The Hydrogen Council predicted that hydrogen would account for 18 \mathrm{\%} of final energy consumption by 2050 [1], thus playing an essential role in future low-carbon energy system [2]. Upscaling to 2030 is critical for meeting the above targets [3]. For net-zero vision, the global hydrogen demand will reach 140 megatons (Mt) in 2030, of which 50 \mathrm{M} \mathrm{t} will originate from newly built renewable or low-carbon hydrogen [3]. China has set high ambitions to become a leader in hydrogen production, accounting for nearly 30 \mathrm{\%} of the global hydrogen demand in 2030 at 40 \mathrm{M} \mathrm{t}, and reaching 200 Mt by 2050 [3].

However, the current situation of hydrogen production in China remains challenging. On one hand, hydrogen is mainly converted from fossil fuels with a very large carbon footprint [4], limiting its role in decarbonization. Additionally, relying on fossil-fuel-based hydrogen may indefinitely lock humans into fossil fuels [5]. However, the scale of hydrogen at terminals is limited to refining and industrial fields such as ammonia production \left(10-11\mathrm{M}\mathrm{t}\cdot {\mathrm{a}}^{-1}\right), oil refining \left(8-9\mathrm{M}\mathrm{t}\cdot {\mathrm{a}}^{-1}\right), and methanol production \left(7-9\mathrm{M}\mathrm{t}\cdot {\mathrm{a}}^{-1}\right), which greatly deviate from the diversified large-scale hydrogen applications under the report of "Hydrogen for net zero" vision [3,6].

Under China’s low-carbon target, the utilization of a large number of installed renewables (more than 1200 GW in 2030 [7] and 5000 GW in 2060 [8]) has become an important challenge for the safe and economic operation of power systems. Electrolytic hydrogen conversion from renewable energy sources has become a two-way choice between power system operation and clean hydrogen production. Recently, China has made significant efforts to develop water electrolysis technologies. For example, the Ningxia solar hydrogen project in China, which became fully operational on December 22, 2021, with a total capacity of 150 MW, accounts for almost three-quarters of the global additions [9]. However, owing to the high investment cost of power-to-hydrogen (P2H) technology and the trade-off between the electricity price and \mathrm{P} 2 \mathrm{H} capacity factors, the cost of electrolytic hydrogen is several times higher than that of coal/natural gas-based hydrogen [10], lowering the pace of hydrogen development.

Many studies have analyzed the low carbon and cost-competitiveness levels of electrolytic hydrogen, where power is obtained from power grids [11], renewables [12,13], or both [14,15]. The results show that low electricity prices can significantly reduce the production cost of electrolytic hydrogen but can result in high carbon emissions if the electricity purchased from the power grid is generated from a high proportion of fossil fuels. Therefore, electrolytic hydrogen must reveal its true potential if we want to use it wisely to contribute to decarbonization [16]. Low- {\mathrm{C}\mathrm{O}}_2 or clean hydrogen has been defined based on its life-cycle carbon intensity, with standard values of 3.0, 2.0, and 4.9 \hspace{0.33em} \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2 \cdot {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1} set in the European Union, United States, and China, respectively [17,18]. The direct use of renewables for hydrogen production can be considered as generating zero carbon emissions, but this could lead to high production costs due to the limited annual utilization hours of electrolysers. This pattern is more suitable for areas with favorable renewable resources.

However, these studies did not consider the close synergy between power systems and hydrogen energy. In other words, the studies do not purchase electricity to produce hydrogen, but further traces the source, optimizes the equipment and networks of the renewable-based power and hydrogen system (RPHS) from the perspective of total cost minimization, and then characterizes the cost of hydrogen production through the incremental cost principle. The advantage of this method is that on the premise of ensuring a basic electric load, the generation units of power systems can also be optimized to produce hydrogen via \mathrm{P} 2 \mathrm{H} under controlled carbon emissions. The non-real-time balance characteristic of hydrogen can enhance the flexibility of power systems in absorbing renewables, thus avoiding redundant renewable allocation problems.

Therefore, in this study, we developed an optimization model of an RPHS to evaluate the national and provincial hydrogen supply costs and potentials, considering the provincial high-precision power system structure, renewable resources and generation potentials, and differentiated hydrogen demand. The cost-reduction effects of power system support and provincial cooperation on clean hydrogen production and competitive performance under different carbon emission constraints were analyzed. The results show that the proposed electrolytic hydrogen development mechanism could provide cost-competitive and large-scale clean hydrogen in the near future, contributing to China’s hydrogen demand target.

First, hourly provincial-level wind and solar capacity factors were calculated using the renewables.ninja platform [18]. The location of the capital of each province was chosen to calculate the average wind and solar capacity factors using meteorological data from to 2010-2020 acquired from the National Aeronautics and Space Administration (NASA) modern-era retrospective analysis for research and applications (MERRA)-2 product [19]. During the photovoltaic (PV) output calculation, a fixed-tilt system was assumed, with the tilt set as a function of the city latitude, and the system loss was set to 0.1 [20]. In the wind power output calculation, a Goldwind GW121 wind turbine (WT) with a rated power of 2.5 \mathrm{M} \mathrm{W} was considered, and the hub height was set to 90 \hspace{0.33em} \mathrm{m} [21]. Owing to data limitations, the hourly provincial electric loads were obtained from provincial power grid companies or fitted based on typical provincial daily and annual load curves [22]. According to the national forecast for 2030, the proportion of newly added wind and solar power generation will account for 15 \mathrm{\%} of the total electric load [23]. Typical unit wind and solar power output and electric load curves are shown in Fig. S1 in Appendix A. The related power-system parameters are listed in Tables S1-S11 in Appendix A. The operating and carbon emission properties of the coal generator (CG) were obtained from a study by Chen et al. [24].

The objective function of the RPHS optimization model is to minimize the total annual cost of all provinces p.

