Capacity Optimization of Pumped–Hydro–Wind–Photovoltaic Hybrid System Based on Normal Boundary Intersection Method

Abstract

Introducing pumped storage to retrofit existing cascade hydropower plants into hybrid pumped storage hydropower plants (HPSPs) could increase the regulating capacity of hydropower. From this perspective, a capacity configuration optimization method for a multi-energy complementary power generation system comprising hydro, wind, and photovoltaic power is developed. Firstly, to address the uncertainty of wind and photovoltaic power outputs, the K-means clustering algorithm is applied to deal with historical data on load and photovoltaic, wind, and water inflow within a specific region over the past year. This process helps reduce the number of scenarios, resulting in 12 representative scenarios and their corresponding probabilities. Secondly, with the aim of enhancing outbound transmission channel utilization and decreasing the peak–valley difference for the receiving-end power grid’s load curve, a multi-objective optimization model based on the normal boundary intersection (NBI) algorithm is developed for the capacity optimization of the multi-energy complementary power generation system. The result shows that retrofitting cascade hydropower plants with pumped storage units to construct HPSPs enhances their ability to accommodate wind and photovoltaic power. The optimal capacity of wind and photovoltaic power is increased, the utilization rate of the system’s transmission channel is improved, and the peak-to-valley difference for the residual load of the receiving-end power grid is reduced.

1. Introduction

Improving the quality and efficiency of new energy generation is essential to accelerating progression to the stage of high-quality development [1]. This involves continual advancements in renewable energy technology, sustained cost reduction, improved efficiency, enhanced competitiveness, and addressing crucial issues such as high-penetration integration, key technological innovations, and the security of supply chains. To effectively implement the “dual-carbon” strategy and accelerate the transformation of energy structure, wind, photovoltaic, and hydropower resources must be combined to achieve a high-penetration rate of renewable energy and harness the synergistic effects [2]. In the southwest region of China, extensive cascade hydropower plants have been established. Incorporating pumped storage stations into these systems and configuring wind power stations and photovoltaic power stations to have a certain capacity will lead to the creation of a co-generation system encompassing wind power, solar power, hydropower, and pumped storage. Leveraging the regulation capabilities of conventional hydropower plants and pumped storage stations will mitigate the instability of wind and photovoltaic power generation, enhance the integration of wind and photovoltaic power, boost the utilization of outbound transmission channels, and establish a comprehensive renewable energy development base [3].

The large-scale grid integration of new energy sources like wind and photovoltaic power introduces considerable instability into the power system due to their stochastic variability. The processes of generating these forms of energy are non-adjustable and often face significant peak-shaving pressure when integrated into grid-constrained systems [4]. Given the limited regulation capabilities of conventional hydropower plants, pumped storage, as a mature energy storage technology, significantly alleviates power system instability caused by large-scale wind and photovoltaic resource integration. Acting as a high-quality regulating power source, pumped storage facilities also play a role in maximizing the accommodation of clean energy [5]. Hence, utilizing hydropower and pumped storage in conjunction with wind and photovoltaic power generation on the supply side represents an effective approach to integrating wind and photovoltaic power and ensuring the stable operation of the grid [6].

Presently, domestic research on pumped–hydro–wind–photovoltaic hybrid power generation systems mainly focuses on the single configuration of pumped storage capacity or of wind and photovoltaic capacity, and research on the coordinated configuration of pumped storage capacity and wind–photovoltaic capacity in such systems is relatively scarce. In [7], the objective is to minimize the intraday volatility of a combined wind and photovoltaic output, taking into account the operating costs of thermal power generation units. In [8], a method for optimizing the configuration of wind unit generators is proposed. The optimal position of the units is evaluated as a function of their variable operating conditions with the aim of maximizing their electricity market revenue, considering that congestion in transmission lines varies with the scale, location, and operational status of generator units in the power system. In [9], an evaluation method for hydro-energy complementarity in mixed energy systems considering changes in power grid load demand is developed. By considering the probability of matching the output power of mixed energy systems with the load demand, two complementarity assessment indicators, namely time and magnitude, are proposed. The complementarity of mixed energy systems is assessed by taking into account the different installed capacities of wind and photovoltaic power stations. In [10], a method is proposed for determining the complementarity of wind and solar energy based on resource characteristics, with the objective of minimizing fluctuations by calculating their capacity ratio. A large-scale hydro–photovoltaic–wind hybrid system scale model and method are introduced, taking into account transmission demand and the comprehensive characteristics of cascade hydropower. The authors present a method for determining the optimal capacity for wind and photovoltaic power based on the complement guarantee ratio and cumulative time proportion. In [11], a scale optimization method that takes into account operational risks and benefits is proposed. A multi-scale nested co-generation operation model considering long-term, short-term, and real-time complementary strategies is established, taking into account the uncertainty of wind and photovoltaic output predictions. Through a detailed assessment of the operational risks and benefits of the hybrid system, the optimal scale is determined.

