Organic Rankine Cycle Turbine Research Articles

Numerical analysis-based performance assessment of the small-scale organic Rankine cycle turbine design for residential applications

The organic Rankine cycle (ORC) is one of the most common ways to use energy resources to utilise waste heat. Integrating ORC with other systems, such as cooling or heating applications, is also helpful for residential uses. In the ORC system, the turbines are the most critical component determining the system's efficiency. This study conducted a computational fluid dynamics study on a regenerative flow turbine that can be used in small-scale organic Rankine cycle systems. For the higher temperature applications, the analyses were performed using n-pentane working fluid for 1500 and 3000 rpm turbine speeds, inlet temperature between 475–550 K, outlet pressure between 0.9–1.2 MPa, and mass flow rates between 0.5–1.0 kg/s. As a result of the analysis, the isentropic efficiency varies between 4.97 % and 12.52 %. It was concluded that the output power obtained from the turbine varies between 0.53 kW and 2.96 kW. The analyses were also performed for lower temperature (363 and 393 K), pressure (0.05 MPa and 0.3 MPa) and mass flows (0.1 to 0.25 kg/s) applications. In this case, the isentropic efficiency of the turbine varies between 6.23 % and 14.52 %, whereas the power generation varies between 0.068 and 0.521 kW.

Evaluation of readiness to commercialize research results with the IRL framework: a case study of ORC turbines in Indonesia

Indonesia's commitment to reducing the use of fossil fuels for power generation has encouraged the exploration of biomass energy from waste materials. Organic Rankine cycle (ORC) turbine technology that converts waste into electrical energy can be an opportunity for the development of waste power plants. The developed ORC turbine has not been assessed for innovation readiness level (IRL). To address this gap, a comprehensive evaluation of the IRL and technology readiness level (TRL) of the ORC turbine is essential. This study uses qualitative and quantitative methods, combining the IRL and TRL frameworks. The results reveal that the ORC turbine market is ready, although the technology is still in the early stages of development (IRL 2). In order to achieve IRL 3 and be prepared to enter the decline stage as part of the market evolution phase, intellectual property protection, product testing, and certification must be carried out. The establishment of a product certification agency with testing facilities to ensure turbine performance is required. IRL and TRL approaches can be used to determine the stages of research activities that can be achieved by looking at the availability of resources needed at each level.

Concept and Design of a Velocity Compounded Radial Four-Fold Re-Entry Turbine for Organic Rankine Cycle (ORC) Applications

The energy sector faces a pressing need for significant transformation to curb CO2 emissions. For instance, Czechia and Germany have taken steps to phase out fossil thermal power plants by 2038, opting instead for a greater reliance on variable renewable energy sources like wind and solar power. Nonetheless, thermal power plants will still have roles, too. While the conventional multistage axial turbine design has been predominant in large-scale power plants for the past century, it is unsuitable for small-scale decentralized projects due to complexity and cost. To address this, the study investigates less common turbine types, which were discarded as they demonstrated lower efficiency. One design is the Elektra turbine, characterized by its velocity compounded radial re-entry configuration. The Elektra turbine combines the advantages of volumetric expanders (the low rotational speed requirement) with the advantages of a turbine (no rubbing seals, no lubrication in the working fluid, wear is almost completely avoided). Thus, the research goal of the authors is the implementation of a 10 kW-class ORC turbine driving a cost-effective off-the-shelf 3000 rpm generator. The paper introduces the concept of the Elektra turbine in comparison to other turbines and proposes this approach for an ORC working fluid. In the second part, the 1D design and 3D–CFD optimization of the 7 kW Elektra turbine working with Hexamethyldisiloxane (MM) is performed. Finally, CFD efficiency characteristics of various versions of the Elektra are presented and critically discussed regarding the originally defined design approach. The unsteady CFD calculation of the final Elektra version showed 46% total-to-static isentropic efficiency.

