Joint Operation Modes and Economic Analysis of Nuclear Power and Pumped Storage Plants under Different Power Market Environments

Abstract

Given the continuous promotion of power market reforms, the joint operation modes and economic analysis of nuclear power and pumped storage hydropower under different market mechanisms are the key to ensuring the low-carbon and economic operation of the power system. First, this study constructed the power expansion optimization model and put forward the allocation ratio by combining the operation characteristics of nuclear power and pumped storage. Second, a simulation model for the joint operation was established to optimize their operation modes. Finally, the joint operation modes and a method for calculating profitability under different power market mechanisms were proposed. A case study in the FJ power grid reveals that the joint operation of nuclear power and pumped storage can increase the annual utilization hours of nuclear power by 1000 h, reduce the operation cost of pumped storage, and increase the market competitiveness of the system. With the improvement in the power market, the joint financial internal rate of return of the system would increase gradually to 11.40% in the long-term mature market. This indicates that the power market reforms would ensure the profitability of the joint operation of nuclear power and pumped storage.

1. Introduction

In response to the growing energy demand and increasingly serious environmental issues, China is vigorously developing clean power sources such as wind, photovoltaic, hydroelectric, and nuclear power. While wind and solar power are important renewable energy sources, they are unstable due to climate impacts; nuclear power generation can serve as a stable base-load energy source and provide stable zero-carbon energy. Therefore, it is important to develop nuclear power under the vision of carbon neutrality. By the end of 2020, China had 54 operational nuclear reactors with a total net capacity of 52.2 GW, ranking third in the world after the United States and France, but the share of nuclear power generation account for 4.9% of the country’s electricity, which is lower than the world average of 10% [1]. There is still spacious room for the development of nuclear power in China. According to the National Development and Reform Commission, China aims to have 200 GW of nuclear power generating capacity in place by 2035, out of a total generating capacity of 2600 GW. In the process of power development, there is a need to fully analyze and demonstrate a reasonable power supply economics, reasonable structure, and scale [2]. Nuclear power is characterized by high construction costs and low operating (fuel) costs. The start-up and shutdown of nuclear power require long intervals due to its inherent characteristics, and frequent power regulation may create safety hazards, cause fuel underutilization, and reduce the economic output of the unit. Therefore, nuclear power is more suitable for maintaining the base-load of the power system. However, with the rapid development of the economy and society, the peak-to-valley difference of the power system load is getting larger and larger, making peak regulation more and more difficult. In order to realize the safe and economical operation of nuclear power in the power system, additional peak shaving measures are urgently needed [3,4,5,6].

Presently, pumped storage hydropower plants are the most widely used energy storage and regulation power source, with a total installed capacity of more than 170 GW, accounting for over 90% of the global grid-connected energy storage [7,8]. These feature flexible operation modes, rapid load regulation, and multiple auxiliary service functions. Compared with other energy storage technologies, pumped hydro storage has the advantages of high efficiency, large capacity, long lifetime, and high safety. In the power system, it can cooperate with low-carbon energy sources such as nuclear power, wind power, and photovoltaic power to ensure safe, stable, and economic operation [9,10,11,12].

Considering the operating characteristics of nuclear power and pumped storage power plants, nuclear power is suitable for operation with a base-load, whereas pumped storage mainly helps maximize capacity benefits. Their joint operation can more effectively satisfy the requirements of the power system [13,14]. Prior studies discussed that the joint operation of nuclear power and pumped storage can satisfy the peak shaving demand of a power grid and ensure the stable operation of nuclear power for the base-load [15,16]. Furthermore, certain studies indicated that the joint operation of nuclear power and pumped storage can reduce the marginal cost of nuclear power over generations and improve the economic advantages of power systems [17]. However, the economic operation of nuclear power and pumped storage power plants can be affected straightforwardly by the power market environment. The market-oriented reform of China’s power market is in its infancy. There is no reasonable business model or mechanism to ensure the profitability of pumped storage stations because of many factors such as investment and financing, planning, an electricity price policy, and an interest mechanism. The development of pumped storage significantly lags behind that of other power sources [18]. However, with the gradual reform of the Chinese electricity market, few studies have investigated the operation of nuclear power and pumped storage under different electricity market environments. Therefore, the joint operation modes of nuclear power and pumped storage and their profitability under different market mechanisms need to be analyzed further [19,20]. Considering factors such as load demand, shipping transportation, and operational safety, nuclear power development in China is mainly concentrated in the eastern coastal areas. This study was designed to develop nuclear power in coastal areas where traditional energy is scarce and use pumped storage as the main regulating power source. Considering the complex fluctuation characteristics of variable wind power and photovoltaic power sources [21], many studies have been conducted on their coordinated operation with pumped storage hydropower [22,23,24]. This study did not consider wind and photovoltaic energy, but instead focused on the joint operation of nuclear power and pumped hydropower.

Based on the YX pumped storage power plant and the ZZ nuclear power station in the FJ power system in the coastal area, this study analyzed the present power system and the prospect of future power market reforms. It also studied the complementary operation modes and corresponding profitability of nuclear power and pumped storage power plants under different power market environments. First, power structure optimization and the allocation of nuclear power and pumped storage capacity were analyzed. Second, the joint operation mode of nuclear power and pumped storage was studied in conjunction with the power configuration and load characteristics of the power grid. Finally, considering the projected development path of the power market, the study analyzed the joint operation modes of nuclear power and pumped storage under the present planned dispatching mode and the short-term, medium-term, and long-term power market environments. It also calculated the profitability of the system and analyzed the impact of different joint operation models on its profitability.

