Capacity-operation collaborative optimization of the system integrated with wind power/photovoltaic/concentrating solar power with S-CO₂ Brayton cycle

Abstract

This paper proposes a new power generating system that combines wind power (WP), photovoltaic (PV), trough concentrating solar power (CSP) with a supercritical carbon dioxide (S-CO₂) Brayton power cycle, a thermal energy storage (TES), and an electric heater (EH) subsystem. The wind power/photovoltaic/concentrating solar power (WP−PV−CSP) with the S-CO₂ Brayton cycle system is powered by renewable energy. Then, it constructs a bi-level capacity-operation collaborative optimization model and proposes a non-dominated sorting genetic algorithm-II (NSGA-II) nested linear programming (LP) algorithm to solve this optimization problem, aiming to obtain a set of optimal capacity configurations that balance carbon emissions, economics, and operation scheduling. Afterwards, using Zhangbei area, a place in China which has significant wind and solar energy resources as a practical application case, it utilizes a bi-level optimization model to improve the capacity and annual load scheduling of the system. Finally, it establishes three reference systems to compare the annual operating characteristics of the WP−PV−CSP (S-CO₂) system, highlighting the benefits of adopting the S-CO₂ Brayton cycle and equipping the system with EH. After capacity-operation collaborative optimization, the levelized cost of energy (LCOE) and carbon emissions of the WP−PV−CSP (S-CO₂) system are decreased by 3.43% and 92.13%, respectively, compared to the reference system without optimization.

Graphical abstract

Keywords

wind power/photovoltaic/concentrating solar power (WP−PV−CSP) / supercritical carbon dioxide (S-CO₂) Brayton cycle / capacity-operation collaborative optimization / sensitive analysis

1 Introduction

Traditional thermal power plants severely pollute the environment, and as fossil fuel sources deplete, global warming and the environmental crisis worsen. Renewable energy, as an alternative to fossil energy, is one of the primary destinations for resolving the energy supply problem [1]. Sustainable energy research, which includes solar, wind, and alternative energy sources, is utilized extensively and has the advantages of sustainability, minimal pollution, and excellent economic efficiency [2]. In 2021, global wind power (WP) and photovoltaic (PV) added 93.60 and 175 GW of new grid-connected capacity, respectively, and the total installed capacity reached 837 and 942 GW [3]. Its output power, however, exhibits extreme instability and intermittency due to the natural characteristics of wind and solar energy [4]. The output of a concentrating solar power (CSP) system is continuous and stable, and the use of low-costs, large-capacity thermal energy storage (TES) equipment allows for rapid and thorough output adjustment. Peaking services for WP and PV can be provided, encouraging the use of random and fluctuating power sources [5,6]. Several studies have proposed using electric heater (EH) to convert redundant electrical energy from wind or PV into thermal energy and store it in the TES system. This integration strategy can improve system integration, allow a greater flexibility for scheduling and operation strategies, and significantly reduce wind and PV abandonment [7]. Pilotti et al. [8] revealed a 3.6% development in economic performance when comparing a hybrid system with and without EH integration. Riffelmann et al. [9] evaluated various integration options for a CSP−PV system with integrated thermal storage and discovered that the scenario whereby EH is utilized daily to convert excessive energy from the PV and store it in the TES achieved the best economics. Gedle et al. [10] investigated CSP−PV power plants with and without EH integration and found that EH reduced the electricity cost of the system by 20%. The present paper aims to enhance the grid-connected security of renewable integrated energy systems and address the waste caused by abandoned wind and solar. Therefore, it integrates a power generation system that combines WP, PV, and CSP system equipped with TES and EH. This integrated system is called the wind power/photovoltaic/concentrating solar power (WP−PV−CSP) system.

The conventional steam Rankine cycle and the upcoming supercritical CO₂ (S-CO₂) Brayton cycle are prevalent kinds of power cycle in CSP systems [11]. The S-CO₂ Brayton cycle mainly consists of isentropic compression, isobaric heat absorption, isentropic expansion, and isobaric cooling, similar to the four processes of the Rankine cycle. Nevertheless, the circulating material in the Brayton cycle does not transform phase [12]. Dostal et al. [13] demonstrated that the S-CO₂ Brayton cycle has a substantially higher thermal cycling efficiency than the steam Rankine cycle at medium pressure (8‒20 MPa) and medium temperature (350‒800 °C). Furthermore, the high density and low volumetric flow rate of the S-CO₂ work mass make the S-CO₂ Brayton cycle more compact, which saves costs [14]. Overall, the S-CO₂ Brayton cycle is frequently employed due to its advantages of high efficiency, compactness, adaptability, and low-costs. The attainment of the operating temperature in the S-CO₂ Brayton cycle is readily achievable through the utilization of currently available solar concentrators and heat absorbers. Furthermore, the thermophysical properties of S-CO₂ facilitate the rapid attainment of the operating temperature, thereby minimizing start-up time and heat dissipation. This approach proves to be highly beneficial in managing the rapid fluctuations in grid demand and the inherent instability of solar input. Therefore, it has been proposed that the S-CO₂ Brayton cycle be employed in CSP plants. The design, operation, and thermal performance of S-CO₂ Brayton CSP systems are the main topics of current research. Xiao et al. [15] constructed a system of trough CSP with different layouts of the S-CO₂ Brayton cycle. When the CO₂ Brayton cycle is employed in a CSP system, it has the potential to achieve emission reduction in comparison to the steam Rankine cycle. Yuan et al. [16] studied the S-CO₂ Brayton cycle power generation system with trough solar collectors as the heat source in-depth, analyzing the effects of turbine inlet pressure, exhaust pressure, and inlet temperature on the system cycle to provide a reference for further research into this system. Yang et al. [17] discussed the optimization of key modules in the integrated design of a CSP system with the S-CO₂ Brayton cycle and the influencing factors and control strategies of integrated system under off-design conditions. They also summarized and reviewed several techniques to enhance the performance of the integrated system. Yang et al. [18] analyzed the annual average efficiency of the system at various installed capacities and modeled the thermal and financial performance of the CSP system with the S-CO₂ Brayton cycle.

Based on the benefits of CSP systems incorporating the S-CO₂ Brayton cycle discussed above, as well as the importance of integrating WP, PV, and CSP generation systems for grid security, the present paper focuses specifically on the study of integrated energy systems incorporating the S-CO₂ Brayton cycle [19]. Liu et al. [20] combined WP, PV, the S-CO₂ Brayton power cycle, TES, hydrogen generation and storage, and battery modules to improve the dependability and economics of an integrated energy system in various situations. Even though the system is quite extensive and advanced, the present paper focuses on applying CSP plants for peaking. Yang et al. [21] evaluated the techno-economic performance of a PV-CSP hybrid system with the S-CO₂ Brayton cycle to optimize the solar field (SF) and TES capacity while keeping matching extent and economic costs as optimization objectives. However, since the optimization variables are not stochastic, and the complete system does not address the scheduling optimization of the operating aspect and the consumption problem of abandoned wind and solar, its optimization approach is similar to the single-objective optimization method. There has been little study on the WP−PV−CSP system integrated with the S-CO₂ Brayton cycle, most of which has focused on system performance.