Thermodynamic assessment of a novel solar powered trigeneration system for combined power generation, heating, and cooling

Solar power tower (SPT) technology is the mature technology among the various concentrated solar technologies for energy generation. Therefore, it is necessary to develop the efficient energy generation system that utilizes the SPT plant. In the current study, a novel trigeneration system was presented to utilize the SPT for combined power generation, heating, and cooling. The trigeneration system consists a helium Brayton cycle and organic Rankine cycle (ORC) with ejector refrigeration system for recovering the waste heat. The power was produced by the helium Brayton cycle and ORC turbine whereas, cooling and heating was produced simultaneously by the condenser and evaporator respectively. For building applications such as hospitals and hostels, the heating and cooling effects were generated at 50°C and 10°C respectively. Finally, the optimal system exhibits exergy and energy efficiency of 25.12% and 23.3%, respectively, when all the studied parameters are taken into consideration. Apart from this power output, heating and cooling productions were observed as 14,998, 60.52 and 8.25 kW and respectively at the 2.3 of compressor pressure ratio, 197.2°C of inlet temperature of ORC turbine.

Non‐parametric measure approximations for constrained multi‐objective optimisation under uncertainty

AbstractIn this article, we propose non‐parametric estimations of robustness and reliability measures approximation error, employed in the context of constrained multi‐objective optimisation under uncertainty (OUU). These approximations with tunable accuracy permit to capture the Pareto front in a parsimonious way, and can be exploited within an adaptive refinement strategy. First, we illustrate an efficient approach for obtaining joint representations of the robustness and reliability measures, allowing sharper discrimination of Pareto‐optimal designs. A specific surrogate model of these objectives and constraints is then proposed to accelerate the optimisation process. Secondly, we propose an adaptive refinement strategy, using these tunable accuracy approximations to drive the computational effort towards the computation of the optimal area. To this extent, an adapted Pareto dominance rule and Pareto optimal probability computation are formulated. The performance of the proposed strategy is assessed on several analytical test‐cases against classical approaches. We also illustrate the method on an engineering application, performing shape OUU of an Organic Rankine Cycle turbine.

A 3E analysis of a multi‐power generation system employing CO2, LNG, and Organic Rankine cycles

AbstractOne avenue in increasing the energy efficiency of energy systems is through utilizing the thermal energy of flue gases of industrial plants. On this thread, herein, a novel combined cascade cycle for heat recovery of flue gases of an industrial plant is proposed comprising of an organic Rankine cycle (ORC), high‐pressure transcritical CO2 cycle, transcritical CO2 cycle, and a liquefied natural gas (LNG) regasification cycle. System analysis is conducted using energy, exergy, and eco‐exergy equations. The optimization is carried out using the TOPSIS multi‐objective method. Exergy efficiency, net output work, and cost are identified as the optimization objectives. The optimization process focused on fine‐tuning variables including the vapor generator pinch point temperature, ORC turbine inlet pressure, ORC condenser pressure, and ORC condenser pinch point temperature, with optimal values gauged at 19.31°C, 29.59 bar, 1.413 bar, and 14.52°C, respectively. The preheater had the largest exergy destruction share, followed by the heat exchanger unit. The analysis showed that the ORC condenser pressure and temperature difference between two working fluids in the heat exchanger were the most critical parameters in the proposed cycle, significantly affecting the system performance. Accordingly, the exergy efficiency, net output work, and cost values in the optimal state were equal to 15.2%, 6416 kW, and 0.7457 $/s, respectively. The advantages of the proposed system include efficient heat recovery through the coupling of the multiple cycles and enhanced energy conversion pertinent to a wider range of temperatures, maximizing the overall energy extraction from the waste heat.

A Design Optimization of Organic Rankine Cycle Turbine Blades with Radial Basis Neural Network

In the present study, a 100 kW organic Rankine cycle is suggested to recover heat energy from commercial ships. A radial-type turbine is employed with R1233zd(E) and back-to-back layout. To improve the performance of an organic Rankine power system, the efficiency of the turbine is significant. With the conventional approach, the optimization of a turbine requires a considerable amount of time and involves substantial costs. By combining design of experiments, an artificial neural network, and Latin hypercube sampling, it becomes possible to reduce costs and achieve rapid optimization. A radial basis neural network with machine learning technique, known for its advantages of being fast and easily applicable, has been implemented. Using such an approach, an increase in efficiency greater than 1% was achieved with minimal design changes at the first and second turbines.