The nomenclature of the symbols used in this paper is provided at the end of the paper.

The total annual cost in each province p is the sum of the annual cost of power-related RPHS {\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_p^{\mathrm{E}} and the annual cost of hydrogen-related RPHS {\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_p^{\mathrm{H}}, which in turn can be further subdivided into the annual investment cost and operation and maintenance (O&M) cost, and the former cost item includes the annual operating cost, as indicated in Eqs. (2) and (3). As shown in Eqs. (4)- (6), the annual investment cost of the power-related RPHS includes the WT, PV, electric storage (ES), alternating current (AC), direct current (DC), CG, and carbon capture, utilization, and storage (CCUS) investment costs in province p. The annual O&M cost of the renewable-based power system (RPS) includes the annual O&M costs of the WT, PV, ES, AC, DC, CG, and CG with CCUS in province p, and the annual operating cost of the power-related RPHS includes the fuel costs and startup costs of the CG and CG with CCUS. The annual cost of hydrogen-related RPHS includes the annual investment cost of \mathrm{P} 2 \mathrm{H} and hydrogen storage (HS), and the corresponding annual O&M cost, as shown in Eqs. (7) and (8). Additionally, {\kappa }^m is the capital recovery factor of equipment m, which is equal to \mathrm{d} \mathrm{r} \cdot {\left(1+\mathrm{d}\mathrm{r}\right)}^{N^m} / \left({\left(1+\mathrm{d}\mathrm{r}\right)}^{N^m}-1\right).

The optimization model must satisfy the following constraints: Specifically, Eq. (9) limits the investment capacity of the various equipment types to a nonnegative value that is lower than the maximum installed capacity based on the installation conditions. The maximum installed capacities of PV, WT, AC, and DC were obtained in a study by Zhuo et al. [25].

Eq. (10) defines the hour-level power balance constraint in province p at time t.

Eqs. (11) and (12) formulate the operating constraints of PV units and WTs.

Eqs. (13) and (14) define the operating constraints of nuclear power generator (NG) and hydropower generator (HG), respectively. Considering that the share of NG and HG in each province varies greatly and the carbon emissions are much lower than those of CG, the expansion planning of NG and HG is not considered in this study. The real-time power and total annual generation of the HG were limited to the current generation levels. Considering that the generation cost of NG is higher than that of CG, other constraints must be added to ensure that higher annual utilization hours can be achieved [24]. Outside the given power-constraint interval, we limit the future utilization hours to the current operating hours.

Eqs. (15)-(20) define the ES operation constraints, as follows: Eqs. (15) and (16) ensure that the ES charging/discharging power and reserve power r_{p,t}^{\mathrm{E}\mathrm{S}} are non-negative values that do not exceed the installed power capacity. Eqs. (17) and (18) ensure that the actual storage energy of the ES does not exceed the installed energy capacity and establish a relationship with the charging and discharging power levels. Eq. (19) expresses the relationship between the stored energy and the discharge and reserve powers. Eq. (20) ensures consistency between the start and end states of the ES.

The relaxed unit cluster operational constraints for CGs can be formulated as follows [26]:

Eq. (21) limits the aggregated power output of the ith cluster \mathrm{C} \mathrm{G}, with and without CCUS, to the interval \left[{\lambda }_i^{\mathrm{C}\mathrm{G}}{O}_{p,i,t}^{\varphi },O_{p,i,t}^{\varphi }\right]. Eq. (22) limits the ramping ability of unit cluster i to the operating capacity of the i th cluster CG with or without CCUS. Eqs. (23)-(26) define the relationships between the online, startup, and shutdown capabilities. Eq. (27) indicates that the net output of CG with CCUS is less than the actual output because the carbon process consumes considerable power. The capture rate of CCUS {\rho }^{\text{ CCUS }} is defined as a fixed value of 0.9 , {\lambda }^{\text{ CCUS }} denotes the required power for {\mathrm{C}\mathrm{O}}_2 capture and storage with a value of 0.296 \mathrm{M} \mathrm{W} \cdot \mathrm{h} per tonne [25]; the value of \gamma is 0.5 \mathrm{\%} to represent the basic energy consumption determined by CCUS capacity [25].

The hourly transmission power of the AC and DC lines between provinces p and q are constrained as follows:

The following reserve capacity constraint for the power grid in each province must satisfy the operating reserve of the power grid, considering the forecast errors of the load and renewables:

Eq. (31) defines the P2H operation constraints to ensure that the electric power consumed during this process does not exceed the \mathrm{P} 2 \mathrm{H} installed capacity. In the configuration of the HS capacity, we used an eight-hour duration limit on-site storage tank at a pressure of 60 bar to provide a buffer between the time of production and use [11,27], as shown in Eq. (32).

Eq. (33) defines the relationship between the \mathrm{P} 2 \mathrm{H} input and output. The gross domestic product (GDP), population, and carbon emissions used for provincial hydrogen demand distribution are listed in Table S12 in Appendix A.

In each province p, the constraint on renewable power generation in the RPHS can be expressed as follows:

To ensure that the amount of electrolytic hydrogen produced in each province was less than the given carbon intensity, the following constraints were added to the RPHS optimization model: E_p^{{\mathrm{R}\mathrm{P}\mathrm{H}\mathrm{S}}_{-}} and E_p^{{\mathrm{R}\mathrm{P}\mathrm{S}}_{-}} are the carbon emissions of the RPHS and RPS, respectively; the latter is calculated in advance according to the subsequent RPS optimization model. \theta is the upper limit of average carbon intensity for hydrogen production using the RPHS system, and its unit is \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2 \cdot {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1}. The physical meaning is the maximum ratio between the newly added carbon emissions of the RPHS compared with the RPS after electrolytic hydrogen chain (EHC) access and the amount of hydrogen produced. For example, its value of 4.9 \hspace{0.33em} \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2 \cdot {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1} can limit the carbon intensity of hydrogen production in the RPHS system and meet the set standard of low- {\mathrm{C}\mathrm{O}}_2 hydrogen in China.

