Elsevier

Energy Conversion and Management
能量转换与管理

Volume 321, 1 December 2024, 119086
第 321 卷，2024 年 12 月 1 日，119086
Energy Conversion and Management

Research Paper 研究论文
A continuous 24-hour power generated PV-TEG-PCM hybrid system enabled by solar diurnal photovoltaic/thermal conversion and nocturnal sky radiative cooling
通过日光光伏/热转换和夜间天空辐射冷却实现连续 24 小时发电的光伏-TEG-PCM 混合系统

https://doi.org/10.1016/j.enconman.2024.119086Get rights and content 获取权利和内容

Highlights 亮点

  • •
    A continuous 24-hour power generation method enabled by solar photovoltaic/thermal conversion and sky radiative cooling;
    通过太阳能光伏/热转换和天空辐射冷却实现 24 小时连续发电；
  • •
    The design, optimization and manufacture of PV-TEG-PCM hybrid system;
    PV-TEG-PCM 混合系统的设计、优化和制造；
  • •
    A full-day experimental test and numerical analysis on the electrical, thermal and radiative cooling performance of system;
    对系统的电气、热和辐射冷却性能进行了全天的实验测试和数值分析；
  • •
    PV electrical efficiency up to 19.6, TEG voltage up to 0.29 V during diurnal hours and 0.15 V at nocturnal hours.
    光伏发电效率达到 19.6，TEG 电压在昼间达到 0.29 V，在夜间达到 0.15 V。

Abstract 摘要

A novel concept of energy harvesting method for continuous 24-hour power generation enabled by solar diurnal photovoltaic/thermal conversion and nocturnal sky radiative cooling by conventional photovoltaic (PV) combined with thermoelectric generator (TEG) and phase change material (PV-TEG-PCM system). The system generated photovoltaic power during diurnal hours, and TEG utilized temperature difference between PV and PCM to achieve full-day power generation. PCM avoided PV overheating during diurnal hours and increased the temperature difference during nocturnal hours. In this paper, the PV-TEG-PCM system was designed, optimized, and manufactured. Firstly, full-day electrical, thermal and radiative cooling experiments on four commercial PV cell were tested. The crystalline silicon solar cell exhibited high solar absorption performance in PV conversion band of 0.3–1.1 μm and strong thermal emission/absorption performance within thermal radiation band of 4–25 μm. In addition, the electrical, thermal and radiative cooling experiments were done under constant light and cold side. The thermoelectrical model was established and verified. By structure optimization, the system achieved peak efficiency and power generation at phase-transition temperature of 38 °C and layer thickness of 30 mm. Thirdly, the full-day electrical, thermal and radiative cooling performance of PV-TEG-PCM system was tested outdoors. The electrical efficiency of PV reached up to 19.6 %, and total maximum electrical efficiency of TEG throughout the day reached 1.2 %, with overall system efficiency reaching up to 20.8 %. The voltage of TEG reached up to 0.29 V during diurnal hours and up to 0.15 V at nocturnal hours, which was used for solar streetlighting and urban building power supply-lighting composite energy system.
一种新概念的能量收集方法，通过传统光伏（PV）结合热电发电机（TEG）和相变材料（PV-TEG-PCM 系统）实现太阳能昼间光伏/热转换和夜间天空辐射冷却，从而实现 24 小时连续发电。该系统在昼间利用光伏发电，而 TEG 则利用光伏和 PCM 之间的温差实现全天发电。PCM 可避免光伏在昼间过热，并增加夜间的温差。本文设计、优化并制造了 PV-TEG-PCM 系统。首先，对四种商用光伏电池进行了全天电、热和辐射冷却实验。晶体硅太阳能电池在 0.3-1.1 μm 的光伏转换波段表现出较高的太阳能吸收性能，在 4-25 μm 的热辐射波段表现出较强的热辐射/吸收性能。此外，还在恒定冷光侧进行了电学、热学和辐射冷却实验。建立并验证了热电模型。通过结构优化，该系统在相变温度为 38 ℃、层厚度为 30 mm 时达到了最高效率和发电量。第三，在室外测试了 PV-TEG-PCM 系统的全天候电、热和辐射冷却性能。光伏的电效率高达 19.6%，TEG 的全天最大总电效率为 1.2%，整个系统的效率高达 20.8%。TEG 的电压在昼间最高达到 0.29 V，在夜间最高达到 0.5 V。夜间为 15 V，用于太阳能路灯和城市建筑供电-照明复合能源系统。

Keywords 关键词

24-hour power generation
Photovoltaic
Thermoelectric power generation
Phase change material
Solar energy

24 小时发电光伏热电相变材料太阳能

Nomenclature 术语

    c
    specific heat capacity, (J/kg·K)
    比热容，（J/kg-K）
    C
    heat conduction 热传导
    cos(β)
    the tilt angle 倾角
    E
    radiation heat transfer, W
    辐射传热，W
    G
    solar radiation intensity, (W·m−2)
    太阳辐射强度，（W-m −2 )
    Hp
    enthalpy value of PCMs, (J·kg−1)
    PCM 的焓值，（J-kg −1 )
    Hs
    critical enthalpy value, (J·kg−1)
    临界焓值，（J-kg −1 )
    hc
    convective exchange coefficient, (W·m−2·K−1)
    对流交换系数，（W-m −2 -K −1 )
    hr
    radiative heat transfer coefficient (W·m−2·K−1)
    辐射传热系数（W-m −2 -K −1 )
    kl
    the thermal conductivity (W·m−2·K−1)
    导热系数（W-m −2 -K −1 )
    kmelt
    rates constant of phase transition
    相变速率常数
    P
    electrical output power,W/m2
    输出功率，瓦/米 2
    Qlatent
    latent heat of the PCMs, J
    PCM 的潜热，J
    Qc
    convective heat transfer, W
    对流传热，W
    Qs
    apparent heat of phase transition, J
    表观相变热，J
    QL
    latent heat of phase change, J
    相变潜热，J
    S
    Seebeck coefficient 塞贝克系数
    sin(h)
    solar hour angle 太阳时角
    T
    temperatures, °C 温度，°C
    Z
    0.004 K−1
    ua
    wind velocity, (m/s) 风速，（米/秒）
    α
    spectral absorptivity 光谱吸收率
    δ
    thickness, m 厚度，米
    ε
    spectral emissivity 光谱发射率
    η
    conversion efficiency 转换效率
    λ
    heat conductivity coefficient
    热导系数
    μ
    dynamic viscosity (Pa·s) 动态粘度（帕-秒）
    ρ
    density, (kg/m3)
    密度，（千克/米 3 )
    σ
    Boltzmann's constant, 5.67 × 10 -8, (W·m−2·K−4)
    波尔兹曼常数，5.67 × 10 -8 , (W-m −2 -K −4 )
    τ
    spectral transmittance 光谱透射率
    Φsolid F solid
    solid phase fraction of PCMs, W
    PCM 的固相分数，W