Additionally, most current research on integrated pumped–hydro–wind–photovoltaic hybrid power generation systems primarily focuses on achieving the lowest electricity cost, maximizing power generation, minimizing the curtailment of renewable energy, and optimizing the utilization of outbound channels. There is relatively limited research on objectives related to minimizing the residual load peak–valley difference for external loads, and there is also a lack of connection with addressing peak–valley differences in scheduling. In [12], the authors propose a methodology for the optimized design of an on-grid hydropower–photovoltaic (PV) system considering power transmission capacity, and then, a design optimization model is established with maximum carbon emission reductions and minimum PV power curtailments. In [13], a two-layer model is established, with the upper-layer objective being the minimization of costs and the lower-layer objective being the maximization of electricity sales revenue. The CCG algorithm is employed for parallel solving, and capacity optimization configuration is conducted while considering robustness. In [14], through an analysis of energy demand in Malawi, a multi-objective coordinated control model for hydro–photovoltaic storage is established. The primary objectives are to meet the power demand during the day and night, with a secondary objective being the minimization of electricity cost and another being the minimization of load loss probability. In [15], a comprehensive energy base integrating hydro, wind, and photovoltaic power is constructed. Under fixed installed capacities for multiple energy sources within the base, simulation operations are conducted based on the output process of each energy source. This allows the authors to determine the power generation process of the system, calculating output indicators such as the power supply guarantee rate and curtailment rate, thereby establishing the relationship between installed capacity and project benefits. In [16], the authors establish a multi-objective model aiming to minimize abandoned wind and photovoltaic energy outputs and maximize the overall installed wind and photovoltaic power capacity, optimizing the capacity configuration of the three energy sources. In [17], the authors focus on the configuration of pumped storage capacity and the coordination of thermal power units to minimize discarded wind and photovoltaic energy and maximize the economic and environmental benefits of these forms of energy. They simultaneously optimize the system’s operation and construct a dual-layer planning model for optimal pumped storage capacity configuration. In [10], the authors consider the proportion and decomposition of long-term electricity and the impact of spot price volatility, proposing a method for capacity configuration in a market environment; this method simultaneously considers the economic and complementary characteristics of multi-energy power generation systems with renewable energy. In [18], the authors optimize the design of a grid-disconnected pumped storage and wind power system with wind power units, pumped storage, and hydropower units as decision variables, aiming to maximize wind power penetration and minimize levelized electricity costs. In [19], the authors concentrate on factors such as the coordination, optimization, and integration of various renewable energy sources within a power system, considering factors like intermittency, variability, and the economic impacts of capacity allocation. The optimal configuration of wind power, photovoltaic power, and pumped storage capacities is vital for the operation and resource utilization of the hybrid hydro–wind–photovoltaic complementary power generation system [20].