In addition, the RPHS optimization model, without considering CCUS technology, needs to remove the CCUS-related terms from Eqs. (4), (6), (9), (10), (21)-(25), and (30), and should not be constrained by the CCUS-related Eqs. (26) and (27). The carbon emissions constraint was replaced by Eqs. (37) and (38) for Eqs. (35) and (36).

Compared with the national province cooperation scenario, the RPHS optimization model under the provincial independence scenario does not consider the interprovincial transmission power optimization problem; AC/DC transmission-related items in Eqs. (4),(5),(9), and (10) should be removed, and transmission constraints of Eqs. (28) and (29) should be deleted.

The objective function of the RPS optimization model is as follows:

where the expressions of all parts in Eq. (40) are the same as Eqs. (4)-(6) and the constraints are Eqs. (9)-(30) and (34), in which the P2H-related items are deleted from Eqs. (9) and (10). The processing of the RPS model without considering the CCUS and interprovincial transmission is consistent with that of the RPHS model. In addition, the carbon emission calculations with and without CCUS are shown in Eqs. (41) and (42), respectively.

Based on the incremental cost principle, the LCOH of each province p is defined as Eq. (43). {\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_p^{\mathrm{R}\mathrm{P}\mathrm{S}} is the optimized total annual cost of the RPS under various equipment and network planning and operation constraints. {\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_p^{\mathrm{R}\mathrm{P}\mathrm{H}\mathrm{S}} is the optimal total annual cost of the RPHS under the above power system constraints, \mathrm{P} 2 \mathrm{H} and HS planning and operation constraints, and carbon emission constraint, as expressed in Eqs. (35) and (37). Therefore, the numerator of {\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_p^{\mathrm{R}\mathrm{P}\mathrm{H}\mathrm{S}} - {\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_p^{\mathrm{R}\mathrm{P}\mathrm{S}} in Eq. (43) represents the incremental cost owing to the addition of the electrolytic hydrogen production. The national average LCOH is defined by Eq. (44). In addition, Appendix Note S1 provides the LCOH optimization model of renewable-based hydrogen production (RHP), which simply uses PV and WT for hydrogen production for comparison with the hydrogen production of the RPHS proposed in this study.

First, we propose the concept of an RPHS, which adopts electricity and hydrogen as energy carriers to help achieve China’s low-carbon targets, as shown in Fig. 1(a). The RPS is defined as a further increase in the wind-solar generation ratio based on current provincial power systems to meet the low-carbon operation requirements of China’s future power systems. This includes renewables, such as wind and solar power; dispatchable power, such as CGs; and grid-level ES to achieve peak-to-valley transfer to meet the electrical load. Unlike the RPS, the RPHS includes an EHC consisting of P2H, HS, and terminal hydrogen demand. The relationship and structure diagrams of the RPS, EHC, and RPHS are shown in Appendix A Fig. S2.

A schematic of a cost-competitive and clean hydrogen supply in an RPHS is shown in Fig. 1(b). In the planning stage, the constraint on the proportion of renewable power generation in the RPS leads to an increased renewable power output and decreased coal-fired power output levels. In the operating stage, the former helps provide clean but fluctuating power, whereas the latter is beneficial for providing low-cost power with high {\mathrm{C}\mathrm{O}}_2 emissions. Given the above problems, the first step is to use the flexibility of the accessed electrolytic hydrogen to help RPS increase their renewable integration. The second step is to establish a low-emission power filter using the {\mathrm{H}}_2 emission standard to guarantee clean hydrogen production. We used CCUS technology to convert high-carbon coal-fired power into low-carbon coal-fired power. Thus, the same carbon-emission constraints could increase the coal-fired power output. Although the addition of CCUS technology can increase system investment costs, the cost of electricity will remain relatively high (and can even decrease) because of the larger number of annual utilization hours of coal-fired power, achieving positive feedback to increase the number of coal-fired power utilization hours and provide more low-carbon coal-fired power. We evaluated the LCOH based on the incremental cost principle and achieved the target of a cost-competitive and clean hydrogen supply in the RPHS.

We used the above LCOH calculation method to analyze the electrolytic hydrogen production performance in each province. It was assumed that the predicted 40 \mathrm{M} \mathrm{t} hydrogen demand in China by 2030 [3] would be met using water electrolysis technology. Considering the potential differences in hydrogen demand among the different provinces, the total hydrogen demand was differentiated according to the current power load in each province (Fig. S3 in Appendix A for the provincial hydrogen demand distributions).

In the case of RHP, the LCOH ranged from 2.08 to 4.40 USD \cdot {\mathrm{k}\mathrm{g}}^{-1}, as shown in Fig. 2(a). The regions with the highest LCOH value were Chongqing, Sichuan, and Shaanxi which reached more than 4 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}, whereas the province with the lowest \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} value was Jiangsu Province. Fig. 2(b) shows that the proportion of the \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} value in renewable investment in the \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} was the highest in the different provinces, with an average of 65 \mathrm{\%}. The second highest proportion was observed for the investment cost of electrolyz-ers, with an average of over 20 \mathrm{\%}. Finally, the proportion of the system O&M costs reached an average of 12 \mathrm{\%}. Under the given parameters, the LCOH was generally lower in the provinces with more abundant wind resources. On one hand, these provinces exhibited a lower levelized cost of energy (LCOE) for renewable power generation than other provinces, while on the other hand, the P2H configuration cost was lower. Even if the LCOE values of wind and solar power generation are the same, as in Xizang autonomous region and Jiangsu Province, the utilization efficiency of the subsequent \mathrm{P} 2 \mathrm{H} equipment would be higher because of the overall higher capacity factor of wind power generation than that of solar power generation, that is, the \mathrm{P} 2 \mathrm{H} investment cost ratio would be lower. Hence, the LCOH in Jiangsu Province, which has better wind power resources, was lower than that in Xizang.