The main contributions and innovations of this paper are as follows: (1) the economic benefit of the joint operation of nuclear power and pumped storage was analyzed and demonstrated. It has important theoretical significance for achieving the efficient operation of nuclear power and pumped storage power plants, promoting energy restructuring, and building economic and clean energy systems. (2) The power market environment has an important impact on the operation mode and economic benefits of nuclear power and pumped storage, so the study analyzed the joint operation modes of nuclear power and pumped storage under the present planned dispatching mode and the short-term, medium-term, and long-term power market environments. It provides a reference for the operation of nuclear power and pumped storage under the situation of power market reform.

2. Materials and Methods

2.1. Research Framework

An economic analysis model of the joint operation of nuclear power and pumped storage was constructed. In addition, the optimal joint operation scheme was analyzed on the premise of satisfying the power demand of the system. The model has a three-layer structure: power expansion optimization, joint operation simulation, and economic analysis under different market mechanisms.

(1) Power expansion optimization model. The scale allocation of nuclear power and pumped storage is optimized based on the power demand and power supply structure in each planning period to minimize the present value of the project investment and the total operation cost of the entire system (including the power plants constructed before the planning period) [25]. This provides a reasonable scale configuration scheme for the lower model.

(2) Joint operation simulation model. To minimize the total fuel consumption for system operation, the operation mode of various power sources in the power system is optimized, and the location, operation mode, and utilization hours of pumped storage and nuclear power plants are determined.

(3) Economic analysis model under different market mechanisms. The operation modes of nuclear power and pumped storage are combined, and the joint operation modes and profitability are analyzed under four market mechanisms: the present planned dispatching mode, short-term power-market reform mode, medium-term relatively mature market mode, and long-term mature market mode.

2.2. Optimization Model for Power Expansion

The power expansion optimization model combines the operation characteristics of various types of power supplies. The present value of the investment of each project in the system and the total operation cost of the entire system (including the power plants constructed before the planning period) are minimized to satisfy the economic and social demand for power consumption in each division within the planning period of the power system. Thereby, it can realize the optimal sizes of pumped storage and nuclear power in the power system. The objective of the model is to minimize the present value of the total cost in the calculation period of the entire system.

$$C=Min{\displaystyle \sum }_{t=1}^T(C_t{\left(1+r\right)}^{-t})$$

(1)

$$C_t={\displaystyle \sum }_{h=1}^{H}C{P}_{h,t}+{\displaystyle \sum }_{i=1}^{I}C{U}_{i,t}+{\displaystyle \sum }_{j=1}^{J}C{Y}_{j,t}+{\displaystyle \sum }_{k=1}^{K}C{W}_{k,t}+{\displaystyle \sum }_{l=1}^{L}C{S}_{l,t}+{\displaystyle \sum }_{m=1}^{M}C{C}_{m,t}+{\displaystyle \sum }_{n=1}^{N}C{Z}_{n,t}$$

(2)

where $C$ is the present value of the total system cost; $T$ is the calculation period;$C_t$ is the total system cost of the period $t$; $r$ is the social discount rate. $C{P}_{h,t}$, $C{U}_{i,t}$, $C{Y}_{j,t}$, $C{W}_{k,t}$, $C{S}_{l,t}$, $C{C}_{m,t}$, and $C{Z}_{n,t}$ are the sum of all costs in period t for the pumped storage $h$, the $j$ nuclear power $i$, the hydropower, the wind power $k$, the solar power $l$, the thermal power $m$, and the other types of power plants $n$, respectively; $H$, $I$, $J$, $K$, $L$, $M$, and $N$ are the total numbers of pumped storage, nuclear power, hydropower, wind power, solar power, thermal power, and other types of power plants, respectively.

The constraints to be considered in the model-solving process include the following: the balance of power consumption in each division, the operating capacity of power plants, the balance of reserve capacity of the entire system, the minimum output of thermal power technology, peak shaving capacity and rotating reserve of base-load thermal power, guaranteed power of hydropower plants, blocked output of hydropower plants, pumping and generating power of pumped storage stations, power balance, reservoir capacity, pumping, and generation hour control.

When multiple pumped storage power plants need to be constructed for the planned system, the sequencing of power sources in the power system becomes complex. Pumped storage power plants can neither be sequenced in conjunction with nuclear power plants nor optimized separately. These should be optimized in conjunction with nuclear power plants. Therefore, pumped storage power plants and nuclear power plants are sequenced by the decomposition coordination method. The solution steps in this method are as follows: (i) preliminarily determine the commissioning time of pumped storage power plants. When the advantages, investment, and operation costs are determined, the objective function of minimizing the present value of the total cost of the power system in the main model is transformed into the minimization of the present value of the cost of nuclear power plants. (ii) Optimize the commissioning time of nuclear power plants to minimize the cost of thermal power plants. (iii) Conduct production simulations to calculate the investment, operating costs, and fuel costs of pumped storage and nuclear power plants for the entire planning period. (iv) Gradually optimize the commissioning time of pumped storage power plants. Repeat the above three steps to minimize the total cost of system power generation capacity expansion.