1. Introduction 1.导言

The global energy crisis and increasing energy consumption had become an urgent problem to be solved in today's era. Most of the world's energy consumption came from non-renewable energy sources such as fossil fuels. However, extracting energy from fossil fuels could lead to pollution and energy waste [1], [2], which had a great impact on global warming and climate. Therefore, the shift to sustainable and renewable energy had become an inevitable trend. A feasible way to solve this problem was to create clean energy [3]. As a rich and environmentally friendly resource, solar energy was one of the most renewable and potential energy sources. Solar energy was a renewable energy source that could be obtained for free and used anywhere [4]. Solar energy could also be converted into electricity through photovoltaic (PV) effects [5], reducing excessive dependence on fossil fuels, and had great potential to reduce energy consumption and carbon emissions [6].
全球能源危机和日益增长的能源消耗已成为当今时代亟待解决的问题。全球大部分能源消耗都来自化石燃料等不可再生能源。然而，从化石燃料中提取能源会造成污染和能源浪费 [1]，[2]，对全球变暖和气候产生巨大影响。因此，向可持续和可再生能源转变已成为必然趋势。解决这一问题的可行方法是创造清洁能源[3]。太阳能作为一种丰富而环保的资源，是最具可再生性和潜力的能源之一。太阳能是一种可再生能源，可以免费获取并在任何地方使用[4]。太阳能还可以通过光伏效应转化为电能[5]，减少对化石燃料的过度依赖，在减少能源消耗和碳排放方面具有巨大潜力[6]。
Solar energy was a renewable energy source that could be obtained for free and used anywhere[4]. Solar energy could also be converted into electricity through photovoltaic(PV) effects[7], reducing excessive dependence on fossil fuels, and had great potential to reduce energy consumption and carbon emissions. PV technology used solar radiation to generate electricity directly, providing a promising solution for sustainable power generation. However, PV systems cannot convert all solar energy into electrical energy, and a large amount was released in the form of heat, which also leaded to a decrease in energy efficiency in high temperature environments[8], [9]. Therefore, the development of waste heat utilization to improve the conversion efficiency of photovoltaic systems was an attractive and challenging issue[10]. Some solutions were used to control the temperature of photovoltaic modules as low as possible[3]. Cooling technology widely used in thermal engineering was widely used by increasing the conduction and convective heat transfer rates[11]. These technologies were generally divided into passive cooling technology and active cooling technology. Passive cooling referred to the cooling medium driven by nature, mainly based on air, liquid (water, nanofluids, etc.), phase change material (PCM) and sky radiation[12].
太阳能是一种可再生能源，可以免费获取并在任何地方使用[4]。太阳能还可以通过光伏效应转化为电能[7]，减少对化石燃料的过度依赖，在减少能源消耗和碳排放方面具有巨大潜力。光伏技术利用太阳辐射直接发电，为可持续发电提供了一个前景广阔的解决方案。然而，光伏系统并不能将所有太阳能转化为电能，大量的太阳能以热能的形式释放出来，这也导致了高温环境下能源效率的降低[8], [9]。因此，开发余热利用技术以提高光伏系统的转换效率是一个具有吸引力和挑战性的问题[10]。一些解决方案被用于尽可能低地控制光伏组件的温度[3]。热能工程中广泛使用的冷却技术是通过提高传导和对流热传导率来实现的[11]。这些技术一般分为被动冷却技术和主动冷却技术。被动冷却指的是由自然界驱动的冷却介质，主要基于空气、液体（水、纳米流体等）、相变材料（PCM）和天空辐射[12]。
In recent years, some researchers had turned their attention to PCM[13]. This material could store and release a large amount of energy during the phase change process, and had applications in the fields of thermal regulation, energy storage and management[14]. By installing the PCM on the back of the PV cell, this PV-PCM module was expected to maintain a lower photovoltaic cell temperature, thereby achieving higher conversion efficiency[15]. As a passive cooling technology, it did not require flowing fluid or additional power, so the PV-PCM system almost did not require maintenance compared to the most traditional PV/T technology. In addition, PCM were considered to be an effective solution to the use of renewable energy thermal energy, and extensive research had been conducted to study their application in solar energy and building energy conservation, which provided a solid foundation for solar cogeneration in PV-PCM systems. In the experiment and simulation using TRNSYS software, Stropnik and Stritih[16] analyzed the improvement of PCM on the efficiency of PV cells. The experimental results showed that compared with the photovoltaic cells without PCM, the PV cells with PCM could keep the temperature of the photovoltaic panels lower by 35.6 °C and generate 7.3 % more electricity per year[17]. Meng et al[18] conducted a numerical study on the heat transfer mechanism of embedded PCM-TEG. Their research shows that the use of PCM could effectively ensure the stable operation of semiconductor TEG panel. Compared with the traditional structure, the efficiency was improved by 28.6 %.
近年来，一些研究人员将目光转向了 PCM[13]。这种材料在相变过程中可以储存和释放大量能量，在热调节、能源储存和管理等领域都有应用[14]。通过在光伏电池背面安装 PCM，这种 PV-PCM 模块有望保持较低的光伏电池温度，从而实现更高的转换效率[15]。作为一种被动冷却技术，它不需要流动的液体或额外的动力，因此与最传统的 PV/T 技术相比，PV-PCM 系统几乎不需要维护。此外，PCM 被认为是利用可再生能源热能的有效解决方案，人们对其在太阳能和建筑节能中的应用进行了广泛的研究，这为 PV-PCM 系统中的太阳能热电联产提供了坚实的基础。Stropnik 和 Stritih[16]利用 TRNSYS 软件进行实验和模拟，分析了 PCM 对光伏电池效率的改善作用。实验结果表明，与不含 PCM 的光伏电池相比，含 PCM 的光伏电池可使光伏板的温度降低 35.6 °C，年发电量增加 7.3%[17]。Meng 等人[18] 对嵌入式 PCM-TEG 的传热机制进行了数值研究。研究表明，PCM 的使用能有效保证半导体 TEG 面板的稳定运行。与传统结构相比，效率提高了 28.6%。
Thermoelectric generator (TEG) had attracted more and more attention in the past few decades, as one of the important environmental energy conversion technologies[19]. TEG manufactured based on Seebeck effect of thermoelectric materials had many advantages such as no noise, zero emission, safety and high reliability[20]. When two sides of a TEG were located in different temperatures, it could directly convert heat into electricity[21]. It had been widely used in energy fields such as waste heat recovery and solar energy industry[22], [23], [24]. However, challenges such as low conversion efficiency and high material cost hindered the wide application of TEG systems[25], [26]. Although TEG had the advantages of high reliability and scalability, its energy conversion efficiency was still low compared with photovoltaic systems. Researchers were constantly trying to improve the performance of TEG panel and explored its potential in various applications[27].
热电发电机（TEG）作为重要的环境能源转换技术之一，在过去几十年中受到越来越多的关注[19]。基于热电材料的塞贝克效应制造的 TEG 具有无噪音、零排放、安全可靠等诸多优点[20]。当 TEG 的两面处于不同温度时，它可以直接将热量转化为电能[21]。它已被广泛应用于余热回收和太阳能产业等能源领域[22]、[23]、[24]。然而，低转换效率和高材料成本等挑战阻碍了 TEG 系统的广泛应用[25], [26]。虽然 TEG 具有可靠性高和可扩展性强等优点，但与光伏系统相比，其能量转换效率仍然较低。研究人员不断尝试提高 TEG 面板的性能，并探索其在各种应用中的潜力[27]。
The integration of PV-TEG-PCM systems aimed to optimize energy utilization by PV cell, TEG panel, and PCM technologies. PV cell captured solar energy during diurnal hours, converting it into electricity through photovoltaic effects[28]. Meanwhile, TEG panel utilized temperature differentials between the PV module and surrounding environment to generate additional electricity, enhancing overall system efficiency[29]. PCM played a crucial role in thermal management by storing excess heat from PV panels. This stored heat was later released during cooler periods or at night, maintaining optimal operating temperatures for PV cell and enhancing their electrical output. Luo et al[30] established a numerical model focusing on the temperature, efficiency and output power of solar cells. The results show that the solar cell temperature of the PV-PCM-TE system was reduced from 79.72 °C to 57.39 °C, compared with 73.62 °C of the PV-TEG system. The efficiency of PV-PCM-TE system was 10.15 % and 2.37 % higher than that of single photovoltaic system and PV-TEG system, respectively. Lv et al[31] constructed a three-dimensional thermal simulation transient model of PV-TEG-PCM system. The effects of melting temperature, thickness and thermal conductivity of phase change material were studied. The results show that the performance of PV-TEG-PCM system is better than that of PV-TEG or single photovoltaic system. During the peak hours of sunshine, the photovoltaic temperature of the PV-TEG-PCM system is lower than that of the PV-TEG system.
PV-TEG-PCM 系统的集成旨在优化 PV 电池、TEG 面板和 PCM 技术的能量利用。光伏电池在昼夜时间捕获太阳能，通过光生伏打效应将其转化为电能[28]。同时，TEG 面板利用光伏组件和周围环境之间的温差产生额外的电能，提高了整个系统的效率[29]。PCM 在热管理方面发挥了重要作用，它可以储存光伏电池板产生的多余热量。这些储存的热量随后会在凉爽时期或夜间释放出来，从而维持光伏电池的最佳工作温度并提高其电力输出。Luo 等人[30] 建立了一个数值模型，重点研究太阳能电池的温度、效率和输出功率。结果表明，与 PV-TEG 系统的 73.62 ℃ 相比，PV-PCM-TE 系统的太阳能电池温度从 79.72 ℃ 降至 57.39 ℃。PV-PCM-TE 系统的效率分别比单一光伏系统和 PV-TEG 系统高 10.15 % 和 2.37 %。Lv 等人[31] 建立了 PV-TEG-PCM 系统的三维热模拟瞬态模型。研究了相变材料的熔化温度、厚度和导热系数的影响。结果表明，PV-TEG-PCM 系统的性能优于 PV-TEG 或单一光伏系统。在日照高峰时段，PV-TEG-PCM 系统的光伏温度低于 PV-TEG 系统。
Radiation cooling was a passive cooling technology, which had attracted wide attention because of its ability to dissipate heat into outer space through atmospheric windows to produce “free” cooling, thereby reducing the temperature of the object below the ambient temperature[32]. Usually, radiant cooling materials were applied to the outer surface of the building or used in combination with cooling devices to reduce the energy consumption of the building. Radiant cooling materials could also be combined with solar heating systems to achieve the dual effects of cooling and heating[33]. At night, the integration of radiative cooling and TEG panel had the potential to significantly increase the temperature difference between the cold side and the hot side, thereby increasing power generation. The photovoltaic cell itself had the effect of nighttime radiative cooling. At present, the research did not consider the increase of nighttime temperature difference caused by PV nighttime radiative cooling in PV-TEG-PCM system.
辐射冷却是一种被动冷却技术，因其能够通过大气窗口向外层空间散热，产生 "自由 "冷却，从而将物体温度降至环境温度以下而受到广泛关注[32]。通常，辐照冷却材料被应用于建筑物的外表面，或与冷却装置结合使用，以降低建筑物的能耗。辐射制冷材料还可与太阳能供热系统结合使用，以达到制冷和供热的双重效果[33]。在夜间，辐射冷却和 TEG 面板的结合有可能显著增加冷侧和热侧之间的温差，从而增加发电量。光伏电池本身具有夜间辐射冷却的效果。目前的研究并未考虑 PV-TEG-PCM 系统中光伏夜间辐射冷却引起的夜间温差增加。
Given the challenges and opportunities faced by PV, TEG, and PCM technologies, an integrated approach was highly desirable. The proposed PV-TEG-PCM system aimed to collaboratively utilize the advantages of each component and overcome the limitations of single technologies. This system used thermoelectric power generation characteristics of TEG to operate in two modes: daylight and night, achieving 24-hour power generation. During the day, PV cell absorbed sunlight and generated heat, transmitted to PCM through TEG panel. This created a temperature gradient at both ends of the TEG panel, generating electricity using the temperature difference. At night, PCM released waste heat, forming an inverse temperature difference with the PV cell, continuing to drive TEG panel to generate electricity. Through modeling, optimization and 24-hour experiment, this design realized all-weather power generation by using temperature difference, ensured the efficient utilization of solar energy, and provided high energy efficiency and stability.
鉴于 PV、TEG 和 PCM 技术所面临的挑战和机遇，综合方法是非常可取的。拟议的 PV-TEG-PCM 系统旨在协同利用每个组件的优势，克服单一技术的局限性。该系统利用 TEG 的热电发电特性，在白天和夜晚两种模式下运行，实现了 24 小时发电。白天，光伏电池吸收阳光并产生热量，热量通过 TEG 面板传递给 PCM。这就在 TEG 面板两端形成了温度梯度，利用温差发电。夜间，PCM 释放余热，与光伏电池形成反向温差，继续驱动 TEG 面板发电。通过建模、优化和 24 小时实验，该设计利用温差实现了全天候发电，确保了太阳能的高效利用，并具有较高的能效和稳定性。

2. Description of PV-TEG-PCM system
2.PV-TEG-PCM 系统说明

The proposed PV-TEG-PCM system was an innovative energy composite system that combines glass cover, PV cell, TEG panel and PCM technologies. Compared with the traditional PV/T system, the PV-TEG-PCM system no longer aimed to generate hot water, but directly converted solar thermal energy into electrical energy. In this system, PV and TEG panels were jointly responsible for the generation of electrical energy, using the light energy and heat energy of solar radiation for conversion. PCM played a key role in storing and regulating heat in the system. By realizing phase transition during the absorption and release of heat, PCM could effectively balance the energy supply and demand of the system, thereby improving the efficiency and stability of the system (Fig. 1).
拟议的 PV-TEG-PCM 系统是一种创新的能源复合系统，它将玻璃盖板、光伏电池、TEG 面板和 PCM 技术结合在一起。与传统的 PV/T 系统相比，PV-TEG-PCM 系统不再以产生热水为目标，而是直接将太阳热能转化为电能。在该系统中，PV 和 TEG 面板共同负责产生电能，利用太阳辐射的光能和热能进行转换。PCM 在该系统中起到了储存和调节热量的关键作用。通过在吸热和放热过程中实现相变，PCM 可以有效平衡系统的能量供需，从而提高系统的效率和稳定性（图 1）。
  1. Download: Download high-res image (694KB)
    下载：下载高清图片 (694KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 1. The synergistic effect of radiation-induced energy collection on cogeneration. a Graphics of daytime solar radiation heating and PCM heat storage and power generation. b Schematic diagram of nighttime PCM heat release and radiation cooling power generation from the universe. c Energy balance and thermal network of hybrid PV-TEG-PCM system by radiative heating during daytime. d Energy balance and thermal network of hybrid PV-TEG-PCM system by radiative cooling during nighttime. e The power generation temperature difference was generated by the synergistic effect caused by PCM heat absorption during the daytime. f The increase of temperature difference caused by photovoltaic radiation cooling had a synergistic effect on reducing the temperature of the cold end of the TEG module at night.
图 1.a 白天太阳辐射加热和 PCM 储热发电示意图。 b 夜间 PCM 放热和宇宙辐射冷却发电示意图。e 白天 PCM 吸热产生的协同效应产生了发电温差。 f 光伏辐射冷却产生的温差增大对降低夜间 TEG 模块冷端温度产生了协同效应。

During the daylight, PV cell converted solar radiation into electricity. At the same time, part of the solar radiation will also be transmitted to TEG through the PV cell. This part of the radiation will cause the surface temperature of the TEG panel to increase, and it was necessary to release excess heat through heat dissipation to maintain the effective operating temperature range of the TEG. In this process, PCM plays a key role. PCM existed in the system as a heat storage and regulator, which could absorb excess heat from the TEG panel. The heat released by the TEG panel was absorbed by PCM, thereby reducing the surface temperature of the TEG panel, which was conducive to maintaining the efficient operation of the TEG. At this stage, the PV cell became the hot end of the system, while the PCM became the cold end of the system. At this time, the temperature gradient was generated at both ends of the TEG panel. The thermoelectric materials in TEG panel will generate electricity through this temperature gradient. Through this effect, the system could convert thermal energy into electrical energy, thereby achieving efficient use of solar energy.
在白天，光伏电池将太阳辐射转化为电能。与此同时，部分太阳辐射也会通过光伏电池传送到 TEG。这部分辐射会导致 TEG 面板表面温度升高，因此有必要通过散热来释放多余的热量，以保持 TEG 的有效工作温度范围。在这一过程中，PCM 起到了关键作用。PCM 在系统中起到蓄热和调节的作用，可以吸收 TEG 面板的多余热量。TEG 面板释放的热量被 PCM 吸收，从而降低了 TEG 面板的表面温度，有利于保持 TEG 的高效运行。在这一阶段，光伏电池成为系统的热端，而 PCM 成为系统的冷端。此时，温度梯度在 TEG 面板两端产生。TEG 面板中的热电材料将通过这一温度梯度发电。通过这种效应，该系统可以将热能转化为电能，从而实现对太阳能的高效利用。
At night, the working mode of the system will change, because there was no sunlight, the heat transfer mode of the system will change accordingly. At this time, the PV cell no longer received solar radiation and therefore no additional heat was generated. On the contrary, the cold side of the PV cell faced the sky, and the heat was distributed to the outer space by means of radiation cooling. At this stage, the heat collected during the daylight was stored by the PCM, making the temperature of the PCM relatively high. In this case, the PV cell was the cold end, the PCM was the hot end, and the temperature gradient was formed again on both sides of the TEG panel. At this time, TEG generated electricity through temperature gradient, and used the thermal difference effect inside the system to convert heat energy into electricity. Therefore, even in the absence of sunlight, the PV-TEG-PCM system could still use the thermal energy stored in the system for power generation. As a heat storage and regulator, PCM enabled the system to continuously generate electricity at night. The flexibility and efficiency of this system design provided an important guarantee for its feasibility and reliability in practical applications. In general, the PV-TEG-PCM system achieved efficient utilization and storage of solar energy by integrating PV, TEG and PCM, and could adjust energy conversion and transmission through demand during the daylight and night, forming a 24-hour all-power generation system.
到了晚上，系统的工作模式会发生变化，因为没有阳光照射，系统的传热模式也会相应改变。此时，光伏电池不再接受太阳辐射，因此不会产生额外的热量。相反，光伏电池的冷面朝向天空，通过辐射冷却将热量散发到外部空间。在这一阶段，白天收集的热量被 PCM 储存起来，使得 PCM 的温度相对较高。在这种情况下，光伏电池是冷端，PCM 是热端，TEG 面板两侧又形成了温度梯度。此时，TEG 通过温度梯度发电，并利用系统内部的热差效应将热能转化为电能。因此，即使在没有阳光的情况下，PV-TEG-PCM 系统仍可利用系统中储存的热能进行发电。作为热能储存和调节器，PCM 使系统能够在夜间持续发电。该系统设计的灵活性和高效性为其在实际应用中的可行性和可靠性提供了重要保障。总的来说，PV-TEG-PCM 系统通过整合 PV、TEG 和 PCM，实现了太阳能的高效利用和储存，并可根据白天和夜间的需求调节能量转换和传输，形成了一个 24 小时全发电系统。

