles were adjusted by adjusting the geometrical parameters until the desired solar image width and interception factor were obtained at the design position.The relationship between solar image width and total error of the concentrators is described by Stine and Harrigan. 36he designed geometrical parameters of the solar dish are listed in Table 1, and Figure 6 shows the ray-tracing image corresponding to this group of geometrical parameters.For clarity, only some of the light rays are depicted in Figure 6.The aperture size of the hybrid energy receiver, D ap , was determined to be 0.3 m. Results indicated that the solar radiation was capable of being concentrated, passing through the aperture, and entering the energy receiver.The heating tubes of the beta-type Stirling engine were placed in a circular arrangement on top of the engine.Thus, the focused rays of light were distributed precisely at the positions of the heating tubes to maximize their heating effects.

| Fluidized-bed gasifier and combustion energy
A photograph of the fluidized-bed gasifier is shown in Figure 7.The capacity of this fluidized-bed gasifier was 20 kW, and it consisted of a bubbling fluidized bed, a wood pellet feeder, a synthesis gas storage tank, a cyclone, and a tar remover.Because of the relatively stable supply of wood pellets in Taiwan, it was selected as the biomass material to produce synthesis gases.In general, the temperature of a reactor must be higher than 800°C for adequate gasification.Gasification converts wood pellets into a gaseous mixture of CO, H 2 , CH 4 , CO 2 , and other gases.Table 2 shows the chemical compositions of the synthesis gases produced and the low heating value (LHV) of the gaseous mixture.The composition of the gaseous mixture was Image of ray-tracing analysis.
F I G U R E 7 Fluidized-bed gasifier system.
T A B L E 2 Chemical composition, heating value, and feeding rate of the synthesis gas.

Chemical composition (wt% dry basis) Value
Carbon monoxide CO measured using a gas analyzer.The combustion energy could then be determined in terms of the LHV and feeding rate of the gaseous mixture using the experimental data provided in Table 2.The feeding rate of the synthesis gas mixture was fixed at 2.0 kg/h.It is essential to note that, owing to the geometry and excellent mixing properties of fluidized beds, they are ideally suited for the generation of clean synthesis gases.However, the chemical compositions of the synthesis gases remained unsatisfactory for high-power applications, and the performance of the present fluidized-bed gasifier required further improvement.The combustion-energy term in Equation (2b) is calculated as follows: where m ˙syn represents the syngas feed rate.The values of LHV syn and m ˙syn are listed in Table 2.

| Switching between solar radiation and synthesis gas combustion modes
The performance of the hybrid Stirling power system was maintained by switching between solar radiation mode and synthesis gas combustion mode based on solar irradiation intensity, I switch .In this study, the critical value of solar irradiation I switch was assigned to be 400 W/m 2 .When the solar irradiation fell below the critical value, the control system activated the combustor to burn the synthesis gas mixture.When the solar irradiation intensity was higher than or equal to 400 W/m 2 , the solar radiation mode was reactivated, and the gas combustion mode was terminated.Furthermore, the control system managed the sun tracking.The GPS sensor mounted on the solar dish transmitted its readings to the controller of the solar tracker; the time, latitude, and longitude of the location were transmitted.The current path of the sun in the sky could be predicted, and the two-axis active solar tracker adjusted the azimuth and zenith angles of the dish to track the trajectory of the sun.