The cornerstone of integrated energy system research has been capacity design and integrated system operation optimization. Liu et al. [22] performed an optimization study on a thermal-storage PV−CSP integrated system and optimized the capacity of the main modules using levelized cost of energy (LCOE) as the optimization objective. However, it was merely a single-objective optimization procedure that did not consider other parameters. Chennaif et al. [23] integrated WP, PV, CSP, TES, and battery modules to identify the perfect integration scheme of the hybrid system with the objectives of LCOE and loss of power supply probability, as well as the size of the WP, PV, and CSP by capacity ratio. However, none of the above research took into account system operating optimization. Tan et al. [24] concluded that the focus at this stage should be on improving operational performance and utilization of existing units rather than increasing total installed capacity, and thus investigated the operating scheduling model of the WP-PV-thermal system to achieve high utilization of distributed energy resources. It can be observed that capacity design is critical for hybrid systems, while operation strategy is also vital for realizing integrated renewable energy systems, which interact with each other. A capacity-operation collaborative optimization approach is essential to simultaneously optimize the operational characteristics and capacity distribution of the integrated energy systems. Pilotti et al. [8] established a mixed-integer linear programming (LP) model to optimize and analyze multiple hybrid CSP−PV plants with LCOE as the objective while recognizing the importance of capacity-operation collaborative optimization. Ding et al. [25] suggested a bi-level approach for optimizing the simultaneous capacity and operation of a multi-source complementary cogeneration system. The upper-level is a multi-objective optimization problem, the lower-level is an LP problem, and the optimal capacity parameters are finally determined to optimize the economic and environmental benefits, which is a novel approach worth investigating.

In conclusion, extensive research has been conducted to investigate integrated energy systems with integrated S-CO₂ Brayton cycle or steam Rankine cycle which primarily focus on performance analysis, capacity optimization, scheduling, and operation optimization. On the one hand, there is a lack of design of the WP−PV−CSP system with the S-CO₂ Brayton cycle, and on the other hand, there is a shortage of capacity-operation collaborative optimization. These two factors contribute to various gaps in the preceding research. Integrating CSP equipped with TES as a peaking plant with WP and PV and the S-CO₂ Brayton cycle as an efficient and cost-effective power cycle in the WP−PV−CSP system will be a new research direction. Meanwhile, the operation and dispatch strategy of the system and the capacity distribution of the system modules should be considered in this renewable energy system.

To address the aforementioned shortcomings, this paper proposes a WP-PV-CSP (S-CO₂) renewable integrated energy system which integrates WP, PV, CSP, TES, and EH subsystems simultaneously, using a trough collector as the heat source and the S-CO₂ Brayton cycle as the thermoelectric conversion module of the CSP system. This paper is innovative because it proposes a novel WP−PV−CSP (S-CO₂) system, which is entirely driven by renewable energy. In addition, it created a bi-level model for capacity-operation collaborative optimization. A non-dominated sorting genetic algorithm-II (NSGA-II) nested LP algorithm is presented to handle this bi-level capacity-operation collaborative optimization problem. Moreover, to filter the collection of Pareto solutions obtained through optimization to determine the ideal compromise solution, it gives a scientific evaluation approach based on the combination of the Analytic Hierarchy Process (AHP)-Entropy weighting method with Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Furthermore, it verifies the feasibility of the proposed system and optimization algorithm by taking Zhangbei, China, as a case study, and conducts a sensitivity analysis to reveal the influence of the capacity configuration of the main modules on economic and environmental performance.

2 System description

2.1 WP−PV−CSP (S-CO₂) system

The WP−PV−CSP (S-CO₂) system studied in this paper is mainly an integrated energy system driven by renewable energy, integrated with WP, PV and CSP with a trough solar collector as the heat source, and the S-CO₂ Brayton cycle as the thermoelectric conversion module. The system diagram is shown in Fig.1. The WP−PV−CSP (S-CO₂) system consists of three forms of energy generation subsystems, WP, PV, and CSP (S-CO₂). The system also includes TES and EH. The WP subsystem works on the principle of converting the kinetic energy of the air into mechanical energy, which is then converted into electrical energy via wind turbine blades and generators. The PV panels are used in the PV subsystem to convert solar energy into electricity. The CSP subsystem comprises the focus solar collector, TES, and thermoelectric conversion. The focus solar collector is a trough SF that first transforms solar energy into thermal energy. The TES employs two tanks for direct thermal storage, employing heat transfer oil as the heat-conducting medium and performing heat exchange with CO₂ in the heat exchanger by actively managing the flow of heat transfer oil when the system requires electricity generation. The thermoelectric conversion section is an S-CO₂ Brayton cycle with CO₂ as the working mass, containing turbines, generators, regenerators, compressors, pre-coolers and heat exchangers. The EH uses the surplus electricity from PV and WP to heat cold oil and store it in a heat storage tank. This operation can realize the complementary coordination and mutual consumption between renewable energy sources, smooth out the output power fluctuation of the system to a certain extent, improve the abandoned wind and solar, sufficiently reduce the amount of abandoned wind and solar, and further increase the flexibility of the system.

2.2 Operation strategy

Designing an operational strategy for this renewable-driven integrated energy system is essential to take full advantage of the rapid peaking capability of the CSP and achieve minimal abandoned wind and solar energy. The capacity parameters of the main components of the system are first given before operation: the number of loops for SF N_Loop, CSP capacity C_CSP, hours of heat storage for TES C_TES, PV capacity C_PV, the number of wind turbines N_WT, EH capacity C_EH. The operational situations of the system can be briefly categorized into the following three cases:

(1)P_{\text{WP,max}}+P_{\text{PV,max}}>P_{\text{load}},

where P_{\text{WP,max}} is the maximum electrical generation of the WP, P_{\text{PV,max}} indicates the maximum electrical generation of the PV, and P_{\text{load}} is the load demand. In situations where the P_{\text{WP,max}} and P_{\text{PV,max}} are sufficient to entirely satisfy the P_{\text{load}}, CSP does not necessitate power generation. The EH can effectively harness and store a portion of abandoned wind and solar energy in the TES system.

(2)P_{\text{WP,max}}+P_{\text{PV,max}}+P_{\text{CSP,max}}>P_{\text{load}}.