3. Experimental 3.实验

3.1. Full-day electrical, thermal and radiative cooling experiments on four commercial PV cell
3.1.对四种商用光伏电池进行的全天候电、热和辐射冷却实验

The experiment was: nighttime radiative cooling, which were completed on April 27. In the radiation cooling experiment, we used radiation cooling photovoltaics of different materials such as polycrystalline silicon, copper indium gallium selenide, single crystal silicon and cadmium telluride. Fig. 2 shows the experimental diagram of nighttime photovoltaic radiative cooling performance. The radiation cooling photovoltaic was placed in the radiation cooling module. The radiative cooling module consisted of a 100 mm × 100 mm × 1 mm square copper plate. In order to enhance the heat dissipation of the cold end at night, the copper plate was coated with radiation cooling coating. The emissivity of the coating in the atmospheric window was 0.91, and the reflectivity in the solar spectrum was 0.92. The emissivity of the radiative cooling paint was measured by the Chinese Institute of Testing and Technology (Chengdu, Sichuan, China), while the reflectivity was measured using a UV/VIS/NIR diffuse reflectance detector (Shimadzu, UV3600) [34]. The experiment was carried out on the roof of the skyscraper of Nanjing Technology University.
实验内容为：夜间辐射冷却，于 4 月 27 日完成。在辐射冷却实验中，我们使用了多晶硅、铜铟镓硒、单晶硅和碲化镉等不同材料的辐射冷却光伏器件。图 2 显示了夜间光伏辐射冷却性能的实验示意图。辐射冷却光伏被放置在辐射冷却模块中。辐射冷却模块由一块 100 mm × 100 mm × 1 mm 的正方形铜板组成。为了增强冷端在夜间的散热，铜板上涂有辐射冷却涂层。涂层在大气窗口中的发射率为 0.91，在太阳光谱中的反射率为 0.92。辐射冷却涂料的发射率由中国测试技术研究院（中国四川成都）测量，而反射率则使用紫外/可见光/近红外漫反射检测器（岛津，UV3600）测量[34]。实验在南京理工大学的摩天大楼屋顶上进行。
  1. Download: Download high-res image (162KB)
    下载：下载高清图片 (162KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 2. The experimental physical diagram of photovoltaic radiation cooling performance at night.
图 2.夜间光伏辐射制冷性能实验物理示意图。

3.2. The electrical, thermal and radiative cooling experiments of PV-TEG-PCM system
3.2.PV-TEG-PCM 系统的电、热和辐射冷却实验

The electrical, thermal and radiative cooling experiments under constant light and cold side. The experiments were carried out in the laboratory of Tiangong Building of Nanjing Technology University. Firstly, the temperature changes of PV cell, TEG panel and PCM under different irradiation intensities (600 W/m2,800 W/m2 and 1000 W/m2) were simulated by using xenon lamp to simulate the light source. In addition, in order to simulate the radiation cooling effect of photovoltaic at night, cold water was used to replace PV cell to achieve auxiliary cooling. Fig. 3 (c) shows the physical layout of the night system experiment. From top to bottom, there were auxiliary cooling modules (iron cold sink), PV cell, TEG panel and containers with PCM. The chilled water was pumped out from the constant temperature and low temperature cold water tank through the pump to ensure that the water temperature was maintained between 10–15 °C at night.
恒定光照和冷侧条件下的电学、热学和辐射冷却实验。实验在南京理工大学天工楼实验室进行。首先，利用氙灯模拟光源，模拟了光伏电池、TEG 面板和 PCM 在不同照射强度（600 W/m 2 、800 W/m 2 和 1000 W/m 2 ）下的温度变化。此外，为了模拟光伏在夜间的辐射冷却效果，用冷水代替光伏电池实现辅助冷却。图 3（c）显示了夜间系统实验的物理布局。从上到下依次为辅助冷却模块（铁制冷水槽）、光伏电池、TEG 面板和装有 PCM 的容器。冷冻水通过水泵从恒温低温冷水箱中抽出，以确保夜间水温保持在 10-15 °C之间。
  1. Download: Download high-res image (791KB)
    下载：下载高清图片 (791KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 3. Indoor hot end physical drawing (a) and flow-chart(b), indoor cold end physical drawing (c) and flow-chart(d), Outdoor experiment physical drawing (e) and flow-chart(f).
图 3.室内热端实物图（a）和流程图（b）、室内冷端实物图（c）和流程图（d）、室外实验实物图（e）和流程图（f）。

The electrical, thermal and radiative cooling experiments under outdoor conditions. Fig. 3 (e) shows the layout of outdoor experimental equipment. The PV-TEG-PCM hybrid system from top to bottom in turn was the solar panel (50 mm × 50 mm), TEG panel (50 mm × 50 mm) and aluminum tank device with PCM (50 mm × 50 mm × 30 mm). In order to enhance the thermal conductivity, the thermal conductive silica gel was used to connect. In order to minimize heat loss and ensure a more accurate measurement of the performance of the system, we had insulated the side walls of the system. On the basis of the results of the simulation, the phase change paraffin with a phase-transition temperature of 38 °C and a thickness of 30 mm was selected as the PCM. The main function of PCM was to absorb heat during the daylight, reduce the temperature of the PV cell, thereby improving its photoelectric conversion efficiency. At the same time, PCM was used as the cold end during the daylight, and PV cell was the hot end. The temperature gradient at both ends made the TEG panel generate electric energy. Due to the storage of a large amount of heat, PCM formed the hot end at night, and PV cell was a cold end due to the radiation cooling effect. The temperature difference was formed at both ends of the TEG panel, which promoted the power generation of the TEG panel.
室外条件下的电气、热和辐射冷却实验。图 3（e）显示了室外实验设备的布局。PV-TEG-PCM 混合系统从上到下依次为太阳能电池板（50 mm × 50 mm）、TEG 电池板（50 mm × 50 mm）和装有 PCM 的铝制水箱装置（50 mm × 50 mm × 30 mm）。为了增强导热性，使用了导热硅胶进行连接。为了尽量减少热量损失，确保更准确地测量系统的性能，我们对系统的侧壁进行了隔热处理。根据模拟结果，我们选择了相变温度为 38 °C、厚度为 30 毫米的相变石蜡作为 PCM。PCM 的主要功能是在白天吸收热量，降低光伏电池的温度，从而提高其光电转换效率。同时，PCM 在白天作为冷端，光伏电池作为热端。两端的温度梯度使 TEG 面板产生电能。由于储存了大量热量，PCM 在夜间成为热端，而 PV 电池由于辐射冷却效应成为冷端。TEG 面板两端形成的温度差促进了 TEG 面板的发电。
The automatic weather station was used to monitor the ambient temperature and wind speed, and the solar irradiation intensity was recorded by the irradiator[35]. The temperature of the PV-TEG-PCM system was measured by a K-type thermocouple connected to the data acquisition system, and the output voltage of the thermoelectric power generation panel was measured directly by the multimeter data acquisition. All automatic weather stations and data acquisition data were recorded at intervals of 10 s. The thermophysical properties of PCM were shown in Table 1. When selecting PCM, we consider the matching between the working temperature of PV cell and TEG panel and the phase-transition temperature of PCM. In this study, organic phase change paraffin PCMs were used for heat storage. PCM had the advantages of high heat storage density, good thermal stability and high thermal conductivity.
自动气象站用于监测环境温度和风速，辐照仪记录太阳辐照强度[35]。PV-TEG-PCM 系统的温度由连接到数据采集系统的 K 型热电偶测量，热发电板的输出电压由万用表数据采集器直接测量。表 1 列出了 PCM 的热物理性质。在选择 PCM 时，我们考虑了光伏电池和 TEG 面板的工作温度与 PCM 相变温度之间的匹配。本研究采用有机相变石蜡 PCM 进行储热。PCM 具有储热密度高、热稳定性好和热导率高等优点。

Table 1. Thermophysical properties of the PCMs.
表 1.PCM 的热物理特性。

Density (g/cm3)
密度（克/厘米 3 )		Thermal conductivity (W/m·K)
导热系数（瓦/米-千克）		Melting point (°C) 熔点（°C）Latent heat (J/g) 潜热（焦耳/克）Specific heats (kJ/kg K) 比热（千焦/千克 K）Supplier 供应商
0.84/0.790.21382152Plasticizing Co., Ltd. 塑化有限公司
The model and accuracy of the experimental instruments were shown in Table 2.
实验仪器的型号和精度见表 2。

Table 2. Experimental instruments.
表 2.实验仪器。

Apparatus 仪器ModelMeasuring parameter 测量参数Accuracy 准确性
Data acquisition instrument
数据采集仪器		Agilent34972 ATemperature, Solar radiation intensity
温度、太阳辐射强度		/
Thermocouple 热电偶K type K 型Temperature 温度±0.5 °C ±0.5 °C
Solar irradiator 太阳能辐照装置TQB-2Global solar radiation 全球太阳辐射±11.04
Hot-wire anemometer 热线风速计KANOMAXAir flow velocity 气流速度±0.01 m/s ±0.01 米/秒