2.3. Joint Operation Simulation Model

The joint operation simulation model with nuclear power and pumped storage stations focuses on the entire power system and considers the operating characteristics of various types of power plants. It simulates the typical 24 h power generation dispatch of the power system month-by-month throughout the year, and determines the best working position and capacity of each power plant on the daily load curve of the system. In this process, priority is given to the power delivery of renewable energy sources such as wind power. First, the maintenance capacity of nuclear power plants and thermal power units in the system is arranged for each period of the year, and the available capacity of each unit is determined. Considering the rotating reserve of the system, the starting capacity of various types of nuclear power and thermal power is allocated according to the optimization principle. Then, the daily load economic distribution method of the power system is used to optimize the operation mode of the pumped storage station, and the annual fuel cost of nuclear power plants and thermal power plants is determined.

The economic distribution of the daily load of the power system is the realization of the optimal energy conservation and emission reduction of the entire system to achieve a power balance of the entire system and each division. The objective function is to minimize the total fuel consumption $Coal$ of the system:

$$Coal=Min{{\displaystyle \sum }}_{j=1}^{24}{{\displaystyle \sum }}_{i=1}^K{N}_{j,i}\cdot C_{j,i}$$

(3)

where $K$ is the total number of various types of units in the system; $N_{j,i}$ is the output of unit $i$ in period $j$; $C_{j,i}$ is the coal consumption rate or nuclear fuel consumption rate of the unit $i$ in period $j$. Its value is related to $N_{j,i}/R_j$,$R_i$ is the unit starting capacity of unit $i$.

The constraints to be satisfied for the joint operation of the system are

$${{\displaystyle \sum }}_{i=1}^K{N}_{j,i}=N{P}_j$$

(4)

$$X_{min}^i\le N_{j,i}/R_i\le X_{max}^i (i=1,2,\dots ,n)$$

(5)

where $N{P}_j$ is the total load carried by thermal or nuclear units in period $j$; $X_{max}^i$ and $X_{min}^i$ are the maximum and minimum technical output coefficients for the unit $i$, respectively.

The Lagrange multiplier method is used to solve the above conditional extreme value problem when only the first constraint exists. The following equation can be obtained:

$$\frac{\partial \left(N_{j,1}\cdot C_{j,1}\right)}{\partial N_{j,1}}=\frac{\partial \left(N_{j,2}\cdot C_{j,2}\right)}{\partial N_{j,2}}=\dots \dots =\frac{\partial \left(N_{j,n}\cdot C_{j,n}\right)}{\partial N_{j,n}}=\Delta C$$

(6)

The above equation expresses the principle of an equal micro increase rate of coal consumption. The solution of the equation becomes complex owing to the above technical output constraints of the unit. It is difficult to satisfy the requirements of the equation. In the calculation, the approximate micro increase rate equivalence principle is used to allocate the output capacity contributed by each type of thermal power unit for each hour. Based on the output allocation, the coal consumption of each type of thermal unit is calculated according to its coal consumption curve. The total fuel cost of thermal (nuclear) units for each hour is calculated according to the coal price for the power plant. Furthermore, the total annual fuel cost of the system is determined by adding the fuel costs for each hour.

2.4. Economic Analysis of Joint Operation of Nuclear Power and Pumped Storage

An economic analysis of the joint operation of nuclear power and pumped storage should consider the present planned dispatching mode and the projected power market environments. Presently, China is undertaking substantial efforts to promote power market reforms. The economic operation period of nuclear power plants and pumped storage power plants would span the present planned dispatching stage. In addition, it would transition gradually into the relatively mature market stage and eventually the mature market stage [12,13]. Therefore, it is necessary to analyze the present planned dispatching mode, short-term power market environment, and long-term power market environment that would gradually attain maturity after the reform. Then, the study should be extended to the joint operation modes of nuclear power plants and pumped storage and their profitability under four power systems: the present planned dispatching mode, short-term power market reform mode, medium-term relatively mature market mode, and long-term mature market mode after the market reform is completed.

2.4.1. Analysis of Joint Operation Modes of Nuclear Power and Pumped Storage

(1)

Present independent operation mode

At present, China stipulates a two-part price system for pumped storage that has been commissioned newly or commissioned without an approved price, i.e., capacity price and energy price. The dispatching of pumped storage power plants is under the unified management of the power grid. The pumping power is provided by the power grid, and the pumping power price is fixed as 75% of the benchmark on-grid price of coal-fired units. In addition, the peak-valley price difference is marginal, and the compensation mechanism for auxiliary service has not been established. Thus, it is difficult to realize the economic advantages of pumped storage without a low pumping power price and reasonable capacity price. In addition, the peak shaving pressure on the power grid is becoming more severe owing to the large peak-valley load difference of the power grid and the gradual increase in the proportion of installed new energy such as wind power. Furthermore, the annual utilization hours of nuclear power plants are decreasing annually. Pumped storage and nuclear power plants adopt the independent operation mode because of being limited by the present power system.

(2)

Short-term joint operation mode

The capacity price of pumped storage has been implemented gradually with the implementation of the two-part price system. However, the low-capacity price cannot fully reflect the capacity service function provided by pumped storage. The power generation revenue of a pumped storage power plant is essentially equal to the pumping cost because of its power generation efficiency of 75% and the “75% benchmark on-grid price of coal-fired units for pumping power price” rule. To improve the economic advantages, pumped storage power plants can obtain pumping electricity at a lower price by purchasing the excess power generated by nuclear power plants to realize a certain amount of electricity revenue. Nuclear power plants can increase the load factor by “leasing” the pumped storage capacity. In addition, these can increase the utilization hours of power generation and reduce the cost per unit kW·h by selling low-cost excess power to pumped storage power plants.