As shown in Eq. (2), P_{\text{CSP,max}} indicates the maximum electrical generation of the CSP. The CSP must conduct quick peaking when WP and PV generation are insufficient to fulfill load demand. The actual power generation and abandoned solar of the CSP are computed by merging the EH and TES limitations.

(3)

When the maximum power generation of WP, PV, and CSP falls short of meeting the load demand, procuring additional power from coal-fired power stations is considered. In this situation, there is no abandoned wind or solar energy.

The detailed operation strategy is shown in Fig.2.

3 Model construction and validation

3.1 PV generation model

The power generation of the PV subsystem is calculated as [26]

(4)P_{\text{PV}}=n_{\text{MOD}}\cdot A_{\text{MOD}}\cdot \text{GI}\cdot {\eta }_{\text{PV}}\cdot {\eta }_{\text{INV}}\cdot f_{\text{PV}},

(5){\eta }_{\text{PV}}\text{=}{\eta }_{\text{PV,NOM}}[1+\epsilon (T_{\text{c}} -T_{\text{c,ref}})],

where n_{\text{MOD}} indicates the number of PV panels,A_{\text{MOD}} is the effective area of a single PV panel (m²), \text{GI} is the global irradiance (W/m²), {\eta }_{\text{PV}}, {\eta }_{\text{INV}}, and f_{\text{PV}} represent the actual PV module efficiency, inverter efficiency and derating factor, respectively, {\eta }_{\text{PV,NOM}} refers to the standard efficiency of PV modules, \epsilon, the temperature coefficient; and T_{\text{c}} and T_{\text{c,ref}} show the actual temperature and reference temperature of the PV panel (K), respectively. The calculation formula is shown in Eq. (6) [27]:

(6)T_{\text{c}}=T_{\text{a}}+(T_{\text{NOMC}}-T_{\text{a,NOMC}})\cdot \frac{\text{GI}}{{\text{GI}}_{\text{NOMC}}}\cdot \frac{U_{\text{L,NOMC}}}{U_{\text{L}}}\cdot \left(1-\frac{{\eta }_{\text{PV}}}{\tau \cdot \alpha }\right),

where T_{\text{a}} is the ambient temperature, T_{\text{NOMC}} and T_{\text{a,NOMC}} indicate the temperature of the PV cell and the environment under rated operating conditions, respectively, U_L and U_L,NOMC indicates the heat transfer coefficients at actual and rated operating conditions, respectively. GI_NOMC denotes the global irradiance at the surface of the PV panel under standard operating conditions, and \tau \cdot \alpha stands for transmittance absorbance. The relevant parameters involved in the above equation are shown in Tab.1 [28].

3.2 WP generation model

The wind turbine model used in the paper is WT1500-D82, and the corresponding parameters are listed in Tab.2. The output power of an individual wind turbine can be calculated from the WP curve as [29]

(7)

The power generation of the WP system is shown in Eq. (8):

(8)P_{\text{WP}}=N_{\text{WT}}\cdot p_{\text{WP}},

where v_{\text{cut,in}}, v_{\text{rated}}, and v_{\text{cut,out}} denote the cut-in wind speed, rated wind speed, and cut-out wind speed of the wind turbine, respectively. p_{\text{rated}} is the rated output power of a single wind turbine, N_{\text{WT}} denotes the number of wind turbines in the WP system, and v is generally the wind speed at hub height (m/s). In this paper, the wind speed is measured at 10 m above the ground. Therefore, v can be calculated and derived from Eq. (9).

(9)\frac{v_2}{v_1}={\left(\frac{h_2}{h_1}\right)}^k,

where v_1 is the wind speed at height h_1 above the ground, v_2 is the wind speed at height h_2 above the ground, k indicates the wind shear coefficient, which usually set to 0.14. If the height of the fan hub is h_2, v_2 is v in Eq. (9).

3.3 Model of S-CO₂ Brayton trough CSP system

The model of the S-CO₂ Brayton trough CSP system consists of a trough collector, a TES, and an S-CO₂ Brayton cycle.

3.3.1 Trough collector model

This paper adopts the LS-2 parabolic trough collector which is usually tracked in a north–south axis to ensure a high collector efficiency, and uses heat transfer oil as a carrier of heat to convert solar radiation collected by the collector into heat from the heat transfer oil. The heat absorbed by the trough collector can be expressed as [23]

(10)Q_{\text{abs}}=\text{DNI}\cdot A_{\text{SF}}\cdot {\eta }_{\text{SF}},

(11){\eta }_{\text{SF}}=K_{\text{IAM}}\cdot {\eta }_{\text{shadow}}\cdot {\eta }_{\text{endloss}}\cdot {\eta }_{\text{field}},

where \text{DNI} indicates the direct normal irradiance (W/m²), A_{\text{SF}} is the overall area of SF, {\eta }_{\text{SF}} represents SF efficiency, K_{\text{IAM}} is the incidence angle correction factor, and {\eta }_{\text{shadow}}, {\eta }_{\text{endloss}}, and {\eta }_{\text{field}} denote shadow loss, end loss, and optical efficiency, respectively.

The useful energy output of a trough SF, Q_{\text{SF}} is obtained by using the heat absorbed by the collector minus its own heat losses and piping losses, which is calculated as shown in Eq. (12).

(12)Q_{\text{SF}}=Q_{\text{abs}}-Q_{\text{heat,loss}}-Q_{\text{pipe,loss}}=Q_{\text{abs}}\cdot {\eta }_{\text{heat}}\cdot {\eta }_{\text{pipe}},

where Q_{\text{heat,loss}} and Q_{\text{pipe,loss}} indicate the heat loss from the collector and the loss from the pipeline transport process, respectively, which can also be expressed in terms of heat loss rate {\eta }_{\text{heat}} and pipeline loss rate {\eta }_{\text{pipe}}.

(13)Q_{\text{heat,loss}}=0.03642 \cdot T_{\text{SF}}+ 8.21\times {10}^{-9}\cdot T_{\text{SF}},

(14)Q_{\text{pipe,loss}}=0.01693 \cdot \mathrm{\Delta }T -0.0001683\cdot \mathrm{\Delta }{T}^2+ 6.78\times {10}^{-7}\cdot \mathrm{\Delta }{T}^3.

The collector with conventional coating was chosen. In Eqs. (13) and (14), T_{\text{SF}} is the temperature of the receiver, and \mathrm{\Delta }T is the difference between the average temperature inside the collector and the ambient temperature (K).

