Machine Learning Cuts Costs in Solar Power Cooling

By Dr Silpaja Chandrasekar, PhDReviewed by Susha Cheriyedath, M.Sc.Aug 28 2024

In a paper published in the journal Scientific Reports, researchers presented a machine learning (ML) system that optimizes the design of dry cooling systems for supercritical carbon dioxide CO₂ Brayton cycle concentrated solar power (CSP) plants.

They developed a physics-based simulator for air-cooled heat exchangers to meet various power requirements under different surface air temperatures. Utilizing high-dimensional Bayesian optimization, they reduced lifetime cooling costs by 67% compared to previous designs. This framework accelerates the development of cost-effective, sustainable energy solutions.

Background

Previous work on dry cooling systems for supercritical CO₂ (sCO₂) Brayton cycle CSP plants has been limited. It focuses mainly on varying power cycle set points and ambient conditions, with little attention to optimizing the cooler design.

Most studies investigated the effect of specific parameters like power cycle conditions, but only one study explored varying individual dry cooler design factors. However, this research did not comprehensively optimize the entire system, leaving current designs far from optimal.

Design Optimization Framework

The optimization approach outlined in this paper focuses on solving the complex problem of designing cost-effective dry coolers for sCO₂ Brayton cycle CSP plants. The challenge lies in optimizing a design configuration that satisfies critical temperature requirements while maintaining the supercritical state of CO₂.

Traditional mixed-integer programming methods are inadequate due to the non-linear nature of the cost and validity functions associated with the design variables. Instead, the problem is reformulated to include a projection function, which adjusts the design to meet necessary constraints, thereby simplifying the optimization process.

To tackle the optimization problem, the paper employs the trust-region Bayesian optimization (TuRBO) method specifically designed for high-dimensional inputs. TuRBO enhances scalability by using multiple local surrogate models operating within a trust region. These models, updated iteratively, allow for a balance between exploring new design possibilities and exploiting known ones to minimize costs.

The effectiveness of TuRBO is demonstrated through its superior performance compared to other state-of-the-art optimization methods in various high-dimensional and complex tasks, highlighting its robustness for the design challenges presented in this study.

By simulating heat transfer between CO₂ and air depending on different design parameters, the heat exchanger simulator created for this work mimics the performance of air-cooled sCO₂ coolers. The simulator uses a segmented approach, dividing the heat exchanger into multiple units for detailed analysis.

Although sCO₂ CSP heat exchanger technology is still in its early stages, the simulator is built on validated models from prior work, ensuring reliable performance predictions despite the lack of physical measurement data.

A refined cost calculator is implemented to support the optimization, incorporating key components such as heat exchanger costs, fan purchase costs, and fan operation costs. This modular approach allows for a more accurate and flexible estimation of manufacturing and operational expenses, ensuring that the optimization process leads to economically viable design solutions. The integration of these tools provides a comprehensive framework for advancing the design of sCO₂ CSP plants, with potential applications extending beyond this specific technology.

Optimized Dry Cooler

The paper presents a dry cooler simulator that calculates heat transfer between sCO₂ and air in finned tubes using the logarithmic mean temperature difference (LMTD) method. The simulator iteratively solves for the outgoing temperature to ensure valid designs, dynamically adjusting tube lengths to meet output temperature requirements.

The design flexibility ensures that the supercritical conditions of sCO₂ are maintained, as illustrated by the relationship between tube length and output temperature. The simulator also calculates the pressure drop across the tubes, showing that pressure drop decreases along the tube length due to temperature variations, and the overall approach is grounded in classical energy conservation principles.

The optimization framework leverages high-dimensional Bayesian optimization to minimize the lifetime cost of dry coolers for sCO₂ CSP plants across various global locations. This method uses local surrogate models to efficiently explore and exploit the design space, integrating real-world pricing data for accurate cost estimation.

The study demonstrates the framework's adaptability to different climates by optimizing designs in locations with varying ambient temperatures, showing that higher direct normal irradiance (DNI) and lower ambient temperatures lead to lower-cost designs due to more effective cooling of the sCO₂ working fluid.

Finally, the study compares the optimized design to previous work, highlighting significant reductions in finned-tube and labor costs. By decreasing the size and thickness of the tubes, the optimized design achieves a 67.1% reduction in lifetime costs compared to the reference design. The framework's temperature sensitivity analysis further emphasizes the importance of adaptive strategies for efficient and cost-effective dry cooler designs in varying temperature conditions.

Conclusion

To sum up, an ML system was developed to optimize the design of dry cooling systems for sCO₂ Brayton cycle CSP plants. The team created a physics-based simulator for air-cooled heat exchangers.

High-dimensional Bayesian optimization was applied, resulting in a 67% reduction in lifetime costs compared to previous designs. This approach enhanced the efficiency of developing cost-effective, sustainable energy systems for varying environmental conditions.