(3)

Medium-term joint operation mode

In the medium term, the power market would improve gradually with the deepening of power system reforms. Pumped storage power plants can be operated jointly with nuclear power plants. In the valley period, pumped storage power plants can use the excess power of the nuclear power plant (at a price lower than the grid price) to pump water and generate power in the peak period to earn an adequate investment income. In addition, the participation of pumped storage in load peak shaving can alleviate the pressure on the power system to a certain extent, and substantially improve the power generation and utilization hours of the nuclear power plant. In addition to providing economic advantages, it ensures the safe and stable operation of nuclear power units and realizes effective cooperation between pumped storage and nuclear power.

(4)

Long-term joint operation mode

In the long term, under the fully market-oriented mode, nuclear power plants and pumped storage power plants can participate in the power market simultaneously. Pumped storage power plants can adopt certain offer strategies while competing in the market because their excess power price has a competitive advantage. Simultaneously, the nuclear power plant can obtain reasonable economic advantages while ensuring safe operation, owing to the excess power generated. The joint investment and operation of nuclear power and pumped storage can effectively improve the utilization rate of pumped storage while safeguarding the operation of nuclear power plants for the base-load. Moreover, the output curve of the joint operation of nuclear power and pumped storage can better conform to the system load characteristics and improve the quality of power output.

2.4.2. Model for Calculating Financial Profitability from Joint Operation of Nuclear Power and Pumped Storage

Based on the operating modes of nuclear power and pumped storage in different power market environments, the financial internal rate of return (FIRR) on capital funds is used to represent the financial profitability of nuclear power and pumped storage, and the FIRR calculation models for nuclear power and pumped storage in different operating modes are established. The FIRR represents the discount rate for which the present value of the net cash flows over the project calculation period is cumulatively equal to zero. The financial profitability of the project is high when the FIRR is greater than or equal to the set benchmark financial rate of return ($i_c$). The FIRR of pumped storage and nuclear power plants is related to their electricity tariffs, and the FIRR of a project can be calculated for a given tariff, while the electricity tariff can be derived by inverse extrapolation when the financial target rate of return or the financial benchmark rate of return is given. The FIRR for pumped storage, nuclear, and their joint operation can be calculated by the following equations (Equations (7)–(9)). The three equations are: solve for the FIRR of pumped storage using the known electricity price of pumped storage (Equation (7)); solve for the FIRR of the nuclear power plant using the known electricity price of nuclear power (Equation (8)); and solve for the joint FIRR of nuclear power and pumped storage plants using the known electricity price of both power plants (Equation (9)), respectively.

$$\underset{FIR{R}_p}{\arg }\left\{{\displaystyle \sum }_{t=1}^T{\left(C_a\cdot P_1+E_f\cdot P_2-E_{cn}\cdot P_3-E_{cd}\cdot P_4-C{O}_p\right)}_t\cdot {\left(1+FIR{R}_p\right)}^{-t}=0\right\}$$

(7)

$$\underset{ FIR{R}_u}{\arg }\left\{{\displaystyle \sum }_{t=1}^T{\left(E_a\cdot P_5+E_{cn}\cdot P_3+E_{dd}\cdot P_4-C{O}_u\right)}_t\cdot {\left(1+FIR{R}_u\right)}^{-t}=0\right\}$$

(8)

$$\underset{FIR{R}_{pu}}{\arg }\left\{{\displaystyle \sum }_{t=1}^T{\left(C_a\cdot P_1+E_f\cdot P_2+E_a\cdot P_5+E_{cn}\cdot P_3+E_{dd}\cdot P_4-E_{cn}\cdot P_3-E_{cd}\cdot P_4-C{O}_p-C{O}_u\right)}_t\cdot {\left(1+FIR{R}_{pu}\right)}^{-t}=0\right\}$$

(9)

The benefits of pumped storage are mainly through the benefits of providing the power capacity and electricity for the power grid minus the cost of pumping and other consumption. In Equation (7), $FIR{R}_p$ is the financial internal rate of return of pumped storage; $P_1$, $P_2$, $P_3$, and $P_4$ are the capacity price, energy price, pumping power price from nuclear power, and pumping power price from the grid, respectively, for the pumped storage station, and the electricity price of each part can be changed with the electricity market environment and power supply quality; $C_a$, $E_f$, $E_{cn}$, and $E_{cd}$ are the on-grid capacity, on-grid energy, pumped energy from nuclear power, and pumped energy from the grid, respectively, which are mainly determined by the operation process of pumped storage in the power system (Section 2.3 and Section 2.4.1); $C{O}_p$ is cash outflows of pumped storage; T is the project calculation period. In Equation (8), $FIR{R}_u$ is the IRR of the nuclear power plant; $E_a$, $E_{cn}$, and $E_{dd}$ are the planned on-grid energy, pumping energy supplied to the pumped storage station, and energy supplied to the grid, respectively, for the nuclear power plant; $P_5$, $P_3$, and $P_4$ are the planned on-grid price, pumping power price for the pumped storage station, and energy price for the grid, respectively, for the nuclear power plant;$C{O}_u$ is the cash outflows of nuclear power plants. In Equation (9), $FIR{R}_{pu}$ is the joint financial internal rate of return of nuclear power and pumped storage power plants.