3.3.2 TES system model

The system uses heat transfer oil as the heat transfer medium, and the useful energy Q_{\text{SF}} output from the SF enters the hot tank (HT) with heat transfer oil as the carrier for storage and preparation for subsequent storage and heat discharge [30]. The charge and discharge processes at the moment t+1 are shown as

(15)Q_{\text{HT}}^{t+1}=Q_{\text{HT}}^t+Q_{\text{SF}}^t\cdot {\eta }_{\text{c}}\cdot \mathrm{\Delta }t,

(16)Q_{\text{HT}}^{t+1}=Q_{\text{HT}}^t+\frac{Q_{\text{HE}}^t}{{\eta }_{\text{d}}}\cdot \mathrm{\Delta }t,

where Q_{\text{SF}}^t is the heat from the SF to the HT at moment t, Q_{\text{HE}}^t is the heat supplied to the heater of the thermoelectric conversion module at moment t, and {\eta }_{\text{c}} and {\eta }_{\text{d}} respectively denote the charge and discharge efficiency of the HT, set at 98% [31].

The power of EH, P_{\text{EH}} comes from the abandoned wind and solar energy. The thermal energy input from EH to HT is expressed as

(17)Q_{\text{EH − HT}}= P_{\text{EH}}\cdot {\eta }_{\text{EH}}\cdot {\eta }_{\text{c}} .

The average efficiency of EH electric rotary heat {\eta }_{\text{EH}} is commonly established at around 95% [32].

3.3.3 Modeling of S-CO₂ Brayton cycle with reheat

This paper ensures that the entire thermoelectric conversion section operates at design conditions by actively controlling the flow of heat transfer oil so that the inlet and outlet parameters of the compressor and turbine remain constant. The corresponding parameters for the design conditions are shown in Tab.3 and Tab.4 [33,34], assuming that the characteristics of each component are consistent under the design conditions. The output power of the generator in the S-CO₂ Brayton cycle is [35]

(18)P_{\text{CSP}}=W_{\text{T}} \cdot {\eta }_{\text{mg}}- W_{\text{C}} \cdot {\eta }_{\text{motor}},

(19)W_{\text{T}} =m_{\text{C}{\text{O}}_2}\cdot (h_{\text{T,in}}-h_{\text{T,out}}),

(20)W_{\text{C}} =m_{\text{C}{\text{O}}_2}\cdot (h_{\text{C,out}}-h_{\text{C,in}}),

where W_{\text{T}} and W_{\text{C}} are the amount of work done by the turbine and compressor, respectively (MW); {\eta }_{\text{mg}} and {\eta }_{\text{motor}} denote the efficiency of the generator and the motor, respectively; m_{\text{C}{\text{O}}_2} indicates the mass flow rate of CO₂ during the cycle (kg/s); h_{\text{T,in}} and h_{\text{T,out}} are the inlet and outlet enthalpy of the turbine; h_{\text{C,in}} and h_{\text{C,out}} are the inlet and outlet enthalpy of the compressor (M/kg). In this paper, the enthalpy values were obtained mainly by calling the REFPROP physical properties library and using the parameters calculated at the design working conditions.

3.4 Model validation

Since the models of WP, PV, and the S-CO₂ Brayton cycle have been constructed with the certainty based on design parameters and operated under design conditions, they have universal characteristics. The utilization of the trough solar collector model may result in variations in its primary results based on the fluctuation of specific input parameters. Therefore, it is imperative to validate the trough solar collector within the WP−PV−CSP system examined in this paper to guarantee the precision of the model.

With the model constructed above, the validation parameter is the collector efficiency (ratio of useful energy Q_SF output from the trough SF to the solar heat input) of the collector. Using the experimental data of Liu et al. [36] as a reference, the DNI and inlet temperature T_{\text{in}} of different intensities are selected for verification, and the results obtained are shown in Tab.5. It can be seen that the collector efficiency of the collector model built in this paper is the same as that of Liu et al. [36], and the maximum error is only 2.08%, which is within an acceptable range. Therefore, the accuracy of the collector model can be verified.

4 Optimization methodology model

In this paper, bi-level optimization outperforms typical single-level optimization. First, bi-level optimization is a type of hierarchical management in which the lower-level optimization obeys the upper-level optimization but has a relative autonomy, with each level controlling a portion of the decision variables to optimize their respective objectives. Second, the objective functions of the two levels are distinct and frequently in conflict. Finally, when making judgments, the upper-level takes precedence, and the lower-level cannot modify the decisions of the upper-level while optimizing, but it can be a constraint on the decisions of the upper-level.

Therefore, a bi-level capacity-operation collaborative optimization model is developed in this paper, where the LCOE and carbon emissions are chosen as the objective functions in the upper-level, and the capacity allocation is used as the decision variable. In the lower-level, the available generation of each module is used as the decision variable, and the maximum utilization of renewable energy is the objective to optimize the operation and scheduling of the system to maximize the balance between supply and demand. The bi-level capacity-operation collaborative optimization model is formulated as

\begin{array}{}\text{(21a)}& \underset{R_{\text{i}}}{min}\left\{F_1\left(R_{\text{i}},f\right),F_2(R_{\text{i}},f)\right\},\end{array}

\begin{array}{}\text{(21b)}& \underset{H_{\text{i}}^t}{max}f\left(P_{\text{i}},H_{\text{i}}^t\right),\end{array}

\begin{array}{}\text{(21c)}& \text{s.t.}{g}_0\left(P_{\text{i}},H_{\text{i}}^t\right)⩽0,\end{array}

which clearly expresses the upper and lower-level optimization problems for bi-level capacity-operation collaborative optimization. The upper-level model (Eq. (21a)) requires that both objective functions F_1 and F_2 are minimized, where R_i is the decision variable and i is the number of variables, in this study a total of six decision variables are set up, all representing the capacity configuration of the main components of the WP-PV-CSP system, which are: N_Loop, C_CSP, C_TES, C_PV, N_WT and C_EH. And f is the objective function of the lower-level. The lower-level model (Eqs. (21b) and (21c)) aims to find the best operational scheduling solution to obtain the maximum annual benefit, and the renewable energy utilization rate is selected as the lower-level objective to achieve the maximum value of this objective function, where P_{\text{i}} is the lower-level decision variable, which in this paper is the available generation of each module before optimization. H_{\text{i}}^t represents the actual power output of the main components, and g₀ is the relevant constraints on power output and balance in the lower-level.

This paper aims to determine the annual hourly power output schedule for the WP−PV−CSP system, considering the optimization of various system components. The system is addressed using a linear planning (LP) model to facilitate the calculation process.

4.1 Objective function

4.1.1 Lower-level objective

The objective function of the lower-level optimization model focuses on renewable energy utilization. Its purpose is to minimize the amount of abandoned wind and solar energy by selecting an appropriate dispatching strategy and maximizing the use of renewable energy for power generation or storage.

4.1.2 Upper-level objective

The upper-level model can be characterized as a multi-objective optimization problem. To achieve an optimal balance between system economy and environment, the LCOE and carbon emissions are selected as the objective functions in the upper-level.