Profile Loss Prediction for Organic Rankine Cycle Turbines: An Experimental Case Study

The results of profile loss measurements, including trailing edge flow details, are presented for the flow of an organic vapor through a linear turbine cascade. The so-called VKI-I blade profile from the open literature was chosen for the cascade, and the working fluid was NOVEC 649. Pitot probes and hot-wire anemometry were employed to measure the flow field up and downstream of the cascade. Details of the unsteady flow caused by the trailing edge of the blades and the turbulent spectrum were investigated using hot-wire anemometry. The new organic vapor flow results were compared with the literature data obtained for air and with the prediction of conventional literature loss models. It was found that, under certain thermodynamic conditions, specific traditional loss models can reasonably predict organic Rankine cycle (ORC) turbines’ profile loss. Still, significant deviations between the loss models and the experimental data can also occur.

Performance investigation of a standalone renewable energy system using response surface methodology (RSM): 4E analysis and multi-objective optimization

This study aimed to identify and present novel findings in the field of hybrid renewable energy systems tailored for off-grid operation through a numerical-experimental investigation. The objective of the research was to contribute to the current knowledge of energy systems by addressing critical aspects of energy, exergy, economic, and environmental (4E) evaluations. The system described in the study is designed to meet the electricity demands of a telecom tower by integrating various components, including a photovoltaic (PV) unit, proton exchange membrane electrolyzer (PEME), proton exchange membrane fuel cell (PEMFC), and battery storage unit. An organic Rankine cycle (ORC) is also incorporated to efficiently recover waste heat from the PEMFC. The PV unit serves as the primary power source, with excess solar power directed to the PEME during periods of high solar irradiation. The PEME generates hydrogen and oxygen, while the PEMFC is fueled by hydrogen stored in metal hydride tanks. This setup ensures consistent power generation year-round. The study employs response surface methodology (RSM) to create regression equation models and utilizes the desirability function approach for multi-objective optimization. The optimal parameters identified include a 12:35 PM time setting, PEMFC current density of 0.693 A/cm2, PEME inlet water temperature of 326.2 K, and ORC turbine inlet pressure of around 580 kPa. These parameters result in impressive 4E outcomes: 50.9 % energy efficiency, 54.7 % exergy efficiency, a $0.53 levelized cost of energy, and a sustainability index of 2.1.

High fidelity simulation of dense vapours with thermodynamic consistent modelling

The paper describes the implementation of thermodynamic modelling within a high-order finite difference scheme. A new method to ensure thermodynamic consistency for Navier–Stokes simulations of real-gas11A real gas being one which does not obey the ideal gas law. flows is outlined. The paper shows that this method is suited to high fidelity simulations of dense-vapour flows with complex equations of state, such as found in Organic Rankine Cycle turbines. The method is illustrated with two examples of siloxane MM flow in a channel and in a turbine vane. The results show that thermodynamic consistency plays a vital role in the accurate prediction of irreversibility and therefore turbine loss.

Performance analysis of a CO2 near-zero emission integrated system for stepwise recovery of LNG cold energy and GT exhaust heat

Combined cooling, heating and power (CCHP) system can further improve energy utilization efficiency while meeting diversified energy demands, and the rational use of the CCHP system is an effective way to alleviate the energy crisis. An innovative cascaded CCHP system based on the transcritical carbon dioxide cycle (TRCC) and organic Rankine cycle (ORC) has been proposed, which is designed to recover the cold energy of liquefied natural gas (LNG) and the exhaust heat from the gas turbine (GT), while achieving near-zero CO2 emissions. The simulation result demonstrates that the system achieves energy utilization efficiency, exergy efficiency and net electrical efficiency of 87.3%, 56.9% and 55.39%, respectively, with a CO2 capture rate of 79.2 kg/h under the design condition. Compared to the mentioned cogeneration systems that recover LNG cold energy and GT waste heat, the proposed system exhibits improvements in energy utilization efficiency, exergy efficiency and net electrical efficiency by 9.84%, 4.37% and 3.4%, respectively. The parameter sensitivity analysis reveals that increasing the pressure ratio of the TCO2 turbine and ORC turbine or reducing the air compressor feed temperature can improve the overall performance of the system. If the focus is solely on energy utilization efficiency and exergy efficiency, appropriately increasing the air compressor pressure ratio or reducing the gas turbine pressure ratio would be beneficial. The proposed system in the study is environmentally friendly and energy-saving, which especially suggests a direction for cold energy cascade utilization in LNG stations integrated with CCHP.