Multi-energy complementary generation systems mostly constitute multi-objective problems due to peaking, cost, and efficiency issues. Additionally, genetic algorithms are currently the main approach to solving multi-objective optimization problems, while the application of normal boundary intersection (NBI) algorithms is less common [21]. The main merit of NBI is that it avoids the selection of arbitrary parameters while generating a set of points, disregarding the scales of the objectives; therefore, it is not affected by the size of the objective function and can obtain a uniformly distributed Pareto front to fully describe the balance between different objectives [22]. Moreover, cone decomposition methods, represented by penalty-based boundary intersection, cannot guarantee a uniform distribution of the obtained frontiers [23]. This is because the radial spatial distribution of their reference lines generally results in an inability to handle strongly convex Pareto frontiers. In contrast, parallel decomposition methods, such as normal boundary intersection, are highly suitable for problems with strongly convex Pareto frontiers. In [24], a multi-objective optimization model is proposed to maximize both the effective load-carrying capability and economic revenue of the hybrid system. An improved normal boundary intersection method is proposed to solve the multi-objective problem and obtain the Pareto surface. In [25], a multi-objective interval power generation scheduling model of a wind–thermal power system is first established, and the minimization of fuel cost and the pollution gas emission cost of the thermal power unit is chosen as the objective functions. Then, to solve the model, the Pareto frontiers of the multi-objective interval power generation scheduling are obtained using an improved normal boundary intersection method, whereby a normal boundary intersection is combined with a bilevel optimization method. In [26], to better leverage the temporal flexibility of the steelmaking process, a what-if-analysis-based strategy coupled with the normal boundary intersection method is proposed to generate a series of evenly distributed Pareto solutions.

However, the studies outlined above fail to account for the impact of wind power and photovoltaic capacity on scheduling operations. Oversized configurations of wind and photovoltaic integration can heighten the operational risks and risk of abandoned electricity. Conversely, undersized configurations lead to underutilization of resources and low utilization rates of transmission channels. Additionally, the economic benefits resulting from optimizing the pumped storage capacity also influence the co-generation system. Oversizing creates an economic burden, while too small a scale diminishes the system’s regulatory capacity. Therefore, the configuration of wind power, photovoltaic power, and pumped storage capacities in complementary power generation systems is particularly crucial. Furthermore, most studies consider either conventional hydropower plants or pumped storage stations as the sole regulating power sources, or they consider the coexistence of wind, photovoltaic, and thermal power in multi-energy complementary power generation systems.

Due to domestic research on pumped–hydro–wind–photovoltaic hybrid power generation systems mainly focusing on the single configuration of pumped storage capacity or of wind and photovoltaic capacity, there is a lack of consideration for scenarios where only cascade hydropower is available, transformed by pumped storage, with an uncertain capacity of wind power, photovoltaic power, and pumped storage units. Therefore, inspired by the above studies, in this paper, a multi-objective optimal operation model is established for the pumped–hydro–wind–photovoltaic hybrid system. The goal is to maximize the utilization rate of the system’s outgoing channels while minimizing the residual load of the hybrid system. First, a nonlinear model is transformed into an MILP model through the integration of the McCormick and linearized transformation methods. Then, the double-objective problem is solved using the proposed NBI method. Finally, using a case study, comparisons are made between a number of factors, such as different scenarios, wind, and photovoltaic power capacity with and without pumped storage. The main contributions of this paper are summarized as follows:

(1)

An efficient multi-objective framework for the optimal configuration and operation of a model of a pumped–hydro–wind–photovoltaic hybrid system is established. Objective functions that simultaneously consider the utilization rate of the outgoing channel and residual load peak-to-valley difference for the remaining load are presented, which can improve the utilization rate of renewable energy more effectively. Compared with the traditional hydro–wind–photovoltaic system, the hybrid pumped storage station can provide a better regulation capacity.

(2)

The McCormick method is integrated with the linearized transformation method to linearize the proposed model and to ensure the optimality of the results. The NBI method is proposed to solve the multi-objective problem, whereby a two-cycle approximation process with a modified payoff matrix is proposed to ensure the convergence and accuracy of the Pareto solution.

The remainder of this paper is organized as follows. In Section 2, a comprehensive scenario-based multi-objective capacity optimization model for a hybrid pumped storage system transformed into a cascade pumped–hydro–wind–photovoltaic co-generation system is presented and linearized. In Section 3, a multi-objective optimization-solving NBI algorithm and a Pareto frontier curve are developed. The simulation results and discussion are presented in Section 4.