3. Case Study

3.1. Study Area

The installed power capacity of the FJ power system is shown in Figure 1. It can be seen that the FJ power system is dominated by thermal power (54% of the installed capacity), followed by hydropower and nuclear power. According to the information provided in the literature [26], the peak-valley difference has been increasing annually with the rapid increase in the power load in the FJ power grid. The maximum peak-valley difference in the entire province increased from 2294 MW in 2000 to 11,619 MW in 2018. At the same time, according to the information collected from the FJ power system, although the installed hydropower capacity in the province is large, the hydropower involved in peaking is less than half of the installed capacity of conventional hydropower. The use of thermal power for long-term deep peaking brings economic problems, while using nuclear power to meet the system peaking demand by lowering output operation also brings safety problems and poorer system operating conditions, which also has a greater impact on the safe and economic operation of the system. Pumped storage is acknowledged as the most economical peak shaving power supply at present. Its joint operation with nuclear power is the best option to fully utilize their respective advantages [13]. Considering the power system of FJ province as an example, this study discussed the joint operation mode and profitability of nuclear power and pumped storage in different power market environments.

3.2. Research Data

The planning period is set from 2020 to 2030 in accordance with the economic and social development plan of FJ province and the power development plan of FJ province. The main planning years are considered as 2025 and 2030. The total power consumption in 2020, 2025, and 2030 would be 258 billion kW·h, 320 billion kW·h, and 364.5 billion kW·h, respectively. The corresponding maximum power load would be 44.2 million kW, 57 million kW, and 66.2 million kW, respectively.

The earliest feasible commissioning time of each power plant is determined according to the preliminary work progress and construction period of each power plant as a constraint for power expansion. The thermal power units of the FJ power grid mainly include coal-fired thermal power and gas-fired units. The coal consumption curve of gas-fired units is converted into standard coal consumption using the standard coal price of 850 CNY/t, by referring to FJ power system current power investment information and considering future price trend changes. The cost of each project is shown in

Table 1. The cost of power sources in FJ power system.

Item	Investment Cost	Operating Costs
Coal power	4200 CNY/kW	850 CNY/t
Natural gas	3700 CNY/kW	2.7 CNY/m3
Nuclear power	15,000 CNY/kW	0.25 CNY/kW·h
Pumped storage power	4500 CNY/kW	112.5 CNY/kW

. The FJ power grid would focus on developing low-carbon and clean energy in the future. Therefore, thermal power was not considered as the alternative power supply in this study. The currently approved thermal power project can replace the small-scale thermal power plants in the system in the future to enhance the overall economic advantages of the system.

4. Results and Discussion

4.1. Calculation of Allocation Ratio of Nuclear Power and Pumped Storage in the Power Grid

The optimization results of power expansion of the FJ power system from 2020 to 2030 based on the aforementioned information are shown in

Table 2. Optimization results for power supply expansion of FJ power system.

Item	2020	2025	2030
Annual power demand (108 kW·h)	2580	3200	3645
Maximum annual load (104 kW)	4400	5700	6620
Installed capacity system (104 kW)	6373	7482	8729
Conventional hydropower (104 kW)	1190	1190	1190
Thermal power (104 kW)	3528	3528	3528
Wind power (104 kW)	555	780	1000
Nuclear power (104 kW)	980	1335	2331
Pumped storage (104 kW)	120	650	680

. The economic scale of pumped storage in 2025 would be 6.5 million kW, accounting for 8.68% of the total installed capacity. It would increase to 7.98 million kW in 2030, accounting for 9.14% of the total installed capacity. This indicates that pumped storage would have significant economic advantages in the future FJ power system. There is a substantial demand for peak shaving capacity in the FJ power system during the planning period, and pumped storage should be included in the power construction plan. According to economic criteria, the large-scale construction of pumped storage power stations will occur in 2025 and 2030. The increased installed capacity of nuclear power from 2020 to 2030 would be 11.24 million kW. This indicates that high-capacity nuclear power would be the main power source that would satisfy the future power demand in FJ province. There are many types of energy storage technology, and each has its own advantages and defects, according to the different ways of energy storage, which are mainly divided into mechanical energy storage, electrochemical energy storage, electromagnetic energy storage, chemical energy storage, and thermal storage, etc. However, at present, China’s only pumped storage large-scale (accounting for more than 90% of energy storage) economic applications are outside, chemical battery energy storage. Currently, there are still technical routes that are not very mature, high cost, and there are also safety risks, and compressed air. At present, the focus of research and development is on improving core devices, optimizing system design, developing new gas storage technology and equipment, and realizing modularization and the scale of equipment. According to the forecast, hydrogen storage is expected to become the most promising long-term energy storage technology in the future around 2050. At present, there is still a problem of high efficiency and low cost in the process of hydrogen production and use. Overall, on the basis of controlling the development of thermal power, it is more economical and effective to prioritize the development of pumped storage of a moderate scale while constructing nuclear power with large capacity units to expand the power supply of the FJ power system during the planning period.