4. System thermal electric model
4.系统热电模型

4.1. Thermal electric conversion model
4.1.热电转换模型

Compared with the photovoltaic system alone, the PV-TEG-PCM hybrid system was more complex in structure. In order to simplify, the following assumptions were used in the numerical simulation[36]:
与单独的光伏系统相比，PV-TEG-PCM 混合系统的结构更为复杂。为了简化，数值模拟中使用了以下假设[36]：
(1) The simulation was based on one-dimensional and steady-state heat transfer processes. On the surface of the same height, the heat flux and temperature values were uniform[37].
(1) 模拟基于一维稳态传热过程。在同一高度的表面上，热通量和温度值是均匀的[37]。
(2) The energy loss only occurred on the top surface of the PV and the bottom surface of the PCM device, while the heat loss from the system through the module side to the environment was ignored.
(2) 能量损失只发生在 PV 的上表面和 PCM 设备的下表面，而忽略了系统通过模块侧向环境的热量损失。
(3) The physical parameters of the material in the system, including the TE characteristics of n-type and p-type semiconductors in TEG, were considered to be constant and temperature-independent.
(3) 系统中材料的物理参数，包括 TEG 中 n 型和 p 型半导体的 TE 特性，被认为是恒定和与温度无关的。
(4) The thermal contact resistance between adjacent layers in the system was considered to be an appropriate constant, which was determined by the thickness of the air layer.
(4) 系统中相邻层之间的热接触电阻被认为是一个适当的常数，它由空气层的厚度决定。
(5) The thermal radiation loss between the phase change device and the ground was zero, and the temperature difference was small[38].
(5) 相变装置与地面之间的热辐射损失为零，温差很小[38]。
Fig. 4(a) illustrates the thermoelectric model of the PV-TEG-PCM hybrid system, while Fig. 4(b) presents the flow diagram of the calculation process.The equations for each node were numerically discretized using the implicit method, and the time step was 10 s. The photothermal model was mainly composed of four parts: glass cover, PV cell, TEG panel and PCMs, respectively. First, the glass at the top absorbed a small part of the solar radiation heat and transmitted most of the solar radiation to the PV cell. At the same time, the glass plate conducted convective heat transfer and radiation heat transfer with the surrounding air and sky. The solar radiation absorbed by the PV cell was converted into heat. Most of the solar radiation absorbed by the photovoltaic cell was converted into electricity, and the waste heat was transmitted to the TEG panel in the form of thermal radiation and heat conduction. Due to the poor heat absorption of the TEG panel, this part of the waste heat will not be absorbed by the TEG panel, but was transmitted to the PCMs through heat conduction. Therefore, a temperature difference was formed on both sides of the TEG panel, and the TEG panel generated electricity at this time.
图 4（a）为 PV-TEG-PCM 混合系统的热电模型，图 4（b）为计算过程流程图。光热模型主要由玻璃盖板、PV 电池、TEG 面板和 PCM 四部分组成。首先，顶部的玻璃吸收了一小部分太阳辐射热，并将大部分太阳辐射传给了光伏电池。同时，玻璃板与周围的空气和天空进行对流换热和辐射换热。光伏电池吸收的太阳辐射转化为热量。光伏电池吸收的大部分太阳辐射被转化为电能，余热则以热辐射和热传导的形式传送到 TEG 面板。由于 TEG 面板的吸热能力较差，这部分余热不会被 TEG 面板吸收，而是通过热传导传递到 PCM。因此，TEG 面板两侧形成了温差，此时 TEG 面板便产生了电能。
  1. Download: Download high-res image (245KB)
    下载：下载高清图片 (245KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 4. Thermal electric model (a) and the calculation process for the thermal model system (b).
图 4.热电模型（a）和热电模型系统的计算过程（b）。

In the numerical model, Tg, Tp, Tteg, and TPCM (°C) were the temperatures of the glass plate, PC cell, TEG panel and PCMs, respectively.
在数值模型中，T g 、T p 、T teg 和 T PCM (°C) 分别为玻璃板、PC 电池、TEG 面板和 PCM 的温度。
The energy balance function for the glass cover was given as:(1)ρgδgcg∂Tg∂t=Gg+hc_abmTabm-Tg+hr_skyTsky-Tg+hr_gpTp-Tg+kgδgTp- Tgwhere ρg was density of glass cover (kg·m−3); δg was thickness of the glass cover (m); cg was the capacity of the glass cover (J·K−1·m−2); Gg was the solar radiation intensity on the surface of glass cover (W·m−2) and could be calculated[39] via the spectral absorptivity αg, as depicted Eq.(2); hc_abm was convective heat transfer coefficient between glass cover and ambient air (W·m−2·K−1) and could be calculated by the ambient wind speed, as depicted Eq.(6); hr_sky was sky temperature radiation coefficient (W·m−2·K−1), radiant heat transfer depended on the Stefan-Boltzmann law, and could be calculated via the emissivity of the object[40], as showed in Eq.(4), where εg was emissivity of the glass cover and σ was the Stefan-Boltzmann; hr_gp was the radiant heat transfer coefficient between the glass cover and PV cell (W·m−2·K−1) and could be calculated via the emissivity of the object, as showed in Eq.(7), where εg and εp were emissivity of the glass and TEG panel, respectively[41]; kg was thermal conductivity of glass cover (W·m−2·K−1).The irradiation intensity at different angles could refer to the Spencer model. The calculation formula of the irradiation intensity of the model was as followed:(2)Gg=∫3004000αgλGλdλsinhcosβ(3)sinh=sinϕsinδ+cosϕcosδcosha(4)hr_sky=σεgTsky+TgTsky2+Tg2(5)Tsky=0.0552Ta1.15(6)hc_abm=6.5+3.3ua(7)hr_gp=σTp+TgTp2+Tg21/εg+1/εp
玻璃盖板的能量平衡函数为 (1)ρgδgcg∂Tg∂t=Gg+hc_abmTabm-Tg+hr_skyTsky-Tg+hr_gpTp-Tg+kgδgTp- Tg 其中，ρ g 为玻璃盖板的密度（kg-m −3 ）；δ g 为玻璃盖板的厚度（m）；c g 为玻璃盖板的容量（J-K −1 -m −2 ）；G g 是玻璃盖板表面的太阳辐射强度（W-m −2 ），可通过光谱吸收率 α g 计算得出[39]，如式（2）所示(2); h c_abm 是玻璃盖板与环境空气之间的对流换热系数（W-m −2 -K −1 ），可通过环境风速计算，如公式 (6) 所示；h r_sky 是玻璃盖板与环境空气之间的对流换热系数（W-m −2 -K −1 ），可通过环境风速计算，如公式(6); h r_sky 为天空温度辐射系数（W-m −2 -K −1 ），辐射传热依赖于斯蒂芬-玻尔兹曼定律，可通过物体的辐射率计算得出[40]，如式（4）所示。(4) 式中：ε g 为玻璃盖板的辐射率，σ 为斯蒂芬-玻尔兹曼定律；h r_gp 为玻璃盖板与光伏电池之间的辐射传热系数（W-m −2 -K −1 ），可通过物体的辐射率计算，如式（7）所示。(7) 式中：ε g 和 ε p 分别为玻璃和 TEG 面板的发射率[41]；k g 为玻璃盖板的导热系数（W-m −2 -K −1 ）。该模型的辐照强度计算公式如下： (2)Gg=∫3004000αgλGλdλsinhcosβ (3)sinh=sinϕsinδ+cosϕcosδcosha (4)hr_sky=σεgTsky+TgTsky2+Tg2 (5)Tsky=0.0552Ta1.15 (6)hc_abm=6.5+3.3ua (7)hr_gp=σTp+TgTp2+Tg21/εg+1/εp
The energy balance function for the PV cell was given as:(8)ρpδpcp∂Tp∂t=Gp-Qe+hc_abmTabm-Tp+hr_gpTg-Tp+hr_ptegTteg-Tp+kpδpTg- Tp+kpδpTteg- Tpwhere ρp was density of PV cell (kg·m−3); δp was thickness of the PV cell (m); cp was the capacity of the PV cell (J·K−1·m−2); Gp was the solar radiation intensity on the surface of PV cell(W·m−2) and could be calculated[39] via the spectral absorptivity αg and αp, as depicted Eq.(2); Qe was the output power of PV cell; hr_pteg was the radiant heat transfer coefficient between the PV cell and TEG panel(W·m−2·K−1) and could be calculated via the emissivity of the object, as showed in Eq.(7), where εp and εteg were emissivity of the PV cell and TEG panel, respectively[41]; kp was thermal conductivity of PV cell (W·m−2·K−1).(9)Gp=∫3004000τgλαpλGλdλsinhcosβ(10)hr_pteg=σTp+TtegTp2+Tteg21/εp+1/εteg
光伏电池的能量平衡函数为 (8)ρpδpcp∂Tp∂t=Gp-Qe+hc_abmTabm-Tp+hr_gpTg-Tp+hr_ptegTteg-Tp+kpδpTg- Tp+kpδpTteg- Tp 其中，ρ p 为光伏电池的密度（kg-m −3 ）；δ p 为光伏电池的厚度（m）；c p 为光伏电池的容量（J-K −1 -m −2 ）；G p 是光伏电池表面的太阳辐射强度（W-m −2 ），可通过光谱吸收率 α g 和 α p 计算得出[39]，如式 (2) 所示；Qe 是光伏电池表面的太阳辐射强度（W-m(2); Qe 是光伏电池的输出功率；h r_pteg 是光伏电池与 TEG 面板之间的辐射传热系数（W-m −2 -K −1 ），可通过物体的发射率计算，如式 (7) 所示。(7) 式中：ε p 和 ε teg 分别为光伏电池和 TEG 面板的发射率[41]；k p 为光伏电池的导热系数（W-m −2 -K −1 ）。 (9)Gp=∫3004000τgλαpλGλdλsinhcosβ (10)hr_pteg=σTp+TtegTp2+Tteg21/εp+1/εteg
The energy balance function for the TEG panel was given as:(11)ρtegδtegcteg∂Tteg∂t=Gteg-Qteg+hr_ptegTp-Tteg+hr_tegpcmTpcm-Tteg+ktegδtegTp-Tteg+ktegδtegTpcm- Ttegwhere ρteg was density of TEG panel (kg·m−3); δteg was thickness of the TEG panel (m); cteg was the capacity of the TEG panel (J·K−1·m−2); Gteg was the solar radiation intensity on the surface of TEG panel(W·m−2) and could be calculated[39] via the spectral absorptivity αp, as depicted Eq.(9); Qteg was the output power of TEG panel; hr_tegpcm was the radiant heat transfer coefficient between the TEG panel and PCM (W·m−2·K−1) and could be calculated via the emissivity of the object, as showed in Eq.(10), where εpcm was emissivity of the PCMs[41]; kteg was thermal conductivity of TEG panel (W·m−2·K−1).(12)Gteg=∫3004000τgλτpλαtegλGλdλsinhcosβ(13)hr_tegpcm=σTteg+TpcmTteg2+Tpcm21/εteg+1/εpcm
TEG 面板的能量平衡函数为 (11)ρtegδtegcteg∂Tteg∂t=Gteg-Qteg+hr_ptegTp-Tteg+hr_tegpcmTpcm-Tteg+ktegδtegTp-Tteg+ktegδtegTpcm- Tteg 其中，ρ teg 为 TEG 面板的密度（kg-m −3 ）；δ teg 为 TEG 面板的厚度（m）；c teg 为 TEG 面板的容量（J-K −1 -m −2 ）；G teg 是 TEG 面板表面的太阳辐射强度（W-m −2 ），可通过光谱吸收率 α p 计算得出[39]，如式（9）所示；Q 是 TEG 面板的输出功率；h r_tegpcm 是 TEG 面板与 PCM 之间的辐射传热系数（W-m −2 -K −1 ），可通过物体的发射率计算得出，如式 (10) 所示。(10) 式中：ε pcm 为 PCM 的发射率[41]；k teg 为 TEG 面板的导热系数（W-m −2 -K −1 ）。 (12)Gteg=∫3004000τgλτpλαtegλGλdλsinhcosβ (13)hr_tegpcm=σTteg+TpcmTteg2+Tpcm21/εteg+1/εpcm
The energy balance function for the PCMs was given as[42], [43]:(14)ρpcmcpcmδpcm∂Tpcm∂t=Gpcm+∂∂xkpcm∂Tpcm∂x+Qlatent+hr_tegpcmTteg-Tpcm+kpcmδpcmTteg-Tpcm+hc_abmTabm-Tpcmwhere ρpcm was density of the PCM (kg·m−3); δpcm was thickness of the PCM layer(m); cpcm was the capacity of the PCM (J·K−1·m−2); Gpcm was the solar radiation intensity on the surface of PCM (W·m−2) and could be calculated[39] via the spectral absorptivity αp, as depicted Eq.(2); Qlatent was the latent heat of the PCMs (J) and could be calculated by Eq. (12);kpcm was thermal conductivity of the PCM (W·m−2·K−1).(15)Gpcm=∫3004000τgλτpλτtegλαpcmλGλdλsinhcosβ(16)Qlatent=ρPCMH∂Φ∂t+∂Φsolid∂twhere H was the latent heat of phase change (J·kg−1); Φ was the phase fraction of the PCMs, which represented the fraction of the liquid phase; Φsolid was the solid phase fraction of PCMs.
PCM 的能量平衡函数为[42]、[43]：<其中，ρ pcm 是 PCM 的密度（kg-m −3 ）；δ pcm 是 PCM 层的厚度（m）；c pcm 是 PCM 的容量（J-K −1 -m −2 ）；G pcm 是 PCM 表面的太阳辐射强度（W-m −2 ），可通过光谱吸收率 α p 计算得出[39]，如式 (2) 所示(2); Q latent 是 PCM 的潜热（J），可通过公式 (12) 计算；k pcm 是 PCM 的导热系数（W-m −2 -K −1 ）。 (15)Gpcm=∫3004000τgλτpλτtegλαpcmλGλdλsinhcosβ (16)Qlatent=ρPCMH∂Φ∂t+∂Φsolid∂t 其中，H 为相变潜热（J-kg −1 ）；Φ 为 PCM 的相分数，代表液相分数；Φ solid 为 PCM 的固相分数。
The change of phase fraction could be expressed by the melting and solidification rate equations:(17)∂Φ∂t=kmeltTPCM-Tmelt(18)∂Φsolid∂t=ksolidTPCM-Tsolidwhere kmelt and ksolid were the rates constant of phase transition; Tmelt and Tsolid were the melting and solidification temperatures of the PCMs, respectively.
相分数的变化可以用熔化和凝固速率方程来表示： (17)∂Φ∂t=kmeltTPCM-Tmelt (18)∂Φsolid∂t=ksolidTPCM-Tsolid 其中 k melt 和 k solid 为相变速率常数；T melt 和 T solid 分别为 PCM 的熔化温度和凝固温度。
TPCM was the internal temperature of PCM. The calculation formula was as followed[42]:(19)Tpcm=Hp/cPCM+TmHp≤HsHp-L/cPCM+TmHp≥HlTmHs<Hp<Hl(20)Hs-Hl= Hwhere Tm was transformation temperature of the PCMs(K); HP was enthalpy value of PCMs(J∙kg−1); Hs was the critical enthalpy value when the PCMs began to liquefy(J∙kg−1); Hl was the enthalpy value when the PCMs were completely melted.
T PCM 是 PCM 的内部温度。计算公式如下[42]： (19)Tpcm=Hp/cPCM+TmHp≤HsHp-L/cPCM+TmHp≥HlTmHs<Hp<Hl (20)Hs-Hl= H 其中 T m 为 PCM 的转化温度（K）；H P 为 PCM 的焓值（J∙kg −1 ）；H s 为 PCM 开始液化时的临界焓值（J∙kg −1 ）；H 为 PCM 完全熔化时的焓值。
After the heat transfer model was established, the energy conservation equations of each part were discretized respectively. The outdoor meteorological parameters measured during the experiment were taken as the boundary conditions of the model. The parameters included solar radiation, outdoor air temperature, and outdoor velocity. Finally, the meteorological parameters were compiled into MATLAB code file and imported into the software for calculation. The initial values of the temperature parameters of each part were the temperatures measured before the start of the experiment. According to the calculation process, the temperatures of each part were calculated in turn. All the physical parameters used in the calculation were shown in Table 3.
建立传热模型后，分别对各部分的能量守恒方程进行离散化处理。实验过程中测得的室外气象参数作为模型的边界条件。这些参数包括太阳辐射、室外气温和室外气流速度。最后，将气象参数编译成 MATLAB 代码文件并导入软件进行计算。各部分温度参数的初始值为实验开始前测得的温度。根据计算过程，依次计算各部分的温度。计算中使用的所有物理参数如表 3 所示。