2. Model Formulation of Capacity Configuration

This paper mainly focuses on a hybrid energy system comprising a hydropower plant (HPP), wind power station, photovoltaic station, and pumped storage station, as shown in Figure 1. Among the components of the system, pumped storage units are used to transform a conventional cascade hydropower plant into a hybrid pumped storage station. Although wind and photovoltaic power units are regarded as uncontrollable generation units, the aim of this system is to enable controllable energy generation and storage. In this work, we establish a planning model for capacity allocation in multi-energy complementary power generation systems, mainly addressing issues related to external transmission channel utilization and residual load, and we optimize wind power, photovoltaic power, and pumped storage capacity allocation within its scheduling cycle.

2.1. Objective Function

In this paper, a multi-objective capacity optimization allocation model is established with the objective of maximizing the utilization rate of the system’s outgoing channels with the minimum residual load. The utilization of the outgoing channels is the utilization rate of the power transmission channel. Improving the utilization rate of the delivery channel can increase the flexibility of the power system. The peak-to-valley difference of the residual load is the external load minus the peak-to-valley difference between the remaining loads of cascade hydropower, wind power, photovoltaic power, and pumped storage. The reduction of the peak–valley difference of the residual load is helpful in smoothing the load curve of the power system and reducing the demand for reserve power generation resources.

2.1.1. Maximum Utilization of Outgoing Channels

$$f_1(\mathit{x})=\max (G)$$

(1)

$$G={\displaystyle \sum _{t=1}^{\mathrm{T}}\left({\displaystyle \sum _{i=1}^{\mathrm{I}}\left(P_{i,t}^{\mathrm{g}}+P_{i,t}^{\mathrm{psh}}-P_{i,t}^{\mathrm{psp}}\right)}+P_{\mathrm{w},t}+P_{\mathrm{pv},t}\right)}/\left(24\ast P_{\mathrm{L},\max }\right)$$

(2)

In the above equations $x$ is a matrix composed of variables $G$ is the utilization rate of the outgoing transmission channel of the combined generation system in a dispatch horizon.

2.1.2. Minimize Peak-to-Valley Difference for Residual System Loads

$$f_2(\mathit{x})=\min \left(\underset{1\le t\le \mathrm{T}}{\max }{P}_{\mathrm{r},t}-\underset{1\le t\le \mathrm{T}}{\min }{P}_{\mathrm{r},t}\right)$$

(3)

$$P_{\mathrm{r},t}=P_{\mathrm{ld},t}-P_{\mathrm{w},t}-P_{\mathrm{pv},t}-{\displaystyle \sum _{i=1}^{\mathrm{I}}\left(P_{i,t}^{\mathrm{g}}+P_{i,t}^{\mathrm{psh}}-P_{i,t}^{\mathrm{psp}}\right)}$$

(4)

2.2. Constraints of Optimal Configuration Model

2.2.1. Wind and Photovoltaic Power Plant Installed Capacity Constraints

$$S_{\mathrm{w},\min }<S_{\mathrm{w}}<S_{\mathrm{w},\max }$$

(5)

$$S_{\mathrm{pv},\min }<S_{\mathrm{pv}}<S_{\mathrm{pv},\max }$$

(6)

2.2.2. Pumped Storage Installed Capacity Constraints

$$S_{\mathrm{ps},\min }\le S_{\mathrm{ps}}\le S_{\mathrm{ps},\max }$$

(7)

2.3. Constraints of Optimal Operation Model

2.3.1. Wind and Photovoltaic Power Plant Output Constraints

$$0\le P_{\mathrm{w},t}\le {\lambda }_{\mathrm{w},t}\cdot S_{\mathrm{w}}$$

(8)

$$0\le P_{\mathrm{pv},t}\le {\lambda }_{\mathrm{pv},t}\cdot S_{\mathrm{pv}}$$

(9)

2.3.2. Wind and Photovoltaic Power Abandonment Constraints

$${\displaystyle \frac{E_{\mathrm{q}}}{E_{\mathrm{total}}}}<\eta$$

(10)

2.3.3. Water Balance Constraints for Cascade Hydropower Plants

$$V_{i,t}=V_{i,t-1}+\left(Q_{i,t}^{\mathrm{in}}-Q_{i,t}^{\mathrm{g}}-Q_{i,t}^{\mathrm{psh}}-Q_{i-1,t}^{\mathrm{psp}}-Q_{i,t}^{\mathrm{wc}}\right)\Delta t$$