In the RPHS without CCUS, the LCOH ranged from 1.92 USD \cdot {\mathrm{k}\mathrm{g}}^{-1} in Jiangsu to 3.90 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1} in Chongqing. After considering the support of the provincial power systems, the \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} in 27 of the 31 provinces could decrease to varying degrees, among which Shaanxi Province attained the highest decrease of 1.04 USD \cdot {\mathrm{k}\mathrm{g}}^{-1}, followed by Gansu \left(0.61\mathrm{U}\mathrm{S}\mathrm{D}\cdot {\mathrm{k}\mathrm{g}}^{-1}\right) and Xinjiang \left(0.60\mathrm{U}\mathrm{S}\mathrm{D}\cdot {\mathrm{k}\mathrm{g}}^{-1}\right). Fig. 2(c) shows the components of LCOH reduction in the RPHS without CCUS case. Overall, the provincial LCOH could be reduced by lowering the renewable and \mathrm{P} 2 \mathrm{H} investment costs and the corresponding O&M costs, but the provincial LCOH could be increased by increasing the fuel and startup costs of thermal units and the investment costs of the CG and ES. It should be noted that the reason for increasing the investment cost of ES in the RPHS without CCUS technology case is the limitation of the maximum wind/solar configuration capacity of the province itself, leaving space for the configuration of ES when low-cost wind or solar power is converted into high-cost solar or wind power. The above maximum configuration capacity limit is also the main reason for the higher LCOH values in Guangdong, Zhejiang, Tianjin, and Shanghai in the RPHS than those in the RHP case. Adopting Shanghai as an example, although its abundant wind resources greatly lower its wind power cost, the corresponding maximum configuration capacity reaches only 4 \mathrm{G} \mathrm{W}, and this capacity cannot meet the requirements of the electricity and hydrogen demands in the RPHS, so solar power with a relatively high LCOE must be configured after complete configuration of wind power. According to the LCOE values of renewables and coal power in Figs. 2(b) and (c), respectively, the LCOE of coal power is generally lower (below 0.04 USD. {\left(\mathrm{k}\mathrm{W}\cdot \mathrm{h}\right)}^{-1}) across most provinces, whereas the LCOE of renewables tends to be higher (above 0.04 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\left(\mathrm{k}\mathrm{W}\cdot \mathrm{h}\right)}^{-1}). However, low-cost coal power has not been fully utilized because of the mandatory integration of renewable energy sources and low-carbon constraints on the hydrogen production process, which limit the proportion of power required to produce hydrogen from coal power.

To address this issue, we further investigated the impact of CCUS technology on provincial LCOH values, where the CCUS technology was installed, through system optimization. In the RPHS with CCUS case, as shown in Fig. 2(a), the CCUS technology reduced the LCOH in all provinces relative to the RHP case, where the LCOH fell below 2.5 USD \cdot {\mathrm{k}\mathrm{g}}^{-1} across all provinces and below 2.0 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1} in the northern region as a whole. Compared with the RPHS without CCUS, CCUS addition could significantly reduce the investment cost of renewables owing to electrolytic hydrogen access (Fig. 2(d)), thereby achieving a low hydrocarbon power supply under the given carbon constraints without requiring the additional allocation of renewables. However, the implementation of the CCUS technology also increases the output of coal power, leading to a significant increase in the proportion of fuel costs of coal power in hydrogen production. Furthermore, the number of annual utilization hours of coal power may increase by several times, as shown in Fig. 2(e). Therefore, although adding CCUS could increase coal power generation costs, the LCOE of coal power generation in most provinces could remain below 0.04 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\left(\mathrm{k}\mathrm{W}\cdot \mathrm{h}\right)}^{-1} due to the improved coal power utilization levels. From the perspective of the CCUS configuration, Guangdong and Shandong Provinces attained the highest configured capacity, reaching 27.3 and 26.7 \hspace{0.33em} \mathrm{G} \mathrm{W}, respectively, while the other provinces attained a CCUS capacity less than 20 \mathrm{G} \mathrm{W}. A comparison of the LCOH values of the three pathways of hydrogen production from newly added coal power, newly added coal power with CCUS technology, and existing coal power units equipped with CCUS technology is shown in Fig. S4 in Appendix A. The first pathway does not consider the carbon emission constraint problem. In contrast, the latter two pathways consider a carbon emission constraint with a maximum hydrogen carbon intensity of 6.5 \hspace{0.33em} \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2 \cdot {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1}, which is close to the minimum carbon emission level of coal power units equipped with CCUS technology in hydrogen production. As can be seen in Fig. S4, the last pathway can achieve an LCOH lower than 2.0 USD \cdot {\mathrm{k}\mathrm{g}}^{-1} in most provinces, and can become a powerful supplementary method for hydrogen production from renewable energy sources.