High-subsonic boundary-layer flows of an organic vapour

Boundary layers of Novec649, a low-global-warming potential fluid of interest for low-grade heat recovery, are investigated numerically by means of linear stability theory, direct numerical simulation (DNS) and large-eddy simulations (LES). This organic vapour is of interest in organic Rankine cycle (ORC) turbines and realistic thermodynamic conditions are selected. Under these conditions, the vapour behaves as a dense gas and, due to its high molecular complexity, real-gas effects occur. In addition, the fluid exhibits large and highly variable heat capacities and density- as well as temperature-dependent transport properties. More specifically we report the first direct and LES of transitional and turbulent boundary layers of Novec649 at high-subsonic conditions$M=0.9$. A controlled transition is performed by using oblique modes determined by linear stability theory extended to dense gases. An oblique-type transition is obtained as in low-speed air flows, where sinuous streaks develop by the lift-up mechanism and break down into turbulence. In the turbulent state, the profiles of dynamic flow properties (velocities, turbulent intensities, turbulent kinetic energy budgets) are little affected by the gas properties and remain very close to incompressible DNS, despite the high-subsonic flow speed. The fluctuations levels for thermodynamic properties have been quantified with respect to air flows. Notwithstanding a drastic reduction, genuine compressibility effects are present. For example, the fluctuating Mach number and the acoustic mode are characteristic of high-speed flows. The influence of forcing frequency and amplitude on the established turbulent state has been investigated using LES. An analysis of integral quantities shows a slow relaxation towards a canonical equilibrium turbulent state for all cases due to the high Reynolds numbers typical of dense gas flows. Overall the present DNS constitutes a valuable reference not only for forthcoming experiments but also for future studies of free-stream transition and loss mechanisms in ORC turbines.

Exergy destruction analysis of a power generation system utilizing the cold energy of LNG

The purpose of this research is in-depth understanding of the internal causes of exergy destruction in various parts of the system and to identify potential improvements for the components. The focus is on a combined cycle power generation system that utilizes the organic Rankine cycle (ORC) and direct expansion cycle (DEC). To investigate the primary sources of exergy destruction in each component, advanced exergy analysis (AEA) is utilized. The result demonstrates that the net out power of the proposed system can reach 106.64 kW with energy efficiency of 11.22%, and exergy efficiency of 21.40%. The heat exchanger is identified as the primary contributor to exergy destruction, constituting 81.70% of the total ratio. Specifically, the condenser exhibits the highest exergy destruction ratio at 59.82%, indicating a need for prioritized optimization efforts. The findings of AEA reveal that the primary source of component irreversibility stems from the endogenous part. This shows that, while most exergy destruction is unavoidable, there remains room for system improvement. Regarding the turbine, its exergy destruction is primarily attributed to inefficiencies, leading to irreversibility. Nevertheless, there is exergy destruction that may be avoidable and can be reduced by 25.93 kW, which is 2.5 times greater than that of the heat exchanger. This finding underscores the high potential for improvement in ORC and DEC turbines, making them a priority for optimization efforts.

Exergy-based techno-economic and environmental assessments of a proposed integrated solar powered electricity generation system along with novel prioritization method and performance indices

This study focused on the two important gaps in the literature. The first is solar energy- powered electricity generation in a more economical way via the integration of flat plate solar collector (FPSC), an Organic Rankine Cycle (ORC), and an absorptional heat transformer (AHT) system. Another gap is advanced exergy analysis of the AHT cycle/ORC process based on renewable energy integration to reveal clues for improving the system. To close these gaps, a novel system including a lithium bromide AHT cycle-ORC with a FPSC system application was proposed in this study. In this proposed system, the temperature of the heat source for the ORC system was upgraded via an integration of the AHT and FPSC cycles. The main components of the AHT cycle are the condenser (ABScon), refrigerant cycle pump (P1), evaporator (EV), absorber (ABS), solution heat exchanger (SHX), absorbent cycle pump (P2), expansion valve (V), generator (Gen), ORC turbine (ORCT) and ORC condenser (ORCcon). To demonstrate the electricity production from solar energy in a more economical way thanks to the proposed system, a comparison was made with similar-scaled existing solar power plants. The results supported the main purpose of this study. The annual electricity production with the proposed system was calculated as 2601 MWh, with initial investment cost and payback period values of US$3.924 million and 4.531 years, respectively. The conventional and advanced exergy, exergoeconomic, environmental impact, and sustainability analyzes were also performed. Based on these, the novel performance parameters and prioritization method were proposed to assess the improvement potential of the system. The results indicated that SHX and FPSC had the highest exergy destruction rates (EDRs) of 23.711% and 21.849% over 5853.89 kW due to the stronger thermal and chemical reactions. Similarly, Gen, FPSC, and SHX had the highest ED cost rates (CRs) of 67.59%, 59.09%, and, 47.98%, respectively. Gen, V, and ORCcon were higher contributors to the exergy destruction rates of almost all the components. However, these showed an adverse manner for irreversibility activities. So, the temperatures of Gen and ORCcon should be optimized carefully. ABScon, P2, P1, ABS, Gen, ORCT, and ORCcon had high development priority to improve the whole system.