(11)

$$Q_{i,t}^{\mathrm{in}}=R_{i,t}+Q_{i-1,t-{\tau }_{i-1}}^{\mathrm{g}}+Q_{i-1,t-{\tau }_{i-1}}^{\mathrm{wc}}+Q_{i,t}^{\mathrm{psp}}$$

(12)

2.3.4. Reservoir Control Constraints

$$V_{i,\min }\le V_{i,t}\le V_{i,\max }$$

(13)

$$V_{i,0}=V_{i,\mathrm{bg}}$$

(14)

$$V_{i,24}=V_{i,\mathrm{end}}$$

(15)

2.3.5. Hydropower Unit Generation and Abandoned Water Flow Limitation Constraints

$$u_{i,t}^{\mathrm{g}}{Q}_{i,\min }^{\mathrm{g}}\le Q_{i,t}^{\mathrm{g}}\le u_{i,t}^{\mathrm{g}}{Q}_{i,\max }^{\mathrm{g}}$$

(16)

$$Q_{i,\min }^{\mathrm{wc}}\le Q_{i,t}^{\mathrm{wc}}\le Q_{i,\max }^{\mathrm{wc}}$$

(17)

2.3.6. Hydropower Unit Output Characteristic Constraints

$$P_{i,t}^{\mathrm{g}}={\eta }_i\cdot Q_{i,t}^{\mathrm{g}}$$

(18)

$$u_{i,t}^{\mathrm{g}}{P}_{i,\min }^{\mathrm{g}}\le P_{i,t}^{\mathrm{g}}\le u_{i,t}^{\mathrm{g}}{P}_{i,\max }^{\mathrm{g}}$$

(19)

2.3.7. Pumped Storage Unit Flow Constraints

$$u_{i,t}^{\mathrm{psh}}{Q}_{i,\min }^{\mathrm{psh}}\le Q_{i,t}^{\mathrm{psh}}\le u_{i,t}^{\mathrm{psh}}{Q}_{i,\max }^{\mathrm{psh}}$$

(20)

$$u_{i,t}^{\mathrm{psp}}{Q}_{i,\min }^{\mathrm{psp}}\le Q_{i,t}^{\mathrm{psp}}\le u_{i,t}^{\mathrm{psp}}{Q}_{i,\max }^{\mathrm{psp}}$$

(21)

2.3.8. Upper and Lower Power Limit Constraints for Pumped Storage Units

$$P_{i,t}^{\mathrm{psh}}={\eta }_i^{\mathrm{psh}}\cdot Q_{i,t}^{\mathrm{psh}}$$

(22)

$$P_{i,t}^{\mathrm{psp}}={\eta }_i^{\mathrm{psp}}\cdot Q_{i,t}^{\mathrm{psp}}$$

(23)

$${\rho }_i^{\mathrm{psh}}{u}_{i,t}^{\mathrm{psh}}{S}_{\mathrm{ps}}\le P_{i,t}^{\mathrm{psh}}\le u_{i,t}^{\mathrm{psh}}{S}_{\mathrm{ps}}$$

(24)

$${\rho }_i^{\mathrm{psp}}{u}_{i,t}^{\mathrm{psp}}{S}_{\mathrm{ps}}\le P_{i,t}^{\mathrm{psp}}\le u_{i,t}^{\mathrm{psp}}{S}_{\mathrm{ps}}$$

(25)

2.3.9. Minimum on–off Time Constraints for Pumped Storage Units

$$u_{i,t}^{\mathrm{psh}}+u_{i,t}^{\mathrm{psp}}\le 1$$

(26)

$$u_{i,t}^{\mathrm{g}}+u_{i,t}^{\mathrm{psp}}\le 1$$

(27)

$${\delta }_{i,t}^{\mathrm{psh}}-{\sigma }_{i,t}^{\mathrm{psh}}=u_{i,t}^{\mathrm{psh}}-u_{i,t-1}^{\mathrm{psh}}$$