Table 3. The physical parameters of each material used in simulation calculation.
表 3.模拟计算中使用的每种材料的物理参数。

Material 材料Glass 玻璃PVPCMTEG
ρ, kg/m3 ρ，千克/米 3 12002330840/7907000
cp, J/kg∙K19007002500390
λ, W/m∙K0.221500.21398
Thickness, m 厚度，米0.010.010.020.05
α0.930.05
ε0.750.02
Transmittance 透射率0.930.1

4.2. Performance evaluation
4.2.绩效评估

Pgen was the electrical output power generated by PV was calculated from the following relation[44]:(21)Pgen=τgαcellQsolηpvwhere Qsol was the total average incoming solar irradiation flux on system; τg was the glass transmissivity; and αcell was the cell absorptivity.
Pgen 是光伏发电的输出功率，由以下关系式计算得出[44]： (21)Pgen=τgαcellQsolηpv 其中 Q sol 是系统上的总平均太阳辐照通量；τ g 是玻璃透射率；α cell 是电池吸收率。
ηpv was the PV conversion efficiency, it was obtained by the following relation[31], [45]:(22)ηpv=ηr1-0.005Tp-25+0.085lnIT/1000where ηr was the reference efficiency of the PV at reference temperature of 25 °C and was taken to be 20 %; Tp was the PV back surface temperature; IT was the solar radiation intensity.
η pv 是光伏转换效率，由以下关系式得出[31]，[45]： (22)ηpv=ηr1-0.005Tp-25+0.085lnIT/1000 其中，η r 是参考温度为 25 °C 时的光伏参考效率，取 20%；T p 是光伏背面温度；I T 是太阳辐射强度。
Pteg was the electrical output power from TEG and may also be expressed as a function of ηpv as[46]:(23)Pteg=τgαcellQsol1-ηpvηtegAt night, Vteg could be calculated by the following formula:(24)Vteg=ΔTSηtegWhere ΔT was the temperature difference between the hot side and the cold side; S was the Seebeck coefficient, which was 10 V/K according to the selected material.
P teg 是 TEG 的输出功率，也可以表示为 η pv 的函数[46]： (23)Pteg=τgαcellQsol1-ηpvηteg 夜间，V teg 可按下式计算： (24)Vteg=ΔTSηteg 其中，ΔT 是热侧和冷侧之间的温差；S 是塞贝克系数，根据所选材料，塞贝克系数为 10 V/K。
ηteg was the conversion efficiency of TEG cell, was given as[31], [44]:(25)ηteg=1-Tcold/Thot×1+ZTteg-11+ZTteg+Tcold/Thotwhere Tcold and Thot were the temperatures at the cold and hot sides of the TEG respectively; Tteg was the average temperature of the TEG and Z was taken as a common value achieved by the commercial TEG products, Z = 0.004 K−1[47].
η teg 为 TEG 电池的转换效率，计算公式为[31]、[44]： (25)ηteg=1-Tcold/Thot×1+ZTteg-11+ZTteg+Tcold/Thot 其中 T cold 和 T hot 分别为 TEG 冷端和热端的温度；T teg 为 TEG 的平均温度；Z 取为商用 TEG 产品的常用值，即 Z = 0.004 K −1 [47]。
During the night, the cooling power produced by the radiative cooling paint (Psur) could be calculated by Ref[34], [48].(26)Psur=∫02πcosθdθ∫3004000εrλ,θEbλ,Trdλwhere λ was the wavelength; θ was the zenith angle; εr (λ, θ) was the emissivity of the radiative cooling paint; Eb (λ, Tr) was the spectral radiance of a blackbody defined by Planck's law at temperature Tr; and Tr was the surface temperature of the radiative cooling paint.
在夜间，辐射冷却涂料产生的冷却功率（P sur ）可由参考文献[34]、[48]计算得出。 (26)Psur=∫02πcosθdθ∫3004000εrλ,θEbλ,Trdλ 其中，λ 是波长；θ 是天顶角；ε r (λ, θ) 是辐射冷却涂料的发射率；E b (λ, Tr) 是普朗克定律定义的黑体在温度 T r 时的光谱辐射率；T r 是辐射冷却涂料的表面温度。
Atmospheric emissivity was relatively complex due to the differences in atmospheric composition, and weather and climatic conditions. Here, we used Equation (27) to derive the atmospheric emissivity[34], [49], [50].(27)εr=0.711+0.56Tdew100+0.73Tdew1002where Tdew was the local dew point temperature.
由于大气成分、天气和气候条件的差异，大气发射率相对复杂。在此，我们使用公式（27）推导大气发射率[34]、[49]、[50]。 (27)εr=0.711+0.56Tdew100+0.73Tdew1002 其中 T dew 为当地露点温度。
Eb (λ, T) could be calculated as follows[34]:(28)Ebλ,T=2hc2λ51ehc/λkBT-1where ε (λ, θr) was the emissivity of the radiative cooling paint dependent on the solar incidence angle θs; EAM1.5 was solar radiation intensity with normal solar spectrum; h was Planck's constant of 6.63 × 10−34 J s; c was the speed of light in vacuum; and kB was Boltzmann's constant of 5.67 × 10−8 W/m2 K4.
E b (λ, T) 的计算公式如下[34]： (28)Ebλ,T=2hc2λ51ehc/λkBT-1 其中，ε (λ, θr) 是辐射冷却涂料的发射率，与太阳入射角 θs 有关；E AM1.5 是正常太阳光谱下的太阳辐射强度；h 是普朗克常数 6.63 × 10 −34 J s；c 为真空中的光速；k B 为波尔兹曼常数 5.67 × 10 −8 W/m 2 K 4 。

5. Results and discussions
5.结果和讨论

5.1. The electrical, thermal and radiative cooling performance of four commercial PV cell
5.1.四种商用光伏电池的电性能、热性能和辐射冷却性能

The irradiation intensity throughout the day ranged from 0 to 1038 W/m2, with an average daylight intensity of 676.6 W/m2. The outdoor air temperature varied between 23 °C and 45 °C (Fig. 5a). To select an optimal photovoltaic material that offers both high conversion efficiency and effective nighttime radiative cooling, we tested the temperature changes of four different photovoltaic materials over a day.
全天的辐照强度从 0 到 1038 W/m 2 不等，平均日照强度为 676.6 W/m 2 。室外气温在 23 °C 和 45 °C 之间变化（图 5a）。为了选择一种既能提供高转换效率又能在夜间有效辐射冷却的最佳光伏材料，我们测试了四种不同光伏材料在一天中的温度变化。
  1. Download: Download high-res image (527KB)
    下载：下载高清图片 (527KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 5. The outdoor weather parameters (a), the temperature change, conversion efficiency(b) and output power (c) of PV cell, and the emissivity of monocrystalline silicon and atmospheric transmittance in ultraviolet and infrared range (e).
图 5.室外天气参数（a）、温度变化、光伏电池的转换效率（b）和输出功率（c），以及单晶硅的发射率和大气在紫外线和红外线范围内的透过率（e）。

PV cells made of cadmium telluride exhibited the lowest temperatures due to their higher conversion capacity, which enabled faster heat-to-electricity conversion. At night, the radiative cooling effects of copper indium gallium selenide, monocrystalline silicon, and polycrystalline silicon photovoltaic cells were similar, while cadmium telluride showed poorer performance (Fig. 5b). This discrepancy was because copper indium gallium selenide, monocrystalline silicon, and polycrystalline silicon have good infrared radiation absorption characteristics, efficiently absorbing thermal radiation from the surface and providing effective cooling. In contrast, cadmium telluride's poorer radiation absorption characteristics resulted in lower efficiency in both absorbing and releasing heat.
由碲化镉制成的光伏电池温度最低，这是因为它们的转换能力较强，能够更快地实现热电转换。在夜间，铜铟镓硒、单晶硅和多晶硅光伏电池的辐射冷却效果相似，而碲化镉的性能较差（图 5b）。出现这种差异的原因是铜铟镓硒、单晶硅和多晶硅具有良好的红外辐射吸收特性，能有效吸收表面的热辐射并提供有效冷却。相比之下，碲化镉的辐射吸收特性较差，导致吸收和释放热量的效率较低。
The average conversion efficiencies for polycrystalline silicon, copper indium gallium selenide, monocrystalline silicon, and cadmium telluride were 14.1 %, 15.3 %, 14.9 %, and 16.3 %, respectively (Fig. 5c). Among these, cadmium telluride PV cells exhibited the highest conversion efficiency due to their high light absorption coefficient, excellent consistency with the solar spectrum, and direct band gap structure (Fig. 5d). These properties enabled cadmium telluride cells to efficiently convert sunlight into electricity, absorb over 95 % of sunlight, and generate electron-hole pairs with minimal energy loss (Fig. 5e). When solar irradiation was constant, the temperature of the PV cells became the dominant factor affecting efficiency. Monocrystalline silicon and cadmium telluride maintained higher efficiency under varying temperature conditions. Considering the heat absorption capacity during daylight and the radiative cooling capacity at night, monocrystalline silicon photovoltaic material emerged as the best choice.
多晶硅、铜铟镓硒、单晶硅和碲化镉的平均转换效率分别为 14.1%、15.3%、14.9% 和 16.3%（图 5c）。其中，碲化镉光伏电池的转换效率最高，这得益于其较高的光吸收系数、与太阳光谱的良好一致性以及直接带隙结构（图 5d）。这些特性使碲化镉电池能够有效地将太阳光转化为电能，吸收 95% 以上的太阳光，并以最小的能量损失产生电子-空穴对（图 5e）。当太阳辐照恒定时，光伏电池的温度成为影响效率的主要因素。单晶硅和碲化镉在不同温度条件下保持较高的效率。考虑到白天的吸热能力和夜间的辐射冷却能力，单晶硅光伏材料成为最佳选择。