Hot-Wire Anemometry in High Subsonic Organic Vapor Flows

Abstract The present contribution reports the outcome of an experimental and numerical investigation of the behavior of a constant-temperature hot-wire anemometer in the high-subsonic flow up to a Mach number of 0.7 of the organic vapor Novec™ 649 at pressure and temperature levels of typical organic Rankine cycle (ORC) turbine applications. The experiments were carried out in the calibration section of a closed-loop organic vapor wind tunnel test facility enabling the independent variation of Reynolds numbers, Mach numbers, and total temperature within a certain range. It was found that the calibration and the determination of the sensitivity coefficients can be done in a way as proposed by de Souza and Tavoularis for air. The sensitivity coefficients for velocity and density were essentially equal for higher overheat ratios which support the interpretation of the signals and data reduction for turbulent quantities. Computational fluid dynamics (CFD) provided additional insight into potential real gas effects for hot-wire performance.

A transient simulation for a novel solar-geothermal cogeneration system with a selection of heat transfer fluids using thermodynamics analysis and ANN intelligent (AI) modeling

Today, due to the reduction of fossil resources and on the other hand the high environmental pollution of these resources, it is necessary to pay attention to alternative resources, including clean and available renewable resources. In this study, solar and geothermal energy sources are combined, generating electricity, cooling, freshwater, and hydrogen, along with selecting a suitable heat transfer fluid for parabolic trough solar collectors. This system consists of parabolic trough solar collectors, a steam Rankine cycle, a steam Rankine cycle with an organic Rankine cycle, a proton exchange membrane electrolyzer, and a reverse osmosis desalination unit. To analyze the performance of solar collectors, Therminol 59, Marlotherm SH, Syltherm 800, and Therminol VP1 heat transfer fluids are selected. Solar radiation intensity, solar collector mass flow rate, turbine and pump efficiency, evaporator pinch-point temperature, and organic Rankine cycle turbine inlet temperature were investigated as design parameters affecting system performance. Maximizing energy efficiency and reducing cost rate were selected as two objective functions and determined using a multi-objective sorting genetic algorithm (NSGA-II). The results showed that Therminol 59 has the highest energy efficiency and net power output compared to other heat transfer fluids. Also, the proposed system produces 1140 kW of electricity in the optimal state, and in the best state, it has an energy efficiency of 32.39% and a cost of 36.32 $/GJ.

Nitrogen Experiments on a Supersonic Linear Cascade For ORC Applications

A novel experiment has been conceived at Politecnico di Milano for the study of the flow within and downstream of supersonic cascades of Organic Rankine Cycle (ORC) turbines. This paper documents the first phase of the research, focused on the preliminary tests and studies performed by operating the facility with nitrogen as working fluid, to demonstrate the technical relevance of the experiment and the validity of the measurement system in a simplified thermodynamic condition. The set of measured data includes, beside the inlet total thermodynamic state, eight static pressure values obtained via taps manufactured on the test section rear end-wall, both within the bladed and semi-bladed region of the cascade, as well as a total pressure probe to retrieve the cascade performance. A double-passage Schlieren equipment was also employed to visualize the density gradients. Experiments show an outstanding repeatability, indicate a quasi-steady cascade operation during the blow-down process for all the pressure signal considered, and demonstrate a remarkable periodicity among two consecutive channels also in off-design conditions. Experimental data were also compared with CFD simulations, resulting in an excellent agreement for the pressure data acquired both within and downstream of the cascade.