1) LCOE

The LCOE is a metric used to assess the overall cost of generating electricity throughout the entire lifespan of an electricity system [37]. The LCOE of the WP−PV−CSP (S-CO₂) system is expressed as

(22)\begin{array}{r}\\ \text{LCOE}={\displaystyle \frac{\text{IC}+{\displaystyle \sum _{n=1}^N{\displaystyle \frac{C_{\text{OM}}\left(n\right)}{{\left(1+i\right)}^n}}}}{{\displaystyle \sum _{n=1}^N{\displaystyle \frac{P_{\text{WP}}\left(n\right)\cdot {(1-d_{\text{WP}})}^{n-1}+P_{\text{PV}}\left(n\right)\cdot {(1-d_{\text{PV}})}^{n-1}+P_{\text{CSP}}\left(n\right)\cdot {(1-d_{\text{CSP}})}^{n-1}}{{\left(1+i\right)}^n}}}}},\end{array}

where \text{IC} denotes the initial investment costs, C_{\text{OM}} is the annual operation and maintenance costs, i indicates the discount rate, which is set to 0.05, n represents the operating cycle, N is the lifetime or expected life of the system, which is set to 25 years in this paper, and d shows the annual degradation factor of each subsystem.

2) CO₂ emission

This paper incorporates various renewable energy sources for the purpose of complementary power generation, thereby promoting environmental sustainability. However, it is important to note that there exists a discrepancy between the current power generation capacity and the demand from users. If it is considered to purchase insufficient power from thermal power plants, this part of carbon emissions remains incorporated within the research system of this paper. Therefore, the optimization objective must prioritize minimizing carbon emissions associated with purchased power. The carbon emissions E_{\text{C}{\text{O}}_{\text{2}}} are calculated as [32]

(23)E_{\text{C}{\text{O}}_{\text{2}}}=B_{\text{s,sum}}\cdot c_{\text{ef}},

(24)B_{\text{s,sum}}=P_{\text{purchase}}\cdot b_{\text{s}} ,

where B_{\text{s,sum}} is the annual standard coal consumption (t), c_{\text{ef}} then represents the carbon emissions factor, which is taken as 2.78 in this paper, and b_s is the standard coal consumption per kWh (g), which is set to 310 g in this paper [32]. P_purchase is the amount of electricity to be purchased by the system, which can be calculated by the operating strategy in Fig. 2.

4.2 Lower-level constraint

1) Power constraint

The power constraints of the WP−PV−CSP (S-CO₂) system are primarily engineered to attain an equilibrium between the supply and demand. The actual generation of each module must not exceed its maximum power generation P_{\text{max}}, and the sum of the actual generation and purchased power P_{\text{purchase}}^t of all modules must equal the customer load P_{\text{load}}^t.

(25)P_{\text{WP}}^t+P_{\text{PV}}^t+P_{\text{CSP}}^t\text{+}{P}_{\text{purchase}}^t=P_{\text{load}}^t ,

(26)\{\begin{array}{c}0⩽P_{\text{WP}}^t⩽N_{\text{WT}}\cdot p_{\text{WP}},\\ 0⩽P_{\text{PV}}^t⩽C_{\text{PV}},\\ 0⩽P_{\text{CSP}}^t⩽C_{\text{CSP}},\\ P_{\text{purchase}}^t⩾0,\end{array}

where C_{\text{PV}} and C_{\text{CSP}} indicate the installed capacity of PV and CSP, respectively.

2) TES system constraint

The heat of the HT is the sum of the initial HT heat Q_{\text{HT}}^t and the heat provided by the EH Q_{\text{EH}}^t and SF Q_{\text{SF}}^t minus the heat consumed by the thermoelectric conversion module.

(27)Q_{\text{HT}}^{t+1}=Q_{\text{HT}}^t+Q_{\text{EH}}^t+Q_{\text{SF}}^t\cdot {\eta }_{\text{c}} \cdot \mathrm{\Delta }t -\frac{P_{\text{CSP}}^t}{{\eta }_{\text{e,CSP}}\cdot {\eta }_{\text{d}}}\cdot \mathrm{\Delta } t,

(28)\{\begin{array}{c}0⩽Q_{\text{HT}}^t⩽Q_{max,\mathrm{H}\mathrm{T}},\\ 0⩽Q_{\text{HT}}^{t+1}⩽Q_{max,\mathrm{H}\mathrm{T}},\\ 0⩽P_{\text{CSP}}^t⩽C_{\text{CSP}},\\ Q_{\text{SF}}^t⩾0,\\ Q_{\text{EH}}^t⩾0,\end{array}

where {\eta }_{\text{e,CSP}} indicates the efficiency of the thermoelectric conversion module of the CSP system. Q_{max\text{,HT}} is the maximum heat storage capacity of the HT, which is derived from the hours of heat storage for TES C_{\text{TES}}.

3) Abandoned wind and solar energy constraint

(29)\{\begin{array}{l}{Q}_{\text{SF}}^t=Q_{\text{HT}}^t+Q_{\text{ab,SF}}^t,\\ Q_{\text{ab,SF}}^t⩾0,\end{array}

(30)\{\begin{array}{l}{P}_{\text{WP}}^t+P_{\text{ab,WP}}^t=P_{\text{WP,max}}^t,\\ P_{\text{WP}}^t⩾0,\\ P_{\text{ab,WP}}^t⩾0,\end{array}

(31)\{\begin{array}{l}{P}_{\text{PV}}^t+P_{\text{ab,PV}}^t=P_{\text{PV}\text{,}\text{max}}^t,\\ P_{\text{PV}}^t⩾0,\\ P_{\text{ab,PV}}^t⩾0,\end{array}

where Q_{\text{ab,SF}}^t denotes the excess solar energy absorbed by the SF, i.e., the solar energy abandoned by the CSP subsystem, P_{\text{ab,WP}}^t and P_{\text{ab,PV}}^t are the electricity power abandoned by WP and PV, respectively.

4) EH constraint

On the one hand, the constraints on EH are that the power going into EH P_{\text{EH}}^t which cannot exceed the power from abandoned wind and solar, and on the other hand, the capacity constraints C_{\text{EH}} are fundamental.