5.2. The electrical, thermal and radiative cooling performance under constant light and cold side
5.2.恒定光照和冷侧条件下的电气、热和辐射冷却性能

Through analysis of the graphic data, it could be clearly known that with the gradual increase of irradiation intensity, the final temperature of each component of the hybrid system also showed a corresponding growth trend (Fig. 6). Not only that, the temperature difference between different parts of the system also expanded. At the same time, it could be also observed that the voltage of the system continued to rise and eventually stabilized at a higher value. This phenomenon was mainly attributed to the excellent heat absorption performance of photovoltaic modules. When the irradiation was stronger, the PV material could absorb and convert these irradiation energies more efficiently, resulting in a faster rise in temperature and eventually reaching a higher temperature level. In addition, it could be further understood that when the cold end temperature of the system was controlled lower, the generated voltage would become higher accordingly.
通过对图形数据的分析，可以清楚地知道，随着辐照强度的逐渐增加，混合系统各部分的最终温度也呈现出相应的增长趋势（图 6）。不仅如此，系统各部分之间的温差也在扩大。与此同时，还可以观察到系统的电压持续上升，并最终稳定在一个较高的值上。这一现象主要归因于光伏组件出色的吸热性能。当辐照较强时，光伏材料可以更有效地吸收和转换这些辐照能量，从而使温度上升更快，最终达到更高的温度水平。此外，可以进一步理解的是，当系统的冷端温度控制得较低时，产生的电压也会相应变高。
  1. Download: Download high-res image (470KB)
    下载：下载高清图片 (470KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig.6. The Schematic diagram of hybrid PV-TEG-PCM system device (a)using a simulated Xenon lamp heat source and the temperature changes of PV cell(b), TEG panel(c) and PCM(d) under different irradiation intensities and the final stable voltage(d).
图 6.使用模拟氙灯热源的 PV-TEG-PCM 混合系统装置示意图（a），以及不同照射强度下 PV 电池（b）、TEG 面板（c）和 PCM（d）的温度变化和最终稳定电压（d）。

In order to study the radiative cooling of the PV system at night, cold water was used as the cold end to simulate its radiation cooling effect. Based on the radiation cooling temperature change of PV cell at night, the cold water was simulated at 10 °C and 15 °C (Fig. 7). This process could effectively reproduce the actual situation of radiation cooling of PV module at night, so as to evaluate their night cooling performance. It could be seen that when the cold end temperature decreased, the final voltage at both ends of the TEG panel will increase. The cold water had a significant simulation effect on the nighttime radiative cooling of the PV cell, and the temperature difference between the cold and hot ends increased first and then decreased. This was because at night, due to its good heat storage performance, the PCM reserved a large amount of heat absorbed during the daylight and maintained the phase-transition temperature for a period of time. Due to the poor heat storage capacity of the PV cell, the temperature will gradually decrease when there was no irradiation, and the temperature difference between the cold and hot ends will gradually increase.
为了研究光伏系统在夜间的辐射冷却效果，使用冷水作为冷端来模拟其辐射冷却效果。根据光伏电池在夜间的辐射冷却温度变化，分别模拟了 10 °C 和 15 °C 的冷水（图 7）。这一过程可有效再现光伏组件夜间辐射冷却的实际情况，从而评估其夜间冷却性能。可以看出，当冷端温度降低时，TEG 面板两端的最终电压会升高。冷水对光伏电池的夜间辐射冷却有明显的模拟作用，冷热端温差先增大后减小。这是因为在夜间，由于 PCM 具有良好的蓄热性能，它保留了白天吸收的大量热量，并在一段时间内保持了相变温度。由于光伏电池的蓄热能力较差，在没有辐照的情况下，温度会逐渐降低，冷热两端的温差会逐渐增大。
  1. Download: Download high-res image (300KB)
    下载：下载高清图片 (300KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 7. The Schematic diagram of hybrid PV-TEG-PCM system device (a)using a simulated radiative cooling source and the temperature changes of cold end and hot end PCM at night and(b) the TEG panel voltage changes at both ends (c) and the final stable voltage(d).
图 7 混合 PV-TEG-PCM 系统装置示意图PV-TEG-PCM 混合系统装置示意图（a）使用模拟辐射冷源，以及夜间冷端和热端 PCM 的温度变化；（b）两端 TEG 面板电压变化（c）和最终稳定电压（d）。

The maximum voltage at both ends of the TEG panel at night was 0.15 V. The final voltage was kept around 0.15 V. This was because the cold-water temperature was kept constant during the simulation of the cold end, resulting in little change in the temperature difference between the cold and hot ends. The trend of the simulation results was consistent with the actual measured trend, which verified the reliability of the model. The effectiveness of mathematical models in analyzing existing systems depended largely on their ability to accurately replicate observed field conditions[51]. Model calibration of thermal conditions was the process of selecting model parameters to reduce the deviation between the model and the observed parameters[52]. This verification was designed to confirm whether the results of the system in long-term operation were consistent with expectations, and whether they met the assumptions and parameter settings of the model[53]. The experimental and simulation results of each part, and clearly showed the good consistency between the simulation and experimental results, which indicated that the established model was accurate (Fig. 8).
夜间 TEG 面板两端的最大电压为 0.15 V，最终电压保持在 0.15 V 左右，这是因为在模拟冷端时冷水温度保持不变，导致冷端和热端的温差变化不大。模拟结果的趋势与实际测量的趋势一致，这验证了模型的可靠性。数学模型在分析现有系统方面的有效性在很大程度上取决于其准确复制现场观测条件的能力[51]。热条件模型校准是选择模型参数以减少模型与观测参数之间偏差的过程[52]。验证的目的是确认系统长期运行的结果是否与预期一致，是否符合模型的假设和参数设置[53]。各部分的实验结果和模拟结果，清楚地表明模拟结果和实验结果之间具有良好的一致性，这表明所建立的模型是准确的（图 8）。
  1. Download: Download high-res image (377KB)
    下载：下载高清图片 (377KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 8. The comparison of simulated and experimental results.
图 8.模拟结果与实验结果的对比。

5.3. Structure optimization of the PV-TEG-PCM system
5.3.PV-TEG-PCM 系统的结构优化

The phase-transition temperature of PCMs had a great influence on the working temperature of the system. Proper phase-transition temperature could make PCMs play the most effective role in the system. The optimal phase-transition temperature depended on the local climate. Therefore, it was necessary to select the PCMs with an optimal phase-transition temperature [31]. The simulation was carried out for the PCMs layer with 10 mm thickness. The phase-transition temperatures of PCMs were 24 °C, 28 °C and 40 °C, respectively.
PCM 的相变温度对系统的工作温度有很大影响。适当的相变温度能使 PCM 在系统中发挥最大作用。最佳相变温度取决于当地气候。因此，有必要选择具有最佳相变温度的 PCM [31]。模拟针对厚度为 10 毫米的 PCM 层进行。PCM 的相变温度分别为 24 °C、28 °C 和 40 °C。

5.3.1. Optimization of phase-transition temperature
5.3.1.相变温度的优化

During the simulation period, the integration of phase change material (PCM) with phase-transition temperatures of 24 °C, 28 °C, 38 °C, and 40 °C as radiators in the system reduced the average PV cell temperature by 5.78 °C, 11.6 °C, 15.2 °C, and 16.4 °C, respectively, compared to the PV system alone. PCMs absorbed heat and melted into a liquid state, effectively storing heat and lowering the PV cell temperature. Higher phase-transition temperatures of PCMs led to greater reductions in PV cell temperature due to the increased heat absorption required to reach the transition point (Fig. 9a).
在模拟期间，与单独的光伏系统相比，将相变温度分别为 24 °C、28 °C、38 °C 和 40 °C的相变材料（PCM）作为散热器集成到系统中，使光伏电池的平均温度分别降低了 5.78 °C、11.6 °C、15.2 °C 和 16.4 °C。PCM 吸收热量并融化成液态，有效地储存了热量并降低了光伏电池的温度。PCM 的相变温度越高，光伏电池的温度降低幅度越大，这是因为达到相变点所需的吸热量增加了（图 9a）。
  1. Download: Download high-res image (732KB)
    下载：下载高清图片 (732KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 9. The temperature, conversion efficiency and power of PV cell(a) and the temperature difference, conversion efficiency and power of TEG panel during the daylight(b) and night (c)with different phase-transition temperatures.
图 9.不同相变温度下，白天（b）和夜晚（c）光伏电池的温度、转换效率和功率（a），以及 TEG 面板的温差、转换效率和功率。

