Assessment of plum rain’s impact on power system emissions in Yangtze-Huaihe River basin of China

As a typical climate that occurs in the Yangtze-Huaihe River basin of China with a size of 500,000 km2, plum rain can reduce the photovoltaic (PV) potential by lowering the surface irradiance (SI) in the affected region. Based on hourly meteorological data from 1980 to 2020, we find that plum rain can lower the SI in the affected region with a weekly peak drop of more than 20% at the most affected locations. This SI drop, coupled with a large number of deployed PV systems, can cause incremental CO2 emissions (ICEs) of local power systems by increasing the additional thermal power. Using a cost optimization model, we demonstrate that the ICEs in 2020 already reached 1.22 megatons and could range from 2.21 to 4.73 megatons, 3.47 to 7.19 megatons, and 2.97 to 7.43 megatons in 2030, 2040, and 2050, respectively, considering a change trend interval of a ±25% fluctuation in power generation and demand in the different years. To offset these ICEs, we compare four pathways integrated with promising technologies. This analysis reveals that the advanced deployment of complementary technologies can improve the PV utilization level to address climate impacts.


Supplementary Note 1. Detailed description of Global Solar Energy Estimator (GSEE) model 2
According to the study by Pfenninger et al 2 , the power output of PV modules depends on the in-plane irradiance G and module temperature Tmod: where P PV STC is the power output at standard test conditions (STC) with in-plane irradiance GSTC of 1000W/m 2 and module temperature Tmod_STC of 25 °C. The hourly instantaneous relative efficiency ηrel, depending on the instantaneous irradiance and temperature, is given by 7 where α is the plane incidence angle, calculated by (1g) with a fixed tilt angle. as is the sun azimuth angle, a is the surface albedo (a=0.3).
( ) = arccos sin( ) cos( ) cos( ) sin( ) cos( ) where h is sun altitude, ap is panel azimuth, and as is sun azimuth angle. Σ is the plane tilt in degrees, calculated by where lat is the latitude in degrees. Considering that the plum rain-affected areas occur near latitude 30°N, we set the optimum tilt angle of the fixed-tilt system to 26.6 degrees, following the study by Chen et al. 8 In the end, the system loss is set to the default value of 0.1.

Supplementary Note 2. Comparison of various pathways.
Based on the above optimization results, we further compare four pathways in offsetting the incremental CO2 emissions caused by plum rain. First, we use the C ES , which is obtained in the first optimization, as a known quantity in the following optimization model to eliminate the influence of electric storage. Then, we also add the calculated ΔE and PV reduction ΔP PV caused by plum rain in the following optimization model to measure the capacity required for each pathway.
The PV reduction ΔP PV can be calculated as are the actual output power of l1-th PV generator in the affected region at the first and second optimization, respectively.

1) Coal power to natural gas power (C2N)
The objective function is revised as follows: where ′ X is the decision variable set X that does not contain C ES , C is the total cost expressed in formula (2) in the main manuscript, except that C ES is a known quantity.
In the original clustered unit commitment (CUC) model (2)-(17) of the main manuscript, the following carbon emission constraints are added to offset the incremental CO2 emissions by converting coal power to gas power.
where (2) E is the CO2 emissions in the second optimization removing the negative effects of plum rain.

2) Demand response (DR) program
First, adding the total DR cost in the objective function: where P DR (t) is the load curtailment at time t, and c DR is the unit compensation cost for DR program. Then, using constraint (4b) to replace constraint (3) in the main manuscript, and adding the following constraints (4c-4e) in the CUC model.
Equation (4b) defines the supply and demand power balance considering DR program. Constraint (4c) bounds the minimum and maximum outputs of DR program, where β denotes the proportion of load curtailment to the total electric load. Constraint (4d) imposes the total load curtailment during the plum rain period less than the PV reductions. In the end, CO2 emission constraint (4e) is added to offset the incremental CO2 emissions.

3) Carbon capture, utilization and storage (CCUS)
Similarly like DR program, the objective function is changed as where P CCUS is the power capacity of coal generators installed with CCUS, and c CCUS is the capture cost per one unit of electricity. Then, using constraint (5b) and (5c) to replace constraints (3) and (4) in the main manuscript, and adding the following constraints (5d)-(5f) in the clustered unit commitment model.
Equations (5b) and (5c) show the power balance and system reserve requirements considering CG with CCUS, respectively, where η CCUS is the CCUS equipment efficiency, σ CCUS is the ratio of consumed power by CCUS equipment. Constraint (5d) imposes the clean energy produced by plum rain period less than the PV reductions. In the end, CO2 emission constraint (5e) is added to offset the incremental CO2 emissions.

4) Long-duration (LD) energy storage
Similarly, the objective function of the UC model considering long-duration storage integration is given as follows: where P LD max and S LD max are the installed power capacity and energy capacity of LD, respectively. c LD P and c LD E are the power capacity cost and energy capacity cost of LD, respectively. r and n LD are the discount rate and lifetime of LD, respectively.
Then, using constraint (6b) to replace constraint (3) in the main manuscript, and adding the following constraints (6c)-(6g) in the CUC model.  Equation (6b) defines the supply and demand power balance considering LD storage. Constraints (6c)-(6f) impose power capacity and energy constraints, respectively, on the charging, discharging, and storage levels of LD storage, where P LD+/-(t) is the hourly charging/discharging power of LD storage, S LD (t) is the hourly storage levels of LD storage, and η LD+/is the charging/discharging efficiency of LD storage. Constraints (6g) guarantees that the LD stores enough energy before the rainy season. Constraint (6h) imposes the net released energy during the plum rain period less than the PV reductions. In the end, CO2 emission constraint (6i) is added to offset the incremental CO2 emissions.