(32)\{\begin{array}{c}{P}_{\text{EH}}^t⩽C_{\text{EH}},\\ 0⩽P_{\text{EH}}^t⩽P_{\text{ab,PV}}^t+P_{\text{ab,WP}}^t.\end{array}

4.3 Solving algorithm

The bi-level capacity-operation collaborative optimization problem for the WP−PV−CSP (S-CO₂) system is a multi-constrained, multi-objective optimization problem, in which the upper-level is a multi-objective nonlinear optimization problem, and the objectives are conflicting with each other. This paper introduces the NSGA-II algorithm, considering the optimization objectives, convergence, and computational efficiency. The NSGA-II algorithm incorporates non-dominated sorting, crowding, and elitist strategies to enhance the efficiency and speed of solving multi-objective optimization problems, and surpassing alternative optimization algorithms [38]. Therefore, the NSGA-II algorithm is used to solve the problem, and the lower-level is a simple LP problem, mainly to solve the extreme value of the linear objective function under linear constraints. This paper uses the algorithm of NSGA-II nested with LP to calculate the Pareto optimal solution of this bi-level optimization problem, and all solution sets finally constitute the Pareto optimal frontier. The relevant models of the algorithm are implemented in MATLAB, and the specific solution process is shown in Fig.3.

Step 1, the basic parameters and initialized populations required for the input algorithm are given. To ensure the convergence of the algorithm, the population size N is set to 200, and the number of iterations \text{Ge}{\text{n}}_{max} is 60 generations. A total of six decision variables are used R_{i,j} (i=1 ,2,.. .,N\text{;}j\text{=}1 ,2,.. .,\text{6}), and for \text{Gen = 1}, a set of random numbers is generated as the initial population R_{i,j} within the boundary conditions of the decision variables. By adjusting the boundary condition of the decision variables to present the best convergence and stability of the Pareto curve, the finalized boundary ranges are shown in Tab.6. N_{\text{Loop}} represents the number of loops of the solar field in the CSP system, and this parameter has a direct connection with the SF area and CSP capacity C_{\text{CSP}}.

Step 2, the population R_{i,j} is used as the input parameter of the lower-level problem, and the LCOE and CO₂ emissions corresponding to each group of individuals are calculated using the LP algorithm by combining the models constructed for each energy system and major component, and the output to the upper-level as the objective function.

Step 3, the non-dominated sorting is conducted on the initial population and the crowding distance of the individuals is calculated.

Step 4, whether the population size equals or exceeds N is determined. If it does not exceed, a child population is generated with a population size 2/N by the selection, crossover, mutation and other operations, combining the parent and child individuals to become a new population, and enter into the lower-level to continue the process of Step 2. Otherwise, a set of better parent populations are selected for the following calculation based on the calculated non-dominated sorting and crowding distance, and the number of evolutionary generations is made to \text{Gen = 1}.

Step 5, if \text{Gen gt Ge}{\text{n}}_{\text{max}}, the algorithm ends and the Pareto front solution is obtained. Otherwise, continue with the next crossover, variation.

Since Ding et al. [25] also used the NSGA-II algorithm model to optimize the multi-source complementary cogeneration system, this paper verifies the accuracy of the algorithmic model using their optimization results. The optimization model employs the net present value (NPV) and CO₂ emissions as optimization objectives to optimize the three variables and ultimately determine the optimal allocation of capacity. The population size and the number of generations are set at 100 and 40, respectively, and the validation results are shown in Fig.4. The algorithmic model constructed in this paper also achieves convergent and stable Pareto frontier curves with a maximum error of 0.95%. This error level falls within an acceptable range, allowing for the validation of the accuracy of the model.

4.4 Compromise solution selection method

Each solution in the Pareto solution set obtained through optimization corresponds to an optimal configuration of capacity and operating characteristics. In contrast to single-objective solution problems, multi-objective optimization presents a more complex problem due to the involvement of multiple factors. Consequently, selecting an optimal compromise solution becomes crucial to this process. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a commonly used method for evaluating and ranking solutions, distinguishing between superior and inferior solutions. This process needs to be considered with the weights occupied by each objective as constraints. The determination of the weights of evaluation indicators must be scientific and reasonable. Subjective assignment methods such as the Analytic Hierarchy Process (AHP), which often make decisions based on subjective experience, can ensure control effects, but the results obtained are highly subjective and arbitrary. In objective weighting methods, such as entropy weighting, the weight of an indicator is determined mainly according to the amount of information it provides in this multi-objective optimization problem, but it has a strong objectivity.

Based on the above disadvantages, this paper integrates the combined the AHP-Entropy weighting method with TOPSIS to select the Pareto optimal compromise solution to make the evaluation process and the results more scientific and reasonable, and constructs the model reference [39–41].

5 Results and discussion

5.1 Case description

Zhangbei (41.2°N, 114.7°E), China, has significant wind and solar energy resources. Therefore, this paper focuses on the WP−PV−CSP (S-CO₂) system, and applies a bi-level capacity-operation collaborative optimization model with meteorological data from the Zhangbei area as the operating conditions. The actual meteorological data for the area are shown in Fig.5, which are provided by the Energy Plus database [42].

The corresponding operating parameters of the system have been listed in Section 3, and the economical parameters of the leading equipment of the system are given in Tab.7 [18, 43–45].

5.2 Pareto front

Using the relevant meteorological data and economic parameters in the case description, the bi-level capacity-operation collaborative optimization problem proposed in the paper uses the NSGA-II algorithm in combination with LP. In addition, the obtained Pareto optimal solution set constitutes the Pareto front, as shown in Fig.6. The Pareto optimal solution set is presented in Tab.8.

The leftmost point of the Pareto front A (0.1360, 2.6299) corresponds to the optimal value of LCOE, and the corresponding capacity configuration is the first row of Tab.8. The number of loop N_{\text{Loop}} and wind turbine N_{\text{WT}} are at the set minimum boundary. Since the investment costs of SF is enormous, in order to make the LCOE at the optimal value, it is necessary to choose the smallest number of loops for SF first. The WP and CSP can complement PV generation at night, and the presence of WP is eliminated from the optimization results in order to minimize LCOE.

The rightmost point B (0.5259, 0.0021) corresponds to the capacity in the last row of Tab.8. It can be seen that all the capacities are within the boundaries, indicating that there exists a set of capacity configurations that make the minimum carbon emissions within the set optimization range.

5.3 Selection of optimal compromise solution

As shown in Tab.9, this paper investigates the optimal compromise solutions obtained from the comprehensive evaluation method of the AHP-Entropy weighting method with TOPSIS. Since the AHP selects the weights by subjective experience, this paper lists all possible topologies in order to analyze the optimal compromise solutions obtained.

From Tab.9, it can be seen that the CO₂ emissions are reduced by 94.85% when LCOE is increased by 59.86%. Therefore, this paper selects the system capacity configuration solution that minimizes carbon emissions as the optimal compromise solution, the weight of LCOE is 8%, the value is 0.4196 $/kWh ($ denoted US dollar), the weight of carbon emissions is 92% with the value of 370 t/a. The area of each loop of the solar field is about 1413 m², and the individual wind turbines are rated at 1.675 MW. Therefore, the SF area, CSP capacity, TES capacity, EH capacity, PV capacity and WP capacity are 6.44 × 10⁵ m², 167 MW, 7 h, 45 MW, 72 MW and 31.825 MW, respectively.