The efficiency of the PV cell initially decreased with rising solar irradiation, causing surface temperature increases and reduced electron flow rate, thereby lowering conversion efficiency and power generation. As solar irradiance weakened, PV cell temperature gradually decreased, restoring efficiency as electron movement within the cell became more active. Consequently, PV system efficiency was inversely related to PV cell temperature. Throughout the simulations, employing PCMs with a phase-transition temperature of 40 °C maximized PV system efficiency, as more heat was necessary for phase transition, enhancing heat absorption and storage. Moreover, PCMs released stored heat during nighttime, maintaining higher system temperatures and further improving overall power generation efficiency.
最初，光伏电池的效率会随着太阳辐照度的增加而降低，导致表面温度升高和电子流动率降低，从而降低转换效率和发电量。随着太阳辐照减弱，光伏电池温度逐渐降低，电池内部电子运动更加活跃，从而恢复了效率。因此，光伏系统的效率与光伏电池的温度成反比。在整个模拟过程中，采用相变温度为 40 °C 的 PCM 可最大限度地提高光伏系统的效率，因为相变需要更多的热量，从而提高了吸热和储热能力。此外，PCM 还能在夜间释放储存的热量，维持较高的系统温度，进一步提高整体发电效率。
During peak sunshine, the PV system achieved a conversion efficiency of 12.9 %. Integrating PCMs with phase-transition temperatures of 24 °C, 28 °C, 38 °C, and 40 °C increased PV efficiency by 1.15 %, 1.24 %, 1.57 %, and 1.69 %, respectively, compared to the PV system alone. The system consistently exhibited higher overall PV efficiency when PCM with a phase-transition temperature of 40 °C was utilized. Throughout most simulation periods, the PV efficiency of the PV-TEG-PCM system surpassed that of the PV system alone, demonstrating the significant impact of PCM selection on system performance. The electrical output power of the PV cell showed an initial increase followed by a decrease. PCM integration enhanced power generation, with higher phase-transition temperatures allowing PCMs to maintain phase-transition states for longer durations, thereby absorbing more heat and enhancing cooling effects on the PV cell. This capability facilitated increased power generation efficiency in the PV-TEG-PCM system.
在日照高峰期，光伏系统的转换效率为 12.9%。与单独的光伏系统相比，相变温度分别为 24 °C、28 °C、38 °C 和 40 °C 的 PCM 使光伏效率分别提高了 1.15 %、1.24 %、1.57 % 和 1.69 %。当使用相变温度为 40 °C 的 PCM 时，系统始终表现出更高的整体光伏效率。在大多数模拟期间，PV-TEG-PCM 系统的光伏效率都超过了单独的光伏系统，这表明 PCM 的选择对系统性能有重大影响。光伏电池的电力输出功率呈现出先上升后下降的趋势。PCM 集成提高了发电量，较高的相变温度使 PCM 能够在更长的时间内保持相变状态，从而吸收更多的热量，增强对光伏电池的冷却效果。这种能力有助于提高 PV-TEG-PCM 系统的发电效率。
The conversion efficiency of the TEG panel exhibited an initial increase followed by a decrease, influenced by the heat absorption and release dynamics of the system across varying temperature conditions. The peak conversion efficiency of the TEG panel within the hybrid PV-TEG-PCM system varied with different phase-transition temperatures, reaching optimal performance at 38 °C. Specifically, when phase-transition temperatures were set at 24 °C, 28 °C, 38 °C, and 40 °C, the peak TEG conversion efficiencies were 0.23 %, 0.34 %, 0.36 %, and 0.25 %, respectively. While these improvements were relatively modest compared to PV efficiency gains under normal operating conditions, they still significantly impacted the overall thermoelectric conversion performance of the system (Fig. 9b).
受系统在不同温度条件下吸热和放热动态的影响，TEG 面板的转换效率呈现先上升后下降的趋势。PV-TEG-PCM 混合系统中 TEG 面板的峰值转换效率随不同的相变温度而变化，在 38 °C 时达到最佳性能。具体来说，当相变温度分别设定为 24 °C、28 °C、38 °C 和 40 °C 时，TEG 的峰值转换效率分别为 0.23 %、0.34 %、0.36 % 和 0.25 %。虽然与正常工作条件下的光伏效率相比，这些改进相对较小，但仍对系统的整体热电转换性能产生了显著影响（图 9b）。
The observed forward shift in peak TEG conversion efficiency at 40 °C was attributed to the higher heat absorption capacity of the PCM at this phase-transition temperature. This elevated PCM temperature reduced the temperatures of the PV cell and TEG panel, thereby enhancing the temperature gradient necessary for efficient TEG operation. TEG panel conversion efficiency depended on the temperatures of the PV cell, TEG panel, and PCMs, making this forward peak acceptable in the context of system performance optimization. Optimal TEG panel conversion efficiency was achieved at a phase-transition temperature of 38 °C due to the superior performance of PCMs as the hot end, especially during nighttime operations. This phase-transition temperature maximized the temperature difference between the hot and cold ends of the TEG panel, significantly enhancing its effectiveness. Specifically, corresponding peak voltages at the ends of the TEG panel were measured at 0.043 V, 0.065 V, 0.17 V, and 0.14 V for phase-transition temperatures of 24 °C, 28 °C, 38 °C, and 40 °C, respectively (Fig. 9c).
在 40 °C 时观察到的 TEG 转换效率峰值前移，归因于 PCM 在此相变温度下具有更高的吸热能力。PCM 温度的升高降低了光伏电池和 TEG 面板的温度，从而增强了 TEG 高效运行所需的温度梯度。TEG 面板的转换效率取决于光伏电池、TEG 面板和 PCM 的温度，因此在系统性能优化的背景下，可以接受这种前向峰值。由于 PCM 作为热端性能优越，特别是在夜间运行时，因此 TEG 面板的最佳转换效率可在相变温度为 38 °C 时实现。该相位转换温度最大限度地扩大了 TEG 面板冷热端的温差，显著提高了其效率。具体来说，在相变温度为 24 °C、28 °C、38 °C 和 40 °C 时，TEG 面板两端测得的相应峰值电压分别为 0.043 V、0.065 V、0.17 V 和 0.14 V（图 9c）。
However, it was observed that when the phase-transition temperature was raised to 40 °C, the temperature difference decreased compared to 38 °C. This phenomenon was attributed to several factors: Lower phase-transition temperatures (24 °C, 28 °C) resulted in poor heat storage capacity of PCMs, leading to lower nighttime PCM temperatures and reduced temperature differentials across the TEG panel ends, thus lowering nighttime voltages. At higher phase-transition temperatures (40 °C), incomplete PCM melting during daylight limited solar energy absorption and heat storage, resulting in reduced heat release at night and diminished continuous heat supply to the system. Consequently, PCM temperatures and the corresponding temperature gradients across the TEG panel diminished during nighttime operation.
然而，观察发现，当相变温度升至 40 ℃ 时，温差比 38 ℃ 时有所减小。这一现象可归因于几个因素：较低的相变温度（24 °C、28 °C）导致 PCM 储热能力差，从而降低了 PCM 的夜间温度，减少了 TEG 面板两端的温差，从而降低了夜间电压。在较高的相变温度（40 °C）下，白天 PCM 的不完全熔化限制了太阳能的吸收和蓄热，导致夜间热量释放减少，系统的持续热量供应减少。因此，在夜间运行期间，PCM 温度和 TEG 面板上的相应温度梯度都会降低。

5.3.2. Optimization of PCM thickness
5.3.2.PCM 厚度的优化

Based on the influence of phase-transition temperature on the efficiency and power generation of the PV cell and TEG panel discussed in Section 5.3.1, PCMs with a phase-transition temperature of 38 °C were selected to study the impact of their thickness on system performance. The analysis focused on the PV-TEG-PCM system with phase-transition temperatures of 38 °C and examined the effects of phase-transition layer thicknesses ranging from 10 mm to 30 mm. Increasing the thickness of the PCM layer led to an increase in heat capacity and sensible heat storage, prolonging the time required to adjust the temperature. Thicker phase-transition layers resulted in lower overall PV cell temperatures and reduced peak temperatures. At night, the PV cell temperature gradually decreased. It was observed that PV cell efficiency was proportional to the thickness of the phase-transition layer. When the phase-transition thickness was set to 30 mm, the system achieved the highest PV cell efficiency. This was because a thicker phase-transition layer required more heat to achieve phase change, enabling more effective heat absorption and storage, thereby reducing the temperature of the photovoltaic module. Power generation of the PV cell increased with the thickness of the phase-transition layer. When the PCM thickness was 10 mm, 20 mm, and 30 mm, daytime power generation of the PV cell increased by 7.29 %, 8.54 %, and 10.4 %, respectively. This increase occurred because a thicker phase-transition layer required more heat to rise in temperature, allowing the system to absorb more heat from the solar panel and providing better cooling (Fig. 10a).
根据第 5.3.1 节中讨论的相变温度对光伏电池和 TEG 面板的效率和发电量的影响，选择相变温度为 38 °C 的 PCM 来研究其厚度对系统性能的影响。分析的重点是相变温度为 38 °C 的 PV-TEG-PCM 系统，并研究了相变层厚度从 10 毫米到 30 毫米不等的影响。增加 PCM 层的厚度可提高热容量和显热储存，延长调整温度所需的时间。相变层越厚，光伏电池的整体温度越低，峰值温度也越低。夜间，光伏电池温度逐渐降低。据观察，光伏电池的效率与相变层的厚度成正比。当相变层厚度设定为 30 毫米时，系统的光伏电池效率最高。这是因为较厚的相变层需要更多的热量来实现相变，能够更有效地吸收和储存热量，从而降低光伏组件的温度。光伏电池的发电量随着相变层厚度的增加而增加。当 PCM 厚度分别为 10 毫米、20 毫米和 30 毫米时，光伏电池的白天发电量分别增加了 7.29%、8.54% 和 10.4%。出现这种增加的原因是，较厚的相变层需要更多的热量来升温，从而使系统能够从太阳能电池板吸收更多的热量，并提供更好的冷却效果（图 10a）。
  1. Download: Download high-res image (587KB)
    下载：下载高清图片 (587KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 10. The temperature, conversion efficiency and power of PV cell(a) and the temperature difference, conversion efficiency and power of TEG panel during the day(b) and night (c)with different phase-transition layer thicknesses.
图 10.不同相变层厚度下白天（b）和夜间（c）光伏电池的温度、转换效率和功率（a），以及 TEG 面板的温差、转换效率和功率。

With increasing PCM thickness, the temperature difference between the PV cell and PCM gradually diminished. This occurred because the heat storage capacity of the PCMs increased with greater phase-transition layer thickness. Thus, a thicker phase-transition layer maintained the phase-transition temperature state longer, enhancing its cooling capacity for the PV cell. As the PV cell absorbed solar energy, the PCM absorbed and stored part of the heat, with thicker layers storing more heat. Consequently, the cooling effect on the PV cell became more significant, and the time the PCM remained at the phase-transition temperature extended, reducing the temperature difference.
随着 PCM 厚度的增加，光伏电池与 PCM 之间的温差逐渐减小。这是因为 PCM 的储热能力随着相变层厚度的增加而提高。因此，相变层越厚，相变温度状态保持的时间越长，对光伏电池的冷却能力就越强。当光伏电池吸收太阳能时，PCM 吸收并储存了部分热量，越厚的相变层储存的热量越多。因此，光伏电池的冷却效果更加显著，PCM 保持在相变温度的时间延长，温差减小。
When the phase-transition layer thickness was 10 mm, 20 mm, and 30 mm, the peak TEG panel conversion efficiencies were 0.36 %, 0.4 %, and 0.42 %, respectively. This occurred for two reasons. Firstly, as the thickness increased, the PCM absorbed more heat from the TEG panel, reducing the TEG panel's temperature and increasing its efficiency. Secondly, thicker PCM layers required more heat for temperature rise, so the PCM remained below the phase-transition temperature longer. This increased the temperature difference between the TEG panel ends, enhancing conversion efficiency. Consequently, TEG panel power generation increased with PCM layer thickness due to improved heat absorption and cooling (Fig. 10b).
当相变层厚度分别为 10 毫米、20 毫米和 30 毫米时，TEG 面板的峰值转换效率分别为 0.36 %、0.4 % 和 0.42 %。出现这种情况有两个原因。首先，随着厚度的增加，PCM 从 TEG 面板中吸收了更多的热量，从而降低了 TEG 面板的温度，提高了效率。其次，较厚的 PCM 层需要更多的热量来升温，因此 PCM 在相变温度以下停留的时间更长。这增加了 TEG 面板两端的温差，提高了转换效率。因此，随着 PCM 层厚度的增加，TEG 面板的发电量也会增加，这是因为吸热和冷却效果得到了改善（图 10b）。
At night, when the PCM layer thickness was 10 mm, 20 mm, and 30 mm, the peak voltages at both TEG panel ends were 0.16 V, 0.18 V, and 0.2 V, respectively. The nighttime voltage was related to the temperature difference between the TEG panel ends: the greater the temperature difference, the higher the voltage. The time of significant temperature difference between PCM and PV cell at night increased with PCM layer thickness, as thicker PCMs stored more heat during the day, maintaining the phase-transition temperature longer at night. However, the effect of thickness on TEG voltage gradually weakened as it increased, suggesting an optimal thickness for heat absorption (Fig. 10c). Beyond this limit, the PCM could not absorb enough heat for storage, reducing its impact on power generation.
夜间，当 PCM 层厚度分别为 10 毫米、20 毫米和 30 毫米时，TEG 面板两端的峰值电压分别为 0.16 伏、0.18 伏和 0.2 伏。夜间电压与 TEG 面板两端的温差有关：温差越大，电压越高。夜间 PCM 和光伏电池之间出现明显温差的时间随着 PCM 层厚度的增加而增加，因为较厚的 PCM 在白天储存了更多的热量，在夜间保持相变温度的时间更长。然而，厚度对 TEG 电压的影响随着厚度的增加而逐渐减弱，这表明吸热有一个最佳厚度（图 10c）。超过这个极限，PCM 就无法吸收足够的热量进行储存，从而降低了其对发电的影响。