In the previous section, we analyzed the provincial LCOH performance of the RPHS using the incremental cost principle without considering the power interaction effects between provinces. Therefore, from a national perspective, this section examines the impact of provincial cooperation on electrolytic hydrogen production in an RPHS with a CCUS by optimizing the transmission capacity and power changes owing to hydrogen energy access. Fig. 3 shows the newly installed equipment under the provincial independence and provincial cooperation scenarios at a supply scale of 40 Mt in 2030, and the corresponding newly installed transmission lines are shown in Appendix A Fig. S5. Under these two scenarios, the provinces exhibited significant differences in equipment investment. The main difference between the two scenarios is the configuration of the coal power units, CCUS, and transmission lines. Under the provincial independence scenario, the CCUS distribution was relatively dispersed, whereas under the provincial cooperation scenario, the CCUS distribution is concentrated in Inner Mongolia and Xinjiang. In particular, Inner Mongolia can provide a significant capacity to export low-carbon power because of its nearly 200 \mathrm{G} \mathrm{W} installed coal power units with CCUS technology and expanded outgoing power transmission channels. According to the potential power transmission channels selected by the Global Energy Interconnection Development and Cooperation Organization [25], the newly added AC and DC transmission capacities under the provincial independence and cooperation scenarios are 148.4 and 88.0 GW, respectively. Fig. 4 shows the annual power transmission and LCOH fluctuations for these two scenarios. Each province was divided into pure output, output greater than input, output less than input, and pure input categories to compare the interprovincial power transmission levels under the two scenarios. The provincial independence scenario included two pure output provinces, eight output greater than the input provinces, 18 output less than the input, and three pure input provinces, while the provincial cooperation scenario included2,12,13, and 6 provinces, respectively, in each category. Fig. 4(c) presents the national LCOH reductions for the two scenarios. Provincial cooperation could further reduce the cost of electrolytic hydrogen production by reducing fuel costs, renewable investment, and \mathrm{P} 2 \mathrm{H} investment, of which fuel cost reduction accounts for more than 80 \mathrm{\%} of the total reduction amount. However, provincial cooperation could increase the cost of electrolytic hydrogen production by increasing the coal power unit, energy storage, transmission line, O&M, and startup costs, among which the coal power unit and transmission line investments accounted for the highest proportion of the total reduction. Overall, the national average LCOH can be reduced by 0.23 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1} after considering interprovincial grid transmission for hydrogen production, from 1.95 to 1.72 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}, satisfying the economically competitive condition of a value less than 2.00 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1} estimated by the US Department of Energy [28].

Considering that the potential distribution of hydrogen demand can affect the provincial cooperation effects based on transmission lines, we further analyzed the impact of hydrogen demand distribution on the LCOH under different division principles, such as GDP, population, carbon emissions, wind resources, PV resources, and coal prices from both the demand and supply perspectives. Figs. 5(a) and (b) show the LCOH fluctuations relative to the base electric load division principle under the provincial independence and cooperation scenarios, respectively. Compared with those under the provincial independence scenario, provincial cooperation could reduce the LCOH by0.19,0.17,0.07,0.57,0.61, and 0.45 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1} under the principles of the GDP, population, carbon emissions, wind resources, PV resources, and coal prices, respectively. Its effect on LCOH reduction under the supply-side division principle was significantly greater than that under the demand-side division principle. The specific cost composition indicated that provincial cooperation could reduce the LCOH by reducing the fuel and startup costs under the different principles. Based on the supply-side principle, provincial cooperation could also effectively reduce the coal power unit and transmission line investments, further reducing the LCOH. Whether using the supply-side division principle or the demand-side division principle, \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} fluctuations are within the range of 0.1 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}. For comparison, the International Energy Agency (IEA) considers pipelines to be the most economical means of hydrogen distribution for distances up to 500 \hspace{0.33em} \mathrm{k} \mathrm{m}, with a low-cost option of 500 \mathrm{t} per day, costing more than 0.25 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1} [10]. Therefore, in-situ hydrogen production based on the demand-side division principle is more feasible.

Electrolytic hydrogen production relying on power system support can effectively reduce LCOH; however, carbon emission constraints determine the support strength of coal power units in the power system. Considering that coal power units equipped with CCUS technology can effectively reduce carbon emissions and increase the proportion of electricity used to produce hydrogen, they are beneficial for reducing LCOH in electrolytic hydrogen. According to the low-emission hydrogen standards in China, hydrogen is classified into clean, low-carbon, and non low-carbon hydrogen according to carbon intensities of 0-4.9, 4.9- 14.5, and \ge 14.5 \hspace{0.33em} \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2 \cdot {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1}, respectively [17]. Fig. 6 shows the influences of the hydrogen carbon intensity and hydrogen supply scale on the LCOH performance, where the hydrogen carbon intensity ranges from 0 to 20 \hspace{0.33em} \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2 \cdot {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1}. A hydrogen carbon intensity of 0 \hspace{0.33em} \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2 \cdot {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1} indicates that the total {\mathrm{C}\mathrm{O}}_2 emissions in the RPHS case are no higher than those in the RPS case, that is, no additional {\mathrm{C}\mathrm{O}}_2 emissions occur during the hydrogen production process. A hydrogen carbon intensity of 20 \hspace{0.33em} \mathrm{k} \mathrm{g} {\mathrm{C}\mathrm{O}}_2. {\left(\mathrm{k}\mathrm{g}{\mathrm{H}}_2\right)}^{-1} indicates that the {\mathrm{C}\mathrm{O}}_2 emissions of hydrogen produced based on the RPHS are comparable to those of coal gasification [10]. With increasing hydrogen supply scale and decreasing carbon intensity, the LCOH of electrolytic hydrogen gradually increases, fluctuating between 1.4 and 1.8 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1} within the given parameter range. Moreover, the LCOH of clean hydrogen ranges from approximately 1.6 to 1.8 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}. At this carbon intensity level, the current LCOH of hydrogen produced from coal with CCUS technology and natural gas with CCUS technology is 1.4 and 2.0 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}, respectively. The \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} of low-carbon hydrogen varies between 1.5 and 1.7 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}, and at this carbon intensity level, the cost of natural gas-based hydrogen is approximately 1.4 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}. The \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} of non low-carbon hydrogen is between 1.45 and 1.60 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}, and for comparison, the current cost of coal-based hydrogen is approximately 1.1 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}. Electrolytic hydrogen production based on the proposed approach is not cost-competitive relative to fossil fuel-based hydrogen production in terms of low-carbon and non low-carbon hydrogen. From the perspective of the hydrogen supply scale, the Hydrogen Council, China Hydrogen Energy Alliance, and IEA expect the electrolytic hydrogen production scale to reach approximately 12,5, and 2 \mathrm{M} \mathrm{t}, respectively, by 2030, with the corresponding hydrogen production costs ranging from 1.65 to 1.75 \mathrm{U} \mathrm{S} \mathrm{D} \cdot {\mathrm{k}\mathrm{g}}^{-1}, as shown in Fig. 6. From the perspective of energy use, the Hydrogen Council predicted that the \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} of hydrogen in 2030 could reach 1.9 USD \cdot {\mathrm{k}\mathrm{g}}^{-1} to realize break-even in hydrogen-based steel production [29]. In contrast, cost levels of approximately 2 and 3 USD \cdot {\mathrm{k}\mathrm{g}}^{-1} could render hydrogen viable in passenger vehicles and commercial mobility applications, respectively. Therefore, combined with the economics of supply and demand, electrolytic hydrogen based on RPHS could play a greater role than expected.