According to the power expansion and optimization scheme of the FJ power grid from 2025 to 2030, and the power scales of various types in 2020, it can be determined that in 2025, with the installed capacity of wind power of 7.8 million kW, those of nuclear power and pumped storage would be 13.35 million kW and 6.5 million kW, respectively. The ratio of nuclear power to pumped storage would be 2.05:1. In 2030, with the installed capacity of wind power of 10 million kW, those of nuclear power and pumped storage would be 23.31 million kW and 6.80 million kW, respectively. The ratio of nuclear power to pumped storage would be 3.43:1.

To summarize, the FJ power grid plans to control coal power while vigorously developing clean energy such as nuclear power. In this context, it is necessary to configure a certain scale of pumped storage power plants. The development model with wind power, nuclear power, and pumped storage as the main incremental power sources can satisfy the future power demand and peak shaving capacity demand of the FJ power system. Considering the nuclear power to pumped storage ratio of 2.05–2.77:1, the ZZ nuclear power plant and YX pumped storage power plant in the area at a distance of 30 km were selected as the joint operation research objects. Their installed capacities are 4800 MW and 1800 MW, respectively, and the ratio is 2.67:1.

4.2. Analysis of Joint Operation Modes of Power System with Nuclear Power and Pumped Storage

Two simulation scenarios of the FJ power system in 2030 were set to compare the role of pumped storage power plants in the system. Scenario 1 represents the case with the ZZ nuclear power plant (4.8 million kW) and without the YX pumped storage power plant (0.0 million kW). Scenario 2 represents the case with both the ZZ nuclear power plant (4.8 million kW) and the YX pumped storage power plant (1.8 million kW). The results of the FJ power system operation in 2030 are shown in

Table 3. Simulation results of FJ power system operation in 2030.

Item	Scenario 1	Scenario 2
Maximum system load (104 kW)	6620	6620
Annual power demand (108 kW·h)	3645	3645
Total installed capacity (104 kW)	8729	8729
Conventional hydropower (104 kW)	1190	1190
Pumped storage (104 kW)	500	680
YX plant	0	180
Thermal power (104 kW)	3528	3528
Nuclear power (104 kW)	2511	2331
FQ + ND plants	1089	1089
ZZ plant	480	480
Additional nuclear power	942	762
Wind power (104 kW)	1000	1000
Annual total power generation (108 kW·h)	3756	3806
Conventional hydropower (108 kW·h)	386	386
Pumped storage (108 kW·h)	83	120
YX plant	0	30
Nuclear power (108 kW·h)	1760	1773
FQ + ND plants	763	807
ZZ plant	336	384
Additional nuclear power	661	581
Wind power (108 kW·h)	307	307
Annual generation hours of pumped storage (hours)	1660	1771
Annual generation hours of YX	0	1675
ZZ nuclear power (hours)	7000	8000
Increase the annual generation hours of ZZ nuclear power (hours)	-	1000

.

According to the simulation results of power system operation in the FJ province in 2030 with and without YX pumped storage, the utilization hours of the ZZ nuclear power plant in Scenario 1 are 7000 h, and the power generated is 33.6 billion kW·h. Meanwhile, in Scenario 2 with the joint operation of the YX pumped storage and ZZ nuclear power, the annual power generation hours of the ZZ nuclear power attain 8000 h, and the power generated is 38.4 billion kW·h. The annual power generation hours of the YX pumped storage are 1675 h, and the daily power generation hours are 5 h. A comparison between Scenarios 1 and 2 shows that the YX pumped storage can replace 1.8 million kW of nuclear power. While satisfying the peak shaving demand of the power system, the ZZ nuclear power plant is in the optimal operating state, and its annual power generation hours increase by 1000 h. Compared with Scenario 1, Scenario 2 increases the storage power plant by 1800 MW more, which can make the installed nuclear power capacity reduced from 25.11 million kW in Scenario 2 to 23.31 million kW, and the nuclear power plant reduced by 1.8 million kW. The results show that nuclear power can ensure the base-load operation status, increase the generation hours, and ensure operational safety and economic performance by operating in conjunction with pumped storage power plants.

4.3. Economic Analysis of Joint Operation of Nuclear Power and Pumped Storage in Different Power Market Environments

4.3.1. Present Planned Dispatching Mode

Nuclear power and pumped storage adopt an independent operation model under the present planned market mode. According to the two-part tariff system, the energy price of a pumped storage power plant is based on the on-grid price, whereas the capacity price is estimated based on the value of auxiliary services such as standby, frequency, and phase regulation. The on-grid capacity and power generation of pumped storage power stations are independent variables. This is equivalent to option 2 in Section 4.2, where 4.8 million kW of nuclear power and 1.8 million kW of pumped storage are operated jointly. The on-grid price of the YX pumped storage power plant is the benchmark on-grid price of a coal-fired unit in FJ province (0.3737 CNY/kW·h). The pumping power price (including tax) is 75% of the benchmark price, i.e., 0.28 CNY/kW·h (also the on-grid price of base-load thermal power plant). The YX pumped storage power plant generates electricity for 5 h each day. Its internal rate of return on capital is 6%, and the capacity price is 562 CNY/kW·year.

The total investment for the fixed assets of the ZZ nuclear power plant is 64.8 billion CNY. The power generation hours are 7000 h within the average annual operation plan, and the on-grid price in the economic period is calculated as 0.43 CNY/kW·h (“Notice on improving the nuclear power tariff mechanism” (No. 1130 [2013] of the National Development and Reform Commission)) to satisfy the requirements of FIRR. The internal rate of return of capital when the actual power generation hours are 6000 h, 6500 h, and 7000 h is estimated to be 5.51%, 7.02%, and 8.59%, respectively.

