## 1. Introduction

In recent years, wind power (WP) and photovoltaic (PV) have achieved sustained and rapid development. However, the output of WP and PV is very unstable. Large-scale WP and PV are connected to the grid and the generation side uncertainty of the power system is aggravated [

1,

2,

3]. In Europe, balancing the power grid is mainly realized by using gas-based power generation units and pumped storage power station (PSPS), but natural gas is imported, and the geographical location of pump storage units is greatly restricted, which brings great difficulties to power grid balancing [

4]. The increasing share of intermittent renewable energy generation and changing patterns of electricity demand pose challenges not only to the balance of the grid but also to the security of the supply. In China, there are many studies on renewable energy and energy storage complementary power generation technologies, but chemical energy storage systems, such as batteries, are generally preferred. The battery has its own disadvantage that cannot be changed. The service life of the battery is affected by frequent charge and discharge, which reduces the system economy. The discarded batteries may cause environmental pollution in the recovery process. The technology of PSPS in China is relatively mature. The participation of PSPSs in dispatching can improve the flexibility of the power system and effectively solve the problem of power grid balancing [

5].

Aiming at the complementary power generation technology of the new energy system and energy storage system, the present research mainly focuses on the optimization operation of the joint system. Reference [

6] established a wind-photovoltaic-pumped storage complementary power generation system under the condition of an isolated network operation, which compared and analyzed the operation status of PSPSs with different capacities, and determined an optimal determination method of pumped storage capacity. Reference [

7] studied the problem of wind-photovoltaic-pumped storage system’s uncertain unit commitment, based on the parameter estimation method to obtain wind-solar output interval, using scene method to describe the uncertainty of wind-photovoltaic output, proposed the binary artificial sheep algorithm (BASA) algorithm to solve it, and verified the validity of the model. Reference [

8] focused on the optimal day-ahead scheduling of hybrid power systems, including WP, PV, cascade hydropower, thermal power units, and PSPS. Taking into account the complementary characteristics of these power sources, a day-ahead joint optimal scheduling model for multi-source power systems with the goal of maximizing safety and economy was established. Reference [

9] proposed an optimal dispatch model for the WP-PV energy storage system, aiming at the frequency stability of the power grid. The optimal control strategy was proposed to reduce the dependence on the energy storage system, reduce equipment operation and maintenance costs, and improve the reliability of the power system. Reference [

10] proposed different control strategies for distributed energy storage (DES) and established a unit commitment model considering inertia constraints, dynamic reserve allocation, and interconnection flexibility. However, the prediction error of PV and WP in this paper was assumed to be normally distributed. The “3-sigma” rule was adopted for PV reserve demand calculation and the “3.5-sigma” rule was adopted for WP reserve demand calculation. Reference [

11] put forward the difference between uncertainty and variable reserves, captured the dual nature of renewable energy power generation, and established a multi-time-scale random unit commitment model without a quantitative analysis of the reserve demand or a detailed description of the influence of energy storage in scheduling. However, the authors did not make a quantitative analysis of the reserve demand, nor did they give a detailed description of the impact of energy storage in scheduling. In reference [

12], a probabilistic microgrid scheduling problem was considered and a hybrid approach combining scene selection optimization and reserve strategy using model predictive control (MPC) framework was proposed. In reference [

13], a framework for quantitative analysis of any energy storage system was proposed for reliability and flexibility in power systems. The authors used a genetic algorithm to solve the combined dispatching of WP and pumped storage power plants. Reference [

14] mainly studied the frequency regulation control architecture of renewable hybrid power plants, including WP, PV, and battery energy storage systems. The results showed that the hybrid power generation system had good frequency regulation ability, stabilized the frequency of the system in a very short time, and improved the reliability of the power system.

The power system needs to be equipped with a sufficient reserve capacity to ensure stable, safe, and continuous power supply. Operation reserve refers to the capacity reserved for quick active power response in order to cope with fluctuations in load and renewable energy output, generator outage, etc., to meet the requirements of reliable and continuous power supply for a load [

15]. The large-scale connection of renewable energy into the grid has brought more uncertainty to the power system and increased the operation reserve demand capacity. Too little reserve capacity configuration leads to system security and reliability reduction; too much configuration improves system reliability, but it compresses units power generation space and causes uneconomical phenomena [

16]. Understanding how to configure the appropriate reserve capacity to ensure the reliability of the power system is very necessary.

The traditional power system reserve decision-making plan is based on a deterministic model. The power system reserve demand per hour of the system is usually determined by the maximum unit capacity or the load percentage. This method does not consider the quantitative relationship between unit output and reserve decision, and the result makes it difficult to achieve global optimization [

17]. With the large-scale integration of renewable energy such as WP to the power grid, the traditional reserve decision-making methods have been difficult to apply to the power system. In order to reduce the uncertainty caused by renewable energy, some scholars proposed a coordinated dispatch model for power generation and reserve, which described the unit output and reserve decision jointly as an optimization problem with constraints, and obtained the optimal solution while satisfying the reliability constraints. Reference [

18] proposed an index of expected load not supplied ratio to quantify the minimum allowable load shedding per hour and derived the quantitative relationship between this indicator and the operation reserve. However, it failed to consider the uncertainty of WP and reserve cost, so it could not meet economic requirements. Reference [

19] analyzed the distribution of wind resources and studied the impact of WP grid connection and its prediction errors on power system dispatching. However, in terms of reserve decision-making, a deterministic method was adopted. The unit output and reserve decision were scheduled in sequence, without taking into account the influence of WP volatility on reserve demand; the overly simple constraint conditions made the results unrepresentative. In reference [

20], a spinning reserve acquisition model was constructed based on the opportunistic constraint programming method. However, the Monte Carlo stochastic simulation may have led to long calculation time and less practicability, and the impact of positive and negative spinning reserve on the system after WP was connected to the grid was not considered. Reference [

21] aimed to achieve the optimal configuration of spinning reserve with the goal of minimum the expected loss of load and the minimum unit operating cost. However, the reserve and unit output in this method were separately optimized, which made it difficult to ensure the optimal overall result. Reference [

22] realized the coordination and optimization of unit output and spinning reserve under the condition of high WP penetration, but it lacked the quantification between system reliability and reserve capacity.