| RESULTS AND DISCUSSION
The effects of solar irradiation at various charged pressures on the performance of the Stirling engine were investigated, and the results are depicted in Figure 8A,B.
Figure 8A depicts the variation in the temperatures of the heating tubes of the Stirling engine with increasing charged pressure at various solar irradiation levels.Under fixed solar irradiation (I ¯), the temperature of the heating tubes decreased as the charged pressure increased.This was because higher charged pressure resulted in a greater mass of working gas in the engine (m).As the solar irradiation (I ¯) remained constant, a larger mass of the working gas was more difficult to heat, resulting in a decrease in the temperature of the heating tubes of the Stirling engine.Figure 8B shows the variations in the output power of the Stirling engine with the charged pressure at various solar irradiation levels.In general, a peak in the curve within approximately 4-5 bar can be observed in this plot.For instance, the output power of the Stirling engine reached 1581 W at 4.5 bar of charged pressure for I ¯= 1000 W/m 2 .As the charged pressure was further increased, the output power decreased, which was attributed to the lower temperatures of the heating tubes of the Stirling engine at higher charged pressures.
Figure 9 illustrates energy flow through a typical system, including power output (W s ), thermal output fed to the boiler and water tank for domestic water heating (Q out ), thermal losses at the hybrid energy receiver , and ap rec rec rad rec refl .
. ), power losses due to pressure drop ( ∆ W p ), and friction in the mechanism (W sf ).In this case, the Stirling engine was charged with 9 bar helium, solar irradiation of 1000 W/m 2 , and a wind speed of 1 m/s, and the tilt angle of the hybrid energy receiver was maintained at 45°.Under these conditions, the heating tube temperature of the Stirling engine reached 893.7K.According to the analysis, the magnitude of reflected radiation was 273.9 W, heat loss from the aperture was 156.7 W, heat loss from the surface of the hybrid energy receiver was 159 W, and the net radiative flux leaving the aperture of the hybrid energy receiver was 1665.9W. In this particular case, the input of thermal power (Q in ) was 12,024.7 W, the thermal power output (W s ) obtained was 1197.4W, and the heat emitted by the Stirling engine for domestic water heating (Q out ) was 10,502 W.
The input climate data used in the present numerical model were based on reports provided by the Observation Data Inquire System of the Central Weather Bureau, Taiwan. 37This data comprised hourly average solar irradiation, ambient temperature, wind direction, and wind speed for Tainan, a city in southern Taiwan.Solar irradiation is intrinsically highly dynamic; therefore, the hourly average value is used to represent the transient nature of solar radiation.
It was expected that in the solar radiation mode, the instantaneous power output of the Stirling generator would vary with solar intensity.According to the climate data, the operating hours for the solar radiation mode were from 08:00 to 16:00.For the rest of the day, the solar intensity was insufficient (<400 W/m 2 ) to maintain the output power; thus, the system was switched to the synthesis gas combustion mode.The dynamic behavior during operation for 24 h is shown in Figure 10.The solar irradiation intensity I, power output of the hybrid power system W s , power of solar irradiation Q ir , and power of synthesis gas combustion Q com are plotted in the upper and lower portions of Figure 10.It was established that the peak solar irradiation period was between 10:00 and 13:00, during which the power output of the Stirling generator exceeded 1200 W. When the synthesis gas combustion mode was switched on, the power output of the Stirling F I G U R E 10 Hourly average solar irradiation 37 and response of hybrid power system.water.At 8:00, the solar irradiation was 545.14 W/m 2 , which was already higher than 400 W/m 2 ; therefore, the system was switched from the synthesis gas combustion mode to the solar radiation mode.However, the solar irradiation was only 545.14 W/m 2 , and the output power of the Stirling generator was slightly reduced to 559 W. At 9:00, the solar irradiation and output power increased to 780.56 W/m 2 and 890 W, respectively.The simulation results displayed in the enlarged plots for 8:00 and 9:00 indicate that the change in the instantaneous power output was caused by the switching of the energy sources.The power output stabilized approximately 6 min after switching.
Figure 11B shows the simulation results for the interval from 11:30 to 13:30 when solar radiation was at its peak.At 11:00 and 12:00, the solar irradiation was 1016.67 and 1019.44 W/m 2 , respectively, and the corresponding solar energy absorbed by the hybrid energy receiver was 14,518.2 and 14,557.8W, respectively.The simulation results indicated that the power output could reach 1220.5 W at 12:00.
From 15:30 to 17:30, the solar energy mode was switched to combustion energy mode again under insufficient solar irradiation.Figure 11C shows the simulation results for this interval.According to climatic data, the solar irradiation was 326.39 W/m 2 at 17:00; therefore, the dual-reflection solar dish was deactivated, and the synthesis gas combustion was activated.When synthesis gas combustion was activated, it delivered 7034.79W directly to the heating tubes of the Stirling engine.Consequently, the power output of the Stirling generator increased slightly to 593.595 W.
According to the 24-h simulation results, switching between the two energy sources could result in a continuous power output ranging from 600 to 1200 W, which could stabilize the power output approximately 6 min after each switch.The waste heat emitted by the Stirling generator and combustor could be channeled into the boiler via a water tank; therefore, it could be utilized for domestic water heating.
Figure 12 depicts the electricity output distribution of the hybrid power system over 24 h.The results showed a slight difference in the electricity output between the synthesis gas combustion and solar energy modes.The solar radiation mode generated 8.108 kWh, while the synthesis gas combustion model generated 8.904 kWh of electricity output.Although the solar-radiation mode had a higher instantaneous power output, its operation time lasted only 9 h.In contrast, the synthesis gas combustion mode could last for 15 h; therefore, it was able to generate more electricity output.With synthesis gas combustion as the auxiliary heat source, the hybrid Stirling power system could be operated continuously, and the overall power production increased by 109.82%compared to a conventional CSP system that only uses solar radiation.