4.3.2. Short-Term Joint Operation Mode

Pumped storage power plants are permitted to receive pumping electricity at a price lower than 75% of the on-grid price under the short-term joint operation mode. The nuclear power plants are permitted to provide low-cost excess power to pumped storage power plants. According to the national policy (“Notice on improving the nuclear power tariff mechanism” (No. 1130 [2013] of the National Development and Reform Commission)), the on-grid price for nuclear power plants is 0.43 CNY/kW·h for up to 7000 h of power generation. The variable cost of power generation after 7000 h is the cost of additional power generation, including nuclear fuel cost, material cost, water cost, and nuclear emergency cost. The incremental power generation cost is 0.097 CNY/kW·h. It can be considered as the lower limit of the price of pumping power supplied to pumped storage power plants by nuclear power plants. Its value is proposed to be 0.10 CNY/kW·h. The upper limit of this price is 75% of the benchmark on-grid price of coal-fired units, i.e., 0.28 CNY/kW·h (on-grid price of base-load thermal power). Therefore, the price range of the excess nuclear power provided as pumping power is 0.10–0.28 CNY/kW·h. Herein, eight schemes are proposed considering 0.03 CNY/kW·h as the step-size: 0.10 CNY/kW·h, 0.13 CNY/kW·h, 0.16 CNY/kW·h, 0.19 CNY/kW·h, 0.22 CNY/kW·h, 0.25 CNY/kW·h, and 0.28 CNY/kW·h.

The relationship between pumping price and the profitability of each power source under the short-term power market environment is shown in Figure 2. The coordinate origin of Figure 2 (0.28) represents the independent operation mode of nuclear power and pumped storage. In this mode, the utilization hours of nuclear power generation are 7000 h, which have no effect on the profitability of pumped storage power plants. The FIRRs of the nuclear power plant and pumped storage power plant are 8.59% and 6.00%, respectively, and the FIRR of the two power sources combined is 8.30%. When the utilization hours of the nuclear power plant attain 8000 h after overgeneration, the FIRR of the pumped storage power plant increases from 6.00% to 16.83% as the pumping power price supplied by the nuclear power plant decreases from 0.28 CNY/kW·h to 0.10 CNY/kWh. That is, the nuclear power plant provides the excess power to the pumped storage power plant as low-cost pumping power. Thereby, the pumped storage power plant can harvest the capacity income as well as obtain a certain amount of power generation income. In addition, the FIRR of the nuclear power plant is significantly higher than that in the case of a stand-alone operation when the utilization hours are increased with the aid of the pumped storage power plant. Overall, the joint financial profitability can be increased to 10.49% by implementing the joint operation of nuclear power and pumped storage. This has a positive effect on the economic performance of the joint operation system.

4.3.3. Medium-Term Joint Operation Mode

Considering the continuous advancement of power market reforms, the peak-valley differential price is implemented on the generation side of the power system in the medium term. The excess power generated by the nuclear power plant can be provided as pumping power directly to the jointly operated pumped storage power plant. When the pumped storage power plant is equivalent to the thermal power unit and operates at the peak load, its on-grid price can be equal to that of the thermal power plant. In order to analyze the peak load electricity price, the FJ thermal power station of the same scale has an installed capacity of 1.8 × 10⁷ kW. Its construction period is 3 years, and the production and operation period is 30 years. The fixed asset investment is 4200 CNY/kW, and the capital is 25% of the total project investment. The on-grid price (i.e., the on-grid price of pumped storage) when the thermal power operates at the peak load is 0.8540 CNY/kW·h. This enables its FIRR to attain the benchmark rate of return of 8%.

The relationship between pumping price and the profitability of each power source under the medium-term power market environment is shown in Figure 3. Overgeneration does not occur when the utilization hours of nuclear power generation are 7000 h (independent operation mode of nuclear power and pumped storage). The FIRR is 8.59% for nuclear power plants and 11.32% for pumped storage power plants. This yields an FIRR of 8.89% when the two are combined. The overgeneration is 1000 h when the utilization hours of nuclear power generation attain 8000 h. As the pumping power price provided by the nuclear power plant increases from 0.10 CNY/kW·h to 0.28 CNY/kW·h, the FIRR of the nuclear power plant increases from 9.49% to 11.15% and that of the pumped storage plant decreases from 20.77% to 11.32%. The joint FIRR can be increased to 11.00%. This model operates the pumped storage hydropower as a production plant of the nuclear power plant. This prevents a conflict of interest between the nuclear power plant and pumped storage. This, in turn, can maximize the operational advantages of the pumped storage power plant while increasing the annual power generation hours of the nuclear power plant.

4.3.4. Long-Term Joint Operation Mode

In the long term, nuclear power plants and pumped storage power plants can participate in the power market simultaneously under the mode with the fully market-oriented price of power. To ensure the safe operation of nuclear power units, nuclear power plants can achieve a higher profit level by maintaining a larger number of annual operation hours. The pumped storage power plant realizes a reasonable profit level through a reasonable peak-valley price difference and by serving the power system. The pumped storage power plant and nuclear power plant have a unified operator under this operation mode. In addition, these can participate in the market quotation as independent subjects (the “separate quotation and operation” mode). The on-grid price of pumped storage is 0.8540 CNY/kW·h. According to a power balance analysis of the system, it can provide the system with auxiliary services with a capacity of 450 MW at a capacity price of 562 CNY/kW·year.