5.4. The electrical, thermal and radiative cooling performance under outdoor conditions
5.4.室外条件下的电气、热和辐射冷却性能

During diurnal hours, the PV cell's strong heat absorption kept its temperature consistently higher than that of the PCM, positioning it as the system's hot end. This significant heat absorption was beneficial during peak sunlight but proved challenging as the irradiation intensity decreased. The PV cell temperature dropped rapidly under reduced sunlight, highlighting its sensitivity to changes in irradiation and resulting in significant temperature fluctuations. In contrast, the PCM demonstrated superior heat storage capacity, exhibiting a much slower rate of temperature reduction. This capability allowed the PCM to effectively store heat and maintain a stable temperature even when irradiation was diminished. The buffering effect provided by the PCM significantly mitigated temperature fluctuations, thereby enhancing the overall system’s efficiency and power generation. The voltage at both ends of the TEG panel initially increased and then decreased, consistent with the simulation results, achieving a maximum voltage of 0.29 V. This performance suggested that, in practical applications, the TEG panel could provide sufficient voltage support for devices such as LED lamps when connected in series, ensuring their normal operation (Fig. 11).
在昼夜时间内，光伏电池强大的吸热能力使其温度始终高于 PCM 温度，成为系统的热端。这种强大的吸热能力在日照最充足的时候是有益的，但随着辐照强度的降低，这种吸热能力就变得具有挑战性。在日照减少的情况下，光伏电池的温度迅速下降，凸显了其对辐照变化的敏感性，并导致温度大幅波动。相比之下，PCM 的储热能力更强，温度降低的速度要慢得多。这种能力使 PCM 能够有效地储存热量，即使在辐照减少时也能保持稳定的温度。PCM 提供的缓冲作用大大缓解了温度波动，从而提高了整个系统的效率和发电量。TEG 面板两端的电压先升高后降低，与模拟结果一致，最高电压为 0.29 V。这一性能表明，在实际应用中，TEG 面板串联后可为 LED 灯等设备提供足够的电压支持，确保其正常工作（图 11）。
  1. Download: Download high-res image (625KB)
    下载：下载高清图片 (625KB)
  2. Download: Download full-size image
    下载：下载全尺寸图片

Fig. 11. The Schematic diagram of hybrid PV-TEG-PCM system device during the daylight(a) and night (b), and the outdoor parameters(c), and the temperature variation of PV cell and PCM(d), and the conversion efficiency(e) and power generation(f) of TEG panel and PV cell(g) during the daylight. and the temperature difference(h) and voltage(i) on both sides of TEG panel.
图 11.PV-TEG-PCM 混合系统装置在白天（a）和夜间（b）的示意图，以及室外参数（c）、PV 电池和 PCM 的温度变化（d）、TEG 面板和 PV 电池在白天的转换效率（e）和发电量（f）、TEG 面板两侧的温差（h）和电压（i）。

The efficiency of the PV cell showed an initial decrease followed by an increase, aligning with the simulation trend. This behavior occurred because the PV cell's temperature rose rapidly during diurnal hours due to strong heat absorption, which reduced its photoelectric conversion efficiency. As the irradiation intensity decreased, the PV cell's poor heat storage capability caused its temperature to drop quickly, leading to a subsequent rise in conversion efficiency. The electrical output power of the PV cell demonstrated an initial increase followed by a decrease. Despite the drop in efficiency as the PV cell temperature increased, the higher irradiation intensity led to greater power generation. Consequently, irradiation intensity emerged as the dominant factor influencing power generation. Overall, the system's ability to harness and store thermal energy, while managing temperature fluctuations through the combined use of PV, TEG, and PCM technologies, resulted in a robust and efficient solution for continuous power generation, suitable for practical applications like solar streetlight nighttime illumination and charging station lighting.
光伏电池的效率出现了先降后升的现象，与模拟趋势一致。出现这种现象的原因是，光伏电池在昼夜温差较大的时段吸热后温度迅速升高，从而降低了光电转换效率。随着辐照强度的降低，光伏电池储热能力差，导致其温度迅速下降，转换效率随之上升。光伏电池的电输出功率显示出先上升后下降的趋势。尽管效率随着光伏电池温度的升高而下降，但较高的辐照强度却带来了更大的发电量。因此，辐照强度成为影响发电量的主要因素。总之，该系统能够利用和储存热能，同时通过结合使用光伏、TEG 和 PCM 技术来管理温度波动，从而为连续发电提供了一个强大而高效的解决方案，适用于太阳能路灯夜间照明和充电站照明等实际应用。
The temperature changes of PV cell and PCM were described during the whole day. It could be seen that due to the strong heat absorption performance of the PV cell, its temperature was always higher than the temperature of the PCM during the daylight, and it always appeared as the hot end. However, as the irradiation intensity decreased, the temperature of the PV cell decreased rapidly. This showed that the PV cell was very sensitive to the change of irradiation intensity, and its temperature fluctuated greatly. In contrast, due to its excellent heat storage performance, the PCM had a significantly slower rate of temperature reduction. Even in the case of reduced irradiation, PCM could effectively store heat and maintain a relatively stable temperature. This characteristic made the PCM played a buffer role in the daylight and reduced the temperature fluctuation, which was of great significance to the efficiency and power generation of the whole system.
对全天光伏电池和 PCM 的温度变化进行了描述。从图中可以看出，由于光伏电池的吸热性能强，其温度在白天始终高于 PCM 的温度，并且始终表现为热端。然而，随着辐照强度的降低，光伏电池的温度迅速下降。这表明光伏电池对辐照强度的变化非常敏感，其温度波动很大。相比之下，由于 PCM 具有出色的储热性能，其温度降低速度明显较慢。即使在辐照度降低的情况下，PCM 也能有效地储存热量并保持相对稳定的温度。这一特性使 PCM 在日光下发挥了缓冲作用，减少了温度波动，对整个系统的效率和发电量具有重要意义。

6. Conclusions 6.结论

This study designed and implemented a PV-TEG-PCM system that integrated photovoltaic (PV) panels, thermoelectric generators (TEG), and phase change material (PCM) to achieve 24-hour continuous power generation. Through modeling validation and experiments, this study obtained the following key results:
本研究设计并实施了一个 PV-TEG-PCM 系统，该系统集成了光伏（PV）面板、热电发电机（TEG）和相变材料（PCM），可实现 24 小时连续发电。通过建模验证和实验，本研究取得了以下主要成果：
(1) Monocrystalline silicon PV cells not only exhibited high heat absorption capacity and photovoltaic conversion efficiency, but also provided effective radiative cooling at night. During diurnal hours, the temperature of the monocrystalline silicon PV cell rose significantly, creating a large temperature difference across the TEG panel. At nocturnal hours, the temperature of the monocrystalline silicon PV cell dropped considerably, maintaining a substantial temperature gradient across the TEG panel. The average conversion efficiencies of polycrystalline silicon, copper indium gallium selenide, monocrystalline silicon, and cadmium telluride were 14.5 %, 15.3 %, 14.9 %, and 16.3 %, respectively.
(1) 单晶硅光伏电池不仅具有较高的吸热能力和光电转换效率，还能在夜间提供有效的辐射冷却。在昼间，单晶硅光伏电池的温度显著升高，在 TEG 面板上形成较大的温差。在夜间，单晶硅光伏电池的温度大幅下降，从而在整个 TEG 面板上保持了较大的温度梯度。多晶硅、铜铟镓硒、单晶硅和碲化镉的平均转换效率分别为 14.5%、15.3%、14.9% 和 16.3%。
(2) Adding PCMs with phase-transition temperatures of 24 °C, 28 °C, 38 °C, and 40 °C to the system as radiators reduced the PV temperature by an average of 5.78 °C, 11.6 °C, 15.2 °C, and 16.4 °C, respectively, compared to the PV system alone. The TEG panel temperature was reduced by 9.31 °C, 12.3 °C, 14.4 °C, and 16.2 °C, respectively. Consequently, PV conversion efficiency increased by 1.15 %, 1.24 %, 1.57 %, and 1.69 %. The TEG panel conversion efficiency peaks for the PV-TEG-PCM system were 0.23 %, 0.34 %, 0.36 %, and 0.25 %, respectively.
(2) 在系统中加入相变温度分别为 24 °C、28 °C、38 °C 和 40 °C 的 PCM 作为散热器，与单独的光伏系统相比，光伏温度平均分别降低了 5.78 °C、11.6 °C、15.2 °C 和 16.4 °C。TEG 面板温度分别降低了 9.31 °C、12.3 °C、14.4 °C 和 16.2 °C。因此，光伏转换效率分别提高了 1.15 %、1.24 %、1.57 % 和 1.69 %。PV-TEG-PCM 系统的 TEG 面板转换效率峰值分别为 0.23 %、0.34 %、0.36 % 和 0.25 %。
(3) With phase-transition layer thicknesses of 10 mm, 20 mm, and 30 mm at a phase-transition temperature of 38 °C, the peak TEG panel conversion efficiencies were 0.36 %, 0.4 %, and 0.42 %, respectively. PV cell power generation during diurnal hours increased by 7.29 %, 8.54 %, and 10.5 %. At nocturnal hours, the peak voltages at both ends of the TEG panel reached 0.16 V, 0.18 V, and 0.2 V, respectively.
(3) 相变层厚度分别为 10 毫米、20 毫米和 30 毫米，相变温度为 38 °C，TEG 面板的峰值转换效率分别为 0.36 %、0.4 % 和 0.42 %。光伏电池在昼间的发电量分别增加了 7.29 %、8.54 % 和 10.5 %。在夜间，TEG 面板两端的峰值电压分别达到 0.16 V、0.18 V 和 0.2 V。
(4) The PV-TEG-PCM hybrid system demonstrated excellent electrical performance. The electrical efficiency of the PV cell reached up to 19.6 %, and the total electrical efficiency of the TEG during the full-day reached 1.2 %, with the overall system efficiency reaching up to 20.8 %. The voltage at both ends of TEG could reach up to 0.29 V during diurnal hours and up to 0.15 V at nocturnal hours, showing significant potential for practical applications, such as solar street lighting at night and charging station lighting, and urban building power supply-lighting composite energy system, especially when combined with boost converters or through series installation.
(4) PV-TEG-PCM 混合系统表现出卓越的电气性能。光伏电池的电效率高达 19.6%，TEG 全天的总电效率高达 1.2%，整个系统的效率高达 20.8%。TEG 两端电压在昼间可达 0.29 V，在夜间可达 0.15 V，在实际应用中，如太阳能夜间路灯照明和充电站照明，以及城市建筑供电-照明复合能源系统，尤其是与升压转换器结合或通过串联安装时，显示出巨大的潜力。
In the future, we aimed to achieve higher voltage output by connecting multiple TEGs in series. This improvement was expected to significantly enhance the overall power generation efficiency of the system and expand its potential for practical applications. We conducted in-depth research on the optimal configuration and operational modes of series-connected TEGs, exploring how to maximize temperature difference utilization and energy conversion efficiency. Additionally, we assessed the performance of this technology in various application scenarios, including but not limited to power supply for remote areas, island energy solutions, and urban smart lighting systems. Through this series of studies, we aimed to achieve new breakthroughs in practicality, cost-effectiveness, and sustainability, contributing to the advancement of renewable energy technologies.
未来，我们的目标是通过串联多个 TEG 来实现更高的电压输出。这一改进有望显著提高系统的整体发电效率，并扩大其实际应用的潜力。我们对串联 TEG 的最佳配置和运行模式进行了深入研究，探索如何最大限度地利用温差和提高能量转换效率。此外，我们还评估了该技术在各种应用场景中的性能，包括但不限于偏远地区供电、岛屿能源解决方案和城市智能照明系统。通过这一系列研究，我们希望在实用性、成本效益和可持续性方面实现新的突破，为推动可再生能源技术的发展做出贡献。

CRediT authorship contribution statement
CRediT 作者贡献声明

Wei Wei: Writing – original draft, Validation, Software, Methodology. Niansi Li: Methodology. Lei Che: Methodology. Yuyan Fan: Data curation. Huifang Liu: Methodology. Jie Ji: Methodology. Bendong Yu: Supervision.
魏巍写作--原稿、验证、软件、方法。李念思：方法论。车磊：方法论方法论范玉燕：数据整理。刘慧芳：方法论。季洁：方法论方法论于本东：指导。

Declaration of competing interest
利益冲突声明

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
作者声明，他们没有任何可能会影响本文所报告工作的已知经济利益或个人关系。

Acknowledgments 致谢

This research is supported by the National Natural Science Foundation of China (No. 52238004 and No. 52278111), Natural Science Foundation of Jiangsu Province (No. BK20221315).
本研究得到国家自然科学基金（编号：52238004和52278111）、江苏省自然科学基金（编号：BK20221315）的资助。

Data availability 数据可用性

The data that has been used is confidential.
所使用的数据是保密的。

References

Cited by (1)

  • Performance optimization of photovoltaic thermoelectric systems based on phase change materials

    2025, Renewable Energy
1
These authors contributed equally to this work and should be considered co-first author.
View Abstract
© 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.