5.4 Annual operating characteristic analysis

As shown in Fig.7, the annual operating characteristics of the optimal capacity configuration optimized in this paper are analyzed to obtain the daily production of output, purchased, and abandoned power of the WP−PV−CSP (S-CO₂) system.

In addition, three reference systems are established. Compared to the WP−PV−CSP (S-CO₂) system, Reference system 1 eliminates the EH, Reference system 2 replaces the S-CO₂ Brayton cycle with the conventional steam Rankine cycle, and Reference system 3 is the unoptimized one. Tab.10 compares the system studied with the reference system regarding the economy, annual operating output, and CO₂ emissions.

The comparison of the WP−PV−CSP (S-CO₂) system with Reference system 1 indicates that the P_{\text{ab}} of the WP−PV−CSP (S-CO₂) system experiences a reduction of 52%. EH converts a portion of the abandoned power into heat in TES, resulting in an increase in P_{\text{CSP}} one. This reduced the LCOE and carbon emissions of the WP−PV−CSP (S-CO₂) system by 2.85% and 76.33%, respectively. The comparison of the WP−PV−CSP (S-CO₂) system with Reference system 2 demonstrates that the WP−PV−CSP (S-CO₂) system has an increase in P_{\text{CSP}}. The S-CO₂ Brayton cycle highlights superior cycle efficiency and economic performance, as revealed by a 4.66% reduction in the LCOE and a decrease of 31.98% in carbon emissions. The comparison of the WP−PV−CSP (S-CO₂) system with Reference system 3 suggests that the P_{\text{ab}} of the optimized system is reduced by 46% and the LCOE and carbon emissions are reduced by 3.43% and 92.13%, respectively.

In conclusion, the WP−PV−CSP (S-CO₂) system demonstrates significant advantages across various domains. The collaborative optimization of the capacity and operation of the system produces positive results regarding LCOE and CO₂ emissions.

5.5 Sensitivity analysis

To further investigate the economy of the WP−PV−CSP (S-CO₂) system and the variation pattern of CO₂ emissions at different capacity configurations, this paper analyzes the effects of the number of loops for SF N_{\text{Loop}}, CSP capacity C_{\text{CSP}}, TES capacity C_{\text{TES}}, PV capacity C_{\text{PV}}, the number of WT N_{\text{WT}}, and EH capacity C_{\text{EH}} on LCOE and carbon emissions, respectively.

The effect of N_{\text{Loop}} on LCOE and CO₂ emissions is shown in Fig.8. The analysis reveals that the LCOE exhibits a pattern of initial decline followed by an increase, reaching its lowest point at 291 loops. The reason for this is that when N_{\text{Loop}} increases, the solar heat gathered by the collector field for utilization by the TES and the thermoelectric conversion module increases dramatically. Currently, C_TES and C_CSP are fixed, and the increase in system costs is solely the SF costs. The CSP power generation P_{\text{CSP}} is expanding rapidly at the moment. The total system costs increase by 0.06% for each increase in N_{\text{Loop}}, and the power generation increases by 0.15%, resulting in a decrease in LCOE in the initial stage. However, because the C_{\text{TES}} and C_{\text{CSP}} are fixed, when N_{\text{Loop}} continues to increase, the generation capacity is constrained not to improve continuously. Therefore, the LCOE has an inflexion point and begins to increase. At 567 loops, the system LCOE is equal to the LCOE corresponding to the smallest number of loops for SF. Therefore, selecting the number of loops within this interval is preferable. Furthermore, N_{\text{Loop}} has an impact on P_{\text{CSP}}, which has a consequential impact on carbon emissions. It can be seen that the CO₂ emissions decrease continuously with the increase of N_{\text{Loop}} and finally level off. The reason for this is that, as N_{\text{Loop}} increases, the thermal power output of the collector increases, causing an increase in P_{\text{CSP}}. Therefore, the CO₂ emissions are reduced during the initial change phase. However, again constrained by C_TES, continuing to increase the heat output has less and less effect on the power generation. Therefore, the CO₂ emissions are at a smaller value and tend to stabilize.

As shown in Fig.9(a), the system LCOE first decreases and then increases as the C_{\text{CSP}} increases. From the components of the CSP system, it is known that the CSP system consists of SF, TES, EH, and thermoelectric converter modules. Therefore, increasing the C_{\text{CSP}} is equivalent to increasing the rated heat that the SF can supply. On the one hand, the heat rating affects the maximum heat flow of the HT. On the other hand, it affects the capacity of the thermoelectric converter module, enabling a larger quantity of heat to be converted into electrical. The increase in P_{\text{CSP}} reveals a substantial impact when there is an increase in the concentration of the initial stage. Based on the calculations, it can be seen that in the range of 0‒70 MW, for every 1 MW increase in C_{\text{CSP}}, the power generation of the WP−PV−CSP (S-CO₂) system increases by 3.25%, and the total costs increase by 0.85%. Therefore, within the 0‒70 MW range, the LCOE decreases when C_CSP increases. Due to the limits of N_Loop, C_{\text{TES}}, N_{\text{WT}}, and C_{\text{PV}}, the heat entering the thermoelectric converter module does not increase as C_{\text{CSP}} increases. There is even a tendency to decline when the heat in the storage tank is expended. Currently, the electricity generation of the system is decreasing, but the costs increase as C_{\text{CSP}} increases. As a result, LCOE is rising in the 70‒200 MW range. When C_{\text{CSP}} increases to 170 MW, the LCOE is identical to the value observed at 0 MW. Therefore, the optimal range for capacity lies between 0 and 170 MW. The decrease in CO₂ emissions appears initially, followed by a stabilization as C_{\text{CSP}} increases. This can be attributed primarily to the constraints imposed by the fixed N_Loop and C_{\text{TES}}, which prevent the continuous growth of P_{\text{CSP}}.

The effect of C_{\text{PV}} on LCOE and CO₂ emissions is shown in Fig.9(b), it can be seen that the LCOE also decreases first and then increases. The PV power generation P_{\text{PV}} increases when additional C_{\text{PV}} is installed during the initial phase, which is necessary to supplement CSP generation to meet the growing demand load. There is a substantial increase in total power generation, whereas the costs associated with PV remain relatively modest. According to calculations, there is a positive correlation between the increase in C_{\text{PV}} by 1 MW, a corresponding generation increase of 1.02% in the WP−PV−CSP (S-CO₂) system, and an increase in the total costs of the system by 0.24%. Consequently, during the initial stage, the LCOE decreases. Nevertheless, because of the constant user demand, the growth of C_{\text{PV}} leads to a corresponding increase in P_{\text{PV}} while simultaneously causing a decline in P_{\text{CSP}}. Currently, there is a decline in the rising rate of the total system power generation, while the costs of PV continue to rise, resulting in an overall increase in the LCOE. Due to the increase in C_{\text{PV}}, the carbon emissions decreases, but due to the constraint of user demand, the CO₂ emissions finally tend to stabilize.