| CONCLUSIONS
In this study, we propose a novel concept for a hybrid power system.This hybrid power system was constructed by integrating a hybrid energy receiver, a solar dish, a Stirling generator, a fluidized-bed gasifier, and a boiler with a water tank.The solar dish was used to concentrate a large area of solar irradiation onto the hybrid energy receiver.The fluidized-bed gasifier was employed to produce synthesis gases that were combusted to provide an auxiliary heat source for the Stirling generator when solar radiation was insufficient.
All subsystems were modeled in this study, and a complete numerical model was developed for system integration.The response of the system performance during switching between solar radiation and combustion energy was predicted.The following conclusions were drawn: 1.The hybrid power system may serve as a base-load power plant regardless of solar conditions.According to the 24-h simulation, switching between the two energy sources can result in a continuous power output ranging from 600 to 1200 W, which can stabilize in approximately 6 min after each switch.2. The waste heat emitted by the Stirling generator and combustor is channeled to the boiler with a water tank; therefore, it can be utilized for heating domestic water.This implies that the hybrid power system is capable of functioning as a CHP system.3. Hybrid energy system modeling includes thermodynamic and dynamic models of the beta-type Stirling engine, a ray-tracing model for the dual-reflection solar dish, an energy model for the hybrid energy receiver, and experimental data for the fluidized-bed gasifier.The dynamic response of the system performance during the switching between solar radiation and combustion energy can be predicted.In the near future, such a comprehensive model may be employed to plan control strategies and optimize operating parameters.

Analysis based on real climate data in southern
Taiwan showed that for this particular demonstration plant, the power output of the Stirling generator peaked at 1220.5 W at solar irradiation of 1019.44 W/ m 2 .With synthesis gas combustion as the auxiliary heat source, the hybrid Stirling power system can be operated continuously, and the overall power output increased by 109.82%compared to a conventional CSP system that only uses solar radiation.

3
Stirling engine (right) combined with hybrid energy receiver (left).
es represents the volume occupied by the movement of displacer; χ χ , e c , and χ b denote the ratios of dead volume to sweep volume for expansion and compression spaces, respectively; e l r e l r ε r l r = / , = / , = ( − )/ , Schematic of the beta-type Stirling engine with rhombic-drive mechanism.

F I G U R E 5
Dual reflection solar dish.(A) Photograph of solar dish.(B) Schematic.

F I G U R E 8
Effects of solar irradiation and charged pressure on performance of Stirling engine.(A) Temperature of the heating tubes at different charged pressure.(B) Output power of the Stirling generator at different charged pressure.

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I G U R E 9 Energy flow of the hybrid energy receiver and the Stirling engine.
maintained at approximately 600 W.Figure11depicts three distinct scenarios illustrating the dynamic response of the hybrid energy system at important intervals: (a) 7:30-9:30, (b) 11:30-13:30, and (c) 15:30-17:30.As shown in Figure11A, when the synthesis gas combustion mode was active before 8:00, the combustion energy input Q in to the heating tubes of the Stirling engine was 7034.79W, and the power output of the Stirling generator was 593.595W. Notably, the waste heat emitted by the Stirling generator and combustor was fed to the boiler for heating domesticF I G U R E11 Dynamic response of the hybrid energy system in important intervals.(A) Combustion energy mode switched to solar energy mode in the morning from 7:30 to 9:30.(B) Strongest solar energy mode at noon from 11:30 to 13:30.(C) Solar energy mode switched to combustion energy mode in the afternoon from 15:30 to 17:30.

F I G U R E 12
Electricity output distribution by the hybrid power system. ,