We assessed the sensitivity of the results to key factors, including the ratio of renewable power generation, investment cost of renewable power, coal price, CCUS investment, and the cost and efficiency of the \mathrm{P} 2 \mathrm{H} process. The key assumptions are summarized in Appendix A Table S13. As shown in Fig. 7, the fluctuation in coal price exerts the greatest impact on the \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} of electrolytic hydrogen production because it determines the level of low-carbon and low-cost coal electricity provided by coal power, followed by the development level of \mathrm{P} 2 \mathrm{H} technology, specifically the levels of investment cost and conversion efficiency. The third most important factor is the CCUS investment cost, whose determines the scale of CCUS installation and impacts the supply level of low-carbon and low-cost coal electricity. The proportion of renewable power generation had the least effect on the LCOH. In contrast to the effects of the above parameters, an increase in the renewable investment cost slightly affected the LCOH of electrolytic hydrogen production, whereas a decrease could greatly reduce the LCOH.

In this study, we propose an incremental cost-principle-based RPHS optimization strategy for electrolytic hydrogen production. The effectiveness of the proposed method was verified by comparing it with RHP. The contribution of CG with CCUS and provincial transmission cooperation to the reduction in LCOH was discussed through a multi-scenario comparative analysis. The performance of the strategy under key parameters or constraints was verified using different hydrogen supply scales, hydrogen demand distributions, and carbon intensities.

This analysis yielded several key results. First, under the premise of differentiated provincial hydrogen demand, the electric-hydrogen development mechanism could effectively reduce the provincial clean hydrogen production cost over pure RHP, which could provide a solution for the development of electrolytic hydrogen in provinces with insufficient wind or solar resources. Second, we explored the role of provincial cooperation relying on interprovincial power transmission to enhance the national clean hydrogen supply capacity, which was mainly achieved by improving the utilization efficiencies of renewables, thermal generation units, and \mathrm{P} 2 \mathrm{H} technology. From the perspective of hydrogen production costs, increasing hydrogen energy development in areas with abundant renewable resources could provide a slight advantage; however, this is not as great as imagined, considering that many major projects are concentrated in areas with abundant renewable resources. Third, the electrolytic hydrogen produced based on the proposed mechanism was only cost-competitive relative to fossil-fuel-based hydrogen in terms of clean hydrogen production. However, this could play a more significant role than expected from a demand perspective.

Additionally, electric hydrogen development mechanisms can benefit power systems. Against the background of the new electric power system proposed by China in 2021 [30], the proportion of renewable power generation has become an important indicator. By the end of 2021, one trillion kWh of electricity from renewable energy sources will be generated in China, accounting for 12 \mathrm{\%} of the total generation. When constructing a new power system, renewable power generation should account for more than 20 \mathrm{\%} by 2030 [31] and more than 50% by 2060 [32]. The use of electrolytic hydrogen as a flexible and controllable load in power systems can significantly improve the consumption of new energy under the constraints of renewable power generation. In addition, the constraint on low-carbon electrolytic hydrogen production is conducive to the reverse promotion of the popularization of CCUS technology and improvement in the utilization level of thermal power, which cannot be achieved simply by increasing renewable indicators.

We acknowledge the support provided by the National Science Fund for Distinguished Young Scholars (52325703), Postdoctoral Innovation Talents Support Program (BX20220066), China Postdoctoral Science Foundation (2022M720709), and State Key Laboratory of Power System Operation and Control (SKLD23KM06).

Guangsheng Pan, Wei Gu, Zhongfan Gu, Jin Lin, Suyang Zhou, Zhi Wu, and Shuai Lu declare that they have no conflict of interest or financial conflicts to disclose.

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2024.05.014.

p , \Xi \hspace{0.33em} Index and set of provinces m , M \hspace{0.33em} Index and set of CG, PV, WT, ES, P2H, HS, AC line, and DC line

i , X^p \hspace{0.33em} Index and set of clustered CGs in provinc

q , {\Gamma }^p \hspace{0.33em} Index and set of transmission lines connected to province p

{\Gamma }_{\mathrm{s}/\mathrm{r}}^p \hspace{0.33em} A subset of {\Gamma }^p representing the power outflow/inflow from p to q t , T \hspace{0.33em} Index and set of time period \tau \hspace{0.33em} Index of auxiliary period for CG

Functions

{\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_p^{\mathrm{R}\mathrm{P}\mathrm{H}\mathrm{S}/\mathrm{R}\mathrm{P}\mathrm{S}} \hspace{0.33em} Annual cost of RPHS / \mathrm{R} \mathrm{P} \mathrm{S} in province p

{\text{ Cost }}_n^E \hspace{0.33em} Annual cost of power-related RPHS in province p

{\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_n^{\mathrm{H}} \hspace{0.33em} Annual cost of hydrogen-related RPHS ir province p

{\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}}_n^{\mathrm{I}\mathrm{N}\mathrm{V}\_\mathrm{E}} \hspace{0.33em} Annual investment cost of power-r RPHS in province p