A Review on the Preliminary Design of Axial and Radial Turbines for Small-Scale Organic Rankine Cycle

Organic Rankine cycle (ORC) is an effective technology to harness low-grade energy. Turbine, as a key component of ORC, takes advantages of its high efficiency and compact size compared with other expanders. Currently, developing suitable turbines with a high performance and a low cost is one of the bottlenecks for wide applications of various ORCs. In this context, technical progress on radial inflow turbines (RITs), axial turbines (ATs), and radial outflow turbines (ROTs) is introduced, and loss models used in the preliminary design are compared, especially for small-scale ORCs. RIT is recommended for medium and small ORCs with an expansion pressure ratio of <10. The power outs and rotational speeds of the designed RITs spanned the ranges of 9.3–684 kW and 3000–114,000 r/min with an efficiency of 56.1–91.75%. In comparison, the power outputs and speeds of ATs were 3–2446 kW and 3000–91,800 r/min with an efficiency of 63–89.1%. AT is suitable for large-scale ORCs with a power output of greater than hundreds of kW. However, AT with impulse stages is feasible for small-scale ORCs when the pressure ratio is high, and the mass flow rate is small. The power outputs of the designed ROTs were relatively small, at 10–400 kW with a speed of 7200–42,700 r/min and an efficiency of 68.7–85%. For organic working fluids with a large expansion pressure ratio, ROT might be employed. Conventional mean-line models may neglect the effects of supersonic flow, which will be encountered in many ORC turbines. Therefore, adequate models for supersonic expansion loss and shock loss need to be added. Meanwhile, a proper multivariable optimization algorithm such as a gradient-based or stochastic search method should be selected. Finally, the challenges and potential research directions are discussed. The outcomes can provide some insights for the development of ORC turbines and the optimization of ORC systems.

Investigation of non-ideal gas flows around a circular cylinder

The aerodynamic performance of a cylinder Pitot probe for velocity measurements in compressible non-ideal gas flows, such as those encountered in Organic Rankine Cycle (ORC) turbines, is investigated by means of Computational Fluid Dynamics. Numerical simulations are performed at subsonic and transonic conditions, and freestream Reynolds numbers are in the cylinder critical regime. The working fluid is the organic vapor Novec™ 649. Air flow simulations at similar inlet conditions are reported for comparison. Steady and unsteady RANS solutions are computed with the Spalart–Allmaras turbulence model. The results are assessed against experimental measurements collected in a wind tunnel. URANS is in good agreement with experimental data for all considered conditions, and delivers reasonably accurate estimations of the cylinder back pressure. Using a dense gas leads to a lower minimum pressure coefficient compared to air, alongside a reduced maximum Mach number due to the non-ideal speed of sound behaviour. In the experimentally studied range of compressibility factors and Mach numbers, discrepancies observed with respect to air flow are mostly an effect of the different isentropic exponents. In the transonic regime, shock waves causing boundary layer separation are weakened in the dense gas, but back pressure is also decreased, contributing to rising form drag.

Modeling and optimization of fuel cell systems combined with a gasifier for producing heat and electricity

In this research, a proton-conducting membrane fuel cell is used in conjunction with a gasifier for producing electricity with air considered as the gasification agent. The simultaneous electricity, heat, and hot water generation of these two when coupled with an Organic Rankine Cycle (ORC) installed within a Thermoelectric Generator (TEG) was studied. Additionally, to utilize the electricity generated from various parts of the process; i.e. the fuel cell, organic Rankine cycle turbine, and the thermoelectric generator, the reverse osmosis (OR) water desalination unit was coupled to the process. The aforementioned system was studied and analyzed based on thermodynamic and thermos-economic aspects. A parametric study was also carried out to analyze the effect of main factors on power output, energy/exergy yield, and the total cost of each system. Finally, a dual objective optimization was achieved by taking the main factors into consideration and using a genetic algorithm. Results indicated that the work generated by the system was not significant; however, the amount of hot water produced was relatively promising. Based on exergy and exergoeconomic evaluation, the After-Burner is an important non-renewable energy source while the fuel cell has a higher inefficiency cost which could be due to low work generation. Results indicate that the moisture in the biomass and the figure of merit, are important parameters that have to be kept as low as possible. The energy yield of the fuel cell was calculated to be 45.05%. Additionally, considering the optimized operating point, pure power output and system cost rate will be 1.81 KW and 5.15 $/hr respectively.