From the variation in Fig.10, it can conclude that the LCOE obtains its minimum value at a C_TES of 3 h. During the initial phase, the expansion of C_{\text{TES}} enables the TES to store a larger quantity of heat for the thermoelectric conversion module. Consequently, P_{\text{CSP}} experiences an enormous spike in this early stage. Moreover, the rise in TES costs remains relatively modest, resulting in a decrease in the LCOE. However, because N_Loop and C_{\text{CSP}} have been determined, N_Loop constraint limits the heat entering the HT, while the C_{\text{CSP}} constraint limits the heat that the thermoelectric conversion module may use. Therefore, P_{\text{CSP}} increases slowly, and with the TES costs rising, the LCOE reaches an inflection point and begins to rise. The difference is that the LCOE does not change again to the same value at the TES capacity of 0 h, indicating that adding a thermal storage system for this renewable energy system is advantageous. The decline in carbon emissions initially occurs before reaching a state of stability, which can be related to the impact of P_{\text{CSP}}. This factor leads to continuous decreases in CO₂ emissions.

Fig.11 illustrates an upward trend between the number of turbines N_{\text{WT}} and LCOE, with no discernible inflection point. This suggests that while P_{\text{WP}} experiences growth, it is accompanied by a proportional cost increase. The increase in P_{\text{WP}} leads to a decrease in carbon emissions. However, when comparing it to Fig.9(b), it becomes evident that the degree of its variation is merely 1% of the decrease in CO₂ emissions resulting from the change of C_{\text{PV}}. On the one hand, it should be mentioned that the maximum capacity of WP is only half that of PV. On the other hand, WP mainly serves as a supplementary source of power generation at night, while it also uses excess WP to facilitate heat storage in EH systems during the daytime to meet the user demand. Consequently, the overall impact of this system on carbon emissions is relatively minimal.

As the increase of C_{\text{EH}} can more fully utilize the abandoned wind and solar energy and increase the heat storage, it will increase the P_{\text{CSP}}. As seen from Fig.12, the LCOE decreases slightly with the increase of C_{\text{EH}}, but the overall remains basically the same, because the costs of EH increase almost in the same proportion as the P_{\text{CSP}}. The change of P_CSP makes the carbon emission decrease, but it is constrained by the C_TES and C_CSP, the CO₂ emissions will not keep decreasing and will eventually stabilize. However, since EH is an electric-to-heat device, effectively transforming high-quality electrical power into low-quality thermal energy, this approach is not recommended when considering the efficient utilization of energy gradients. Consequently, the notion that a larger EH device is not supported.

The sensitivity analysis shows that the LCOE of the system decreases and then increases with the increase of N_Loop, C_CSP, C_PV and C_TES. The similarity in the trends can be attributed to the reasons that during the initial phase, the decline in the LCOE is primarily driven by the rapid growth of generation faster than the costs increase. However, the inflection point and subsequent upward trend are due to the constraints of the remaining factors. For example, N_Loop, C_CSP and C_TES are mutually constrained, and C_PV is constrained by customer load demand. These constraints prevent the system generation from growing rapidly and continuously. The growth rate gradually decreases after the constraints are imposed, and the LCOE shows an increasing trend. Therefore, the significance of the sensitivity analysis lies in determining capacity configurations by considering the interaction among different components.

The comprehensive sensitivity analysis above reveals that the change of C_CSP and C_TES has a significant impact on carbon emissions, which fully reflects the peaking effect of CSP, and also indicates that equipping TES enables a fast peaking of CSP and has a positive effect on the system. The impact of TES on LCOE is also the most significant, as the C_TES will affect all aspects of abandoned wind and solar energy, CSP generation, and EH output at the same time. Therefore, equipping TES in the CSP system is the current and future trend of the integrated energy system.

6 Conclusions

This paper focuses on a WP−PV−CSP (S-CO₂) renewable integrated energy system which integrates WP, PV, CSP, TES, and EH subsystems simultaneously, using a trough collector as the heat source and the S-CO₂ Brayton cycle as the thermoelectric conversion module of the CSP system. It proposes a bi-level capacity-operation collaborative optimization approach to simultaneously optimize the capacity and annual load dispatch of the main modules of the system. It selects LCOE and CO₂ emissions as the upper-level objectives, and maximum renewable energy utilization is selected as the objective at the lower-level. It solves the problem using a combined nested algorithm incorporating the NSGA-II and LP. It uses the hourly meteorological data and load demand of Zhangbei, China as the basic parameters for the case study. It comes to the following main conclusions:

1) The Pareto front of the system is obtained by solving the bi-level optimization problem using the NSGA-II nested LP algorithm, and different weights are set for LCOE and carbon emission by using the comprehensive evaluation method of the AHP-entropy weighting method with TOPSIS proposed by the institute. The optimal compromise solution for LCOE and CO₂ emissions is determined to be the solution with a weight of [0.08, 0.92]. The corresponding SF area, C_CSP, C_TES, C_EH, C_PV, and wind turbine number are 6.44 × 10⁵ m², 167 MW, 7 h, 45 MW, 72 MW, and 31.825 MW, respectively, when the LCOE and CO₂ emissions are 0.4196 $/kWh and 370 t/a, respectively.

2) The optimal capacity configuration is analyzed for annual operation characteristics, which can maximize the demand load and reduce abandoned wind and solar energy in the operation strategy. Three reference systems are established to compare the annual operating characteristics with the WP−PV−CSP (S-CO₂) system, demonstrating the advantages of using the S-CO₂ Brayton cycle and equipping the system with EH. After implementing capacity-operation collaborative optimization, the WP−PV−CSP (S-CO₂) system shows a 3.43% and 92.13% reduction in LCOE and carbon emissions compared to the reference system without optimization.

3) Sensitivity analysis shows that as N_Loop, C_CSP, C_PV, and C_TES increase, the system LCOE decreases and then increases, and the LCOE increases linearly when the WP capacity increases. EH has almost a minimal effect on the LCOE. All carbon emissions are first reduced and then stabilized. In addition, there are better optimization intervals for N_Loop, C_CSP, and C_PV. The capacity configuration corresponding to the optimal compromise solution obtained in this paper falls within this interval, demonstrating the accuracy of the sensitivity and optimization results. A comparison of the curves reveals that C_CSP and C_TES significantly impact carbon emissions, which fully reflects the peaking role of CSP in integrated renewable energy systems. In addition, the impact of C_TES on LCOE is also the most significant, indicating that equipping TES in the CSP system is the current and future trend of the integrated energy system.

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