Annual O&M cost of the power-related RPHS p in province p

{\text{ Cost }}_n^{O{P}_{-}E} \hspace{0.33em} Annual operating cost of power-related p \hspace{0.33em} RPHS in province p

{\text{ Cost }}_n^{\text{ INV\_H }} \hspace{0.33em} Annual investment cost of hydrogen-related P \hspace{0.33em} RPHS in province p

Annual O&M cost of hydrogen-related RPH p in province p

E^{\text{ RPHS\_CCUS }} Annual carbon emissions of the RPHS wi {}^p CCUS technology in province p

E_{\mathrm{n}}^{{\mathrm{R}\mathrm{P}\mathrm{S}}_{-}} CCUS Annual carbon emissions of the RPS with P CCUS technology in province p

E_{\mathrm{n}}^{\mathrm{R}\mathrm{P}\mathrm{H}\mathrm{S}} \hspace{0.33em} Annual carbon emissions of the RPHS without CCUS technology in province p Annual carbon emissions of the RPS without CCUS technology in province p

{\mathrm{L}\mathrm{C}\mathrm{O}\mathrm{H}}_p \hspace{0.33em} \mathrm{L} \mathrm{C} \mathrm{O} \mathrm{H} in province p Parameters \Delta t \hspace{0.33em} Time interval {\kappa }^m \hspace{0.33em} Capital recovery factor of equipment m

N^m \hspace{0.33em} Lifetime of equipment m

dr Discount rate

c_p^{\mathrm{I}\mathrm{N}\mathrm{V}\_\mathrm{W}\mathrm{T}/\mathrm{P}\mathrm{V}} \hspace{0.33em} Unit investment cost of WT / \mathrm{P} \mathrm{V} in province p

c_n^{\mathrm{I}\mathrm{N}\mathrm{V}\_\mathrm{E}\mathrm{S}\mathrm{P}/\mathrm{E}\mathrm{S}\mathrm{E}} \hspace{0.33em} Unit power and energy investment cost of ES in province p

c_{na}^{\mathrm{I}\mathrm{N}\mathrm{V}-\mathrm{A}\mathrm{C}/\mathrm{D}\mathrm{C}} \hspace{0.33em} Unit investment cost of the \mathrm{A} \mathrm{C} / \mathrm{D} \mathrm{C} transmission line between provinces p and q CINV-CG Unit investment cost of the i th cluster CG in c_{p,i} province p

c_{ni}^{\mathrm{I}\mathrm{N}\mathrm{V}-\mathrm{C}\mathrm{C}\mathrm{U}\mathrm{S}} \hspace{0.33em} Unit investment cost of the CCUS equipped p ” on the i th cluster CG in province p

Unit O&M costs of WT / \mathrm{P} \mathrm{V} in province p

Unit O&M costs of the AC/DC transmission 1 line between provinces p and q

Unit O&M cost of the i th cluster CG in p, r or province p

Unit power/energy O&M cost of ES systems p in province p

c_{\text{ ret }}^{\mathrm{C}\mathrm{G}/\mathrm{S}\mathrm{U}} \hspace{0.33em} Unit fuel/startup cost of the i th cluste p, t \hspace{0.33em} province p

c_p^{\mathrm{I}\mathrm{N}\mathrm{V}-\mathrm{P}2\mathrm{H}/\mathrm{H}\mathrm{S}} \hspace{0.33em} Unit investment cost of \mathrm{P} 2 \mathrm{H} / \mathrm{H} \mathrm{S} in province Unit O&M costs of \mathrm{P} 2 \mathrm{H} / \mathrm{H} \mathrm{S} in province p

C_n^{\mathrm{P}\mathrm{V}/\mathrm{W}\mathrm{T}\_\mathrm{M}\mathrm{A}\mathrm{X}} \hspace{0.33em} Maximum installed capacities of PV/WT in p or province p

C_{\text{ na }}^{\mathrm{A}\mathrm{C}/{\mathrm{D}\mathrm{C}}_{-}\mathrm{M}\mathrm{A}\mathrm{X}} \hspace{0.33em} Maximum installed \mathrm{A} \mathrm{C} / \mathrm{D} \mathrm{C} transmis Capacity between provinces p and q

C_n^{\mathrm{P}\mathrm{V}/\mathrm{W}\mathrm{T}\_\text{ exist }} Existing installed capacity of PV/WT in province p

C_{\mathrm{p},i}^{\mathrm{C}\mathrm{G}-\text{ exist }} \hspace{0.33em} Existing installed capacity of the i th cluster PR CG in province p

C_{\text{ ma }}^{\mathrm{A}\mathrm{C}/\mathrm{D}\mathrm{C}\_\text{ exist }} Existing AC/DC transmission capacity p q \hspace{0.33em} between provinces p and q

C_p^{\mathrm{H}\mathrm{G}/\mathrm{N}\mathrm{G}\_\text{ exist }} Existing \mathrm{H} \mathrm{G} / \mathrm{N} \mathrm{G} capacity in province p

D_{p,t}^{\mathrm{E}} \hspace{0.33em} Electric load in province p at time t

D_p^{\mathrm{H}} \hspace{0.33em} Annual hydrogen demand in province p

e_i^{\mathrm{C}\mathrm{G}} \hspace{0.33em} Carbon emission of the unit i th cluster \mathrm{C} \mathrm{G} in province p

{\rho }_{Dt}^{\mathrm{P}\mathrm{V}/\mathrm{W}\mathrm{T}} \hspace{0.33em} Unit output curves of \mathrm{P} \mathrm{V} / \mathrm{W} \mathrm{T} in province p at p , t time t

h^{\mathrm{N}\mathrm{G}/\mathrm{H}\mathrm{G}} \hspace{0.33em} Annual utilization hours of NG and \mathrm{H} \mathrm{G} in province p

T^{\mathrm{O}\mathrm{N}/\mathrm{O}\mathrm{F}\mathrm{F}} \hspace{0.33em} Minimum on/off time periods of i th clusterCG