In the research of renewable energy output models, there are two main types. One is to establish a deterministic model to obtain the specific value of renewable energy output. This method takes into account many factors, is difficult, and the result error is large, and thus it is challenging to provide a reliable basis for the power system. The other is to establish a probability distribution model to obtain the probability density function of a renewable energy output [

23,

24]. Compared with the deterministic model, the latter can better explain the uncertainty of renewable energy, with higher credibility and a wider range of applications. In establishing the probability distribution model of a renewable energy output, the parameter estimation method is generally adopted, assuming that the wind speed probability obeys the Weibull distribution and the light intensity probability obeys the Beta distribution. Then, the probability distribution functions of WP and PV output are obtained according to WP unit output function and PV panel output function [

25,

26]. The modeling process of this method is simple, but WP output and PV output are not only affected by wind speed and light intensity, so the results have large errors. The probability model established by the non-parametric estimation method does not require model assumptions about wind speed and light intensity, and only needs to estimate the probability model based on the historical data of renewable energy output, which can effectively reveal the statistical information hidden in the historical data and reduce the influence of uncertain factors on the probability model [

27]. Reference [

28] adopts the autoregressive moving average method with normal distribution of WP prediction error to model the wind speed time series and obtain the probability distribution of the WP output. Then, the Monte Carlo simulation was used to generate random samples of wind speed to generate WP output scenes. This method is inefficient and time-consuming, and requires a large number of samples to get good results. In reference [

29], the authors successfully deduced the analytic expression of WP density function and the fourth-order statistics based on the historical data of the WP output, and extended the model of the WP output to a regional scale. References [

30,

31,

32] adopted the non-parametric kernel density estimation method to calculate the probability density functions of different WP prediction errors. The obtained results had higher accuracy and better adaptability than the traditional wind speed parameter distribution method, and were applied to the field of reserve capacity demand determination and power generation scheduling.

The wind-photovoltaic-pumped storage system is mainly based on the wind farms and PV power stations, according to the local favorable terrain [

33]. PSPS transfers and stores the unstable and fluctuating power supply that exist in wind farms and PV power stations during the generation process, and then converts it into stable power input. According to the characteristics of the WP output in northwest China, the wind speed at night is generally greater than that during the day [

34]. Therefore, when the WP output increases, the excess energy can be stored in the PSPS. The pumping operation is performed by starting the water pump and then the excess electric energy of the wind farm is converted into the gravity potential energy of water for storage. In the same way, PV power stations convert energy through the same operation. When the grid load is high and the system power supply is difficult to balance the power demand, the PSPS generates power to release energy, which can reduce load shedding loss, improve the system’s utilization of new energy, and reduce the impact of power fluctuation on the grid. The structure of wind power-photovoltaic-pumped storage system is shown in

Figure 1.

In summary, many scholars have used the parameter estimation method to model the WP output and PV output. The modeling process of this method is simple, but the WP and PV outputs are not only affected by wind speed and light intensity, so the results obtained by using the parameter method have a large error. The traditional reserve decision scheme of the power system is based on the deterministic model. This method performs sequential scheduling of the unit output and reserve decisions, in turn, without considering the quantitative relationship between unit output and reserve decisions. As a result, it is difficult to achieve global optimal results and the traditional reserve decision method is difficult to apply to the power system. Aiming at the above problems, the main objectives and main innovations and contributions of this paper are as follows.

The primary aims of this paper, which are also its main novelty and contributions, are to: (a) consider that, under some special circumstances, the parameter estimation method for the prediction error of renewable energy output is invalid. Thus, this paper adopts the non-parameter kernel density estimation method to model the prediction error of the renewable energy output and obtain the probability distribution function of the prediction error of renewable energy output. (b) According to the probability distribution function obtained, the Latin hypercube sampling (LHS) method was used to sample the prediction error of renewable energy output, and a large number of renewable energy output scenes were obtained. A representative set of scenes were obtained by the simultaneous backward reduction (SBR) method. (c) A method for determining the operating reserve demand capacity based on the reliability index of power system is proposed and the quantitative relationship between the up-regulated operation reserve and the expected energy not supplied (EENS) per hour is derived. Moreover, the quantitative relationship between the down-regulated operation reserve and the expected WP and PV curtailed (EWPPC) per hour is derived. (d) A coordinated optimization model of power generation and standby is established, aiming at the minimum wind and light abandoning electricity quantity and the minimum total operating cost of thermal power units, gas units, and PSPSs. We optimized the reserve supply and optimal unit allocation scheme for each hour operation by coordinated dispatching. Finally, the validity of the proposed model is verified by comparing with the deterministic model.

The paper is structured as follows. In

Section 2, the probability distribution model of renewable energy output ultra-short-term prediction error is mainly studied. In

Section 3, the uncertainty of the WP and PV outputs are described by the scenario method. Based on the reliability index of the power system, the quantitative relationship between the hourly reserve demand and reliability index is derived in

Section 4. The coordinated dispatching model considering generation and operating reserve is proposed in

Section 5, and the case study is presented in

Section 6. Finally, conclusions are drawn in

Section 7.