The relationship between pumping price and the profitability of each power source under the long-term power market environment is shown in Figure 4. Overgeneration does not occur when the utilization hours of nuclear power generation are 7000 h. The profitability of the nuclear power plant and pumped storage power plant are 8.59% and 15.55%, respectively. The joint financial profitability is 9.36%. Overgeneration of 1000 h occurs when the utilization hours of nuclear power generation attain 8000 h. As the price of pumping power provided by the nuclear power plant increases from 0.10 CNY/kW·h to 0.28 CNY/kW·h, its FIRR increases from 9.49% to 11.15%, and that of the pumped storage power plant decreases from 23.83% to 15.55%. In addition, the joint FIRR can increase to 11.40%. This shows that although the price of pumping power provided by the nuclear power plant increases the pumped storage operation cost, it increases the advantage to the entire system.

4.4. Comparison of Different Joint Operation Modes of Nuclear Power and Pumped Storage

The joint operation of nuclear power and pumped storage can improve the overall economic competitiveness of the system. The advantages for nuclear power can be considered according to the following two aspects. First, pumped storage can replace part of the peak shaving capacity of nuclear power. Thereby, nuclear power can maintain a base-load operation and improve its load factor while safeguarding its safe operating requirements. Second, nuclear power can earn additional revenue and achieve improved profitability by providing its excess power to pumped storage. For pumped storage, the operating costs can be reduced, and profitability improved, by obtaining the excess nuclear power as a low-cost power for pumping water.

The following conclusions were drawn based on the analysis of the current dispatching mode and the promotion of power market reforms. Under the short-term power market reform mode, it is suitable to adopt the joint operation mode of nuclear power and pumped storage wherein the low-cost excess nuclear power generated would be provided to the pumped storage. Under the relatively mature power market mode in the medium term, pumped storage can earn profits through the peak-valley power price difference of the power grid and the low-cost pumping power price provided by nuclear power. Under the fully market-oriented mode in the long term, nuclear power and pumped storage can participate in the market quotation and operation simultaneously. The results show that the joint operation mode of nuclear power and pumped storage becomes more flexible with the improvement in the power market.

A comparison of the profitability of the joint system of nuclear power and pumped storage under different power market environments at present and in the short, medium, and long term reveals that the joint FIRR (the coordinate system on the left shows histogram) increases steadily with the gradual advancement of power market reforms. The profitability of pumped storage power plants (the coordinate system on the right shows histogram) also increases gradually. However, it decreases with the increase in pumping power prices (Figure 5). This indicates that the advancement of power market reforms helps better utilize various types of power resources. The role and advantages of pumped storage power plants with multiple public service functions are reflected fully, and the system can obtain better economic advantages.

There are certain challenges in the present research. For example, this study investigated the reasonable capacity ratio of nuclear power to pumped storage from the perspective of the economy. This was aimed mainly at the optimal allocation of power resources. In the next stage, the power generation capacity of nuclear power and pumped storage could be optimized based on certain financial indicators considering the power market. Moreover, this study considered the power structure and operation mode in 2030 as an example. In the next step, the power structure and operation mode could be optimized annually during the entire planning period to analyze the profitability of the joint operation of nuclear power and pumped storage.

5. Conclusions

This study started from the technical and economic characteristics of nuclear power and pumped storage hydropower plants. It then analyzed the joint operation modes of nuclear power and pumped storage under different power market environments. It also calculated the financial profitability of the joint operation system, which has an important theoretical significance and reference value for the efficient operation of nuclear power and pumped storage and the construction of a safe and economic clean energy system. The study considered the joint operation system of nuclear power and pumped storage of the FJ power grid as an example. The following conclusions were drawn:

• Using the power expansion optimization model, we could preliminarily obtain a suitable ratio of installed nuclear power to pumped storage of approximately 2.05–2.77:1 in 2025–2030 for the FJ power grid. The development mode with wind power, nuclear power, and pumped storage as the main incremental power sources can better address the future power demand and peak shaving capacity requirements of the power system.
• Joint operation of nuclear power and pumped storage can improve the economic competitiveness of the system. For nuclear power, pumped storage can ensure its base-load operating status, increase the utilization hours of power generation by 1000 h, and improve the operating economic performance. Pumped storage can obtain low-priced pumping power from nuclear power. This would effectively reduce the operating costs.
• Both nuclear power and pumped storage operate independently in the present planned dispatching stage. Moreover, their FIRRs are lower than the benchmark rate of return of 8% for the power industry. These cannot yield reasonable profits. Meanwhile, the FIRR of the joint operation of nuclear power and pumped storage increases, and profitability improves steadily under the short-term power market reform mode, medium-term relatively mature market mode, and long-term mature market mode. In the case of full marketization in the long term, the joint FIRR can attain up to 11.64%. This indicates that the promotion of power market reform would help fully utilize nuclear power and pumped storage hydropower.

The outcomes of this study will be helpful in providing a reference for the joint operation of nuclear power and pumped storage power in different power market environments. In addition, the analyzing method could be applied to other energy sources. Future research needs to consider the combined operation of nuclear and pumped storage with other power sources (e.g., wind and solar power) and the competition of systems in the power market.