N_{p,i}^{\mathrm{C}\mathrm{G}} \hspace{0.33em} Number of the i th cluster \mathrm{C} \mathrm{G} in province p

R^{\mathrm{d}/\mathrm{w}/\mathrm{p}} \hspace{0.33em} Forecasting errors of the electric load/WT output/PV output

{\alpha }_i^{\mathrm{R}\mathrm{u}/\mathrm{R}\mathrm{d}} \hspace{0.33em} Maximum upward/downward ramping ratio to online capacity of i th cluster CG

{\eta }^{\mathrm{P}2\mathrm{H}} \hspace{0.33em} \mathrm{P} 2 \mathrm{H} conversion efficiency

{\eta }^{\mathrm{E}\mathrm{S}+/-} \hspace{0.33em} ES charging/discharging efficiency

\phi \hspace{0.33em} Ratio of the annual renewable power generation to the annual power demand

{\lambda }_i^{\mathrm{C}\mathrm{G}} \hspace{0.33em} Minimum power generation levels of i th cluster CG

{\lambda }^{\mathrm{N}\mathrm{G}} \hspace{0.33em} Minimum power generation levels of NG

{\lambda }^{\text{ CCUS }} Capture rate of CCUS

{\rho }^{\text{ CCUS }} \hspace{0.33em} Required power for per tonne {\mathrm{C}\mathrm{O}}_2 capture and storage

\gamma \hspace{0.33em} Basic energy consumption rate of CCUS

\theta \hspace{0.33em} Carbon intensity of electrolytic hydrogen

C_n^{\mathrm{W}\mathrm{T}/\mathrm{P}\mathrm{V}} \hspace{0.33em} Newly installed capacity of PV/WT in p or province p

C_{na}^{\mathrm{A}\mathrm{C}/\mathrm{D}\mathrm{C}} \hspace{0.33em} Newly installed AC/DC transmission p q \hspace{0.33em} capacity between provinces p and q

C_{ni}^{\mathrm{C}\mathrm{G}} \hspace{0.33em} Newly installed power capacity of the i th p, cluster CG in province p

C_{\text{ ni }}^{\text{ CCUS }} \hspace{0.33em} Newly installed CCUS capacity of the i th Pre cluster CG in province p

Capacity of the i th cluster CG with CCUS in

C_{nj}^{{\mathrm{C}\mathrm{G}}_{-}\mathrm{C}\mathrm{C}\mathrm{U}\mathrm{S}} \hspace{0.33em} province p

C_n^{\mathrm{E}\mathrm{S}\mathrm{P}/\mathrm{E}\mathrm{S}\mathrm{E}} \hspace{0.33em} Newly installed ES power/energy capacity in province p

C_n^{\mathrm{P}2\mathrm{H}/\mathrm{H}\mathrm{S}} \hspace{0.33em} Newly installed power capacity of the P2I HS in province p

P_{\text{ nit }}^{\mathrm{C}\mathrm{G}} \hspace{0.33em} Power output of the i th cluster \mathrm{C} \mathrm{G} in province p at time t

P_{\text{ nit }}^{\mathrm{C}\mathrm{G}-\mathrm{C}\mathrm{C}\mathrm{U}\mathrm{S}} \hspace{0.33em} Power output of the i th cluster \mathrm{C} \mathrm{G} wit {}^{p,t,c} CCUS in province p at time t

P_{\text{ Dift }}^{\mathrm{C}\mathrm{G}-\mathrm{C}\mathrm{C}\mathrm{U}\mathrm{S}\mathrm{*}} \hspace{0.33em} Net power output of the i th cluster \mathrm{C} \mathrm{G} w CCUS in Province p at time t

P_{p,t}^{\mathrm{P}\mathrm{V}/\mathrm{W}\mathrm{T}} \hspace{0.33em} Power output of \mathrm{P} \mathrm{V} / \mathrm{W} \mathrm{T} in province p at p , t time t

P_{p,t} P^{\mathrm{H}\mathrm{G}/\mathrm{N}\mathrm{G}} \hspace{0.33em} Power output of \mathrm{H} \mathrm{G} / \mathrm{N} \mathrm{G} in province p at p , t time t

r_{p,t} P_{nt}^{\mathrm{P}2\mathrm{H}} \hspace{0.33em} Power consumed by \mathrm{P} 2 \mathrm{H} in province p at p , t time t

P_{\text{ net }}^{\mathrm{E}\mathrm{S}+/-} \hspace{0.33em} Charging/discharging power of the ES p, t system in province p at time t

P_{\text{ par }}^{\mathrm{A}\mathrm{C}} \hspace{0.33em} Transmission power of \mathrm{A} \mathrm{C} transmission p q, between provinces p and q at time t

P_{\text{ post }}^{\mathrm{D}\mathrm{C}\mathrm{s}} \hspace{0.33em} Transmission power of DC transmission line p q, t \hspace{0.33em} from province p to q at time t

P_{\text{ Par }}^{\mathrm{D}\mathrm{C}\mathrm{r}} \hspace{0.33em} Transmission power of DC transmission line [P], t from province q to p at time t

S_{nt}^{\mathrm{E}\mathrm{S}} \hspace{0.33em} Stored electricity of ES in province p at time t

r_{p,t}^{\mathrm{E}\mathrm{S}} \hspace{0.33em} Reserve power of ES in province p at time t

O / SU / {\text{ SD }}_{\text{ ret }}^{\text{ CG }} \hspace{0.33em} Online/startup/shutdown capacity of i th ’ cluster CG without CCUS in province p at time t

O / SU / {\text{ SD }}_{\text{ nier }}^{{\text{ CG }}_{-}\text{ CCUS }} \hspace{0.33em} Online / startup / shutdown capacity of i th cluster CG with CCUS in province p at time t