(28)

$${\delta }_{i,t}^{\mathrm{psh}}+{\sigma }_{i,t}^{\mathrm{psh}}\le 1$$

(29)

$${\delta }_{i,t}^{\mathrm{psp}}-{\sigma }_{i,t}^{\mathrm{psp}}=u_{i,t}^{\mathrm{psp}}-u_{i,t-1}^{\mathrm{psp}}$$

(30)

$${\delta }_{i,t}^{\mathrm{psp}}+{\sigma }_{i,t}^{\mathrm{psp}}\le 1$$

(31)

$$\max \left\{{\displaystyle \sum _{t=1}^{\mathrm{T}}{\delta }_{i,t}^{\mathrm{psh}}},{\displaystyle \sum _{t=1}^{\mathrm{T}}{\sigma }_{i,t}^{\mathrm{psh}}}\right\}\le N_i^{\mathrm{psh}}$$

(32)

$$\max \left\{{\displaystyle \sum _{t=1}^{\mathrm{T}}{\delta }_{i,t}^{\mathrm{psp}}},{\displaystyle \sum _{t=1}^{\mathrm{T}}{\sigma }_{i,t}^{\mathrm{psp}}}\right\}\le N_i^{\mathrm{psp}}$$

(33)

2.4. Model Transformation

2.4.1. Objective Function Linearization

Since the objective function Equations (3) and (4) for minimizing the peak-to-valley difference for the residual load is nonlinear, they cannot be solved directly using the MILP model, so this paper introduces the auxiliary variables $R_{\max }$ and $R_{\min }$ to show the maximum and minimum values of the residual load, respectively, in order to enable the linear transformation of the objective function.

The linearized model is shown in Equations (35) and (36). It is linearized as follows:

$$f_2(\mathit{x})=\min \left(R_{\max }-R_{\min }\right)$$

(34)

$$R_{\max }\ge P_{\mathrm{r},t}\hspace{1em}\forall t=1,2,\cdots ,24$$

(35)

$$R_{\min }\le P_{\mathrm{r},t}\hspace{1em}\forall t=1,2,\cdots ,24$$

(36)

2.4.2. McCormick Envelope-Based Bilinear Constraint Transformation

Since the installed capacities of wind power, photovoltaic power, and pumped storage are optimization variables, the operation constraints Equations (24) and (25) are nonlinear due to the bilinear terms $u_{i,t}^{\mathrm{psh}}{S}_{\mathrm{ps}}$ and $u_{i,t}^{\mathrm{psp}}{S}_{\mathrm{ps}}$. In this paper, the nonlinear constraints can be transformed into a linear constraint based on the McCormick envelope [27]. Here, the transformation process is demonstrated to be linearizing, as shown in Equations (37) and (38).

$$\{\begin{array}{l}{\omega }_1\ge u_{i,t}^{\mathrm{psh}}{S}_{\mathrm{ps}}^{\mathrm{L}}\\ {\omega }_1\ge S_{\mathrm{ps}}+u_{i,t}^{\mathrm{psh}}{S}_{\mathrm{ps}}^{\mathrm{U}}-S_{\mathrm{ps}}^{\mathrm{U}}\\ {\omega }_1\le S_{\mathrm{ps}}+u_{i,t}^{\mathrm{psh}}{S}_{\mathrm{ps}}^{\mathrm{L}}-S_{\mathrm{ps}}^{\mathrm{L}}\\ {\omega }_1\le u_{i,t}^{\mathrm{psh}}{S}_{\mathrm{ps}}^{\mathrm{U}}\\ {\rho }_i^{\mathrm{psh}}{\omega }_1\le P_{i,t}^{\mathrm{psh}}\le {\omega }_1\end{array}$$

(37)

$$\{\begin{array}{l}{\omega }_2\ge u_{i,t}^{\mathrm{psp}}{S}_{\mathrm{ps}}^{\mathrm{L}}\\ {\omega }_2\ge S_{\mathrm{ps}}+u_{i,t}^{\mathrm{psp}}{S}_{\mathrm{ps}}^{\mathrm{U}}-S_{\mathrm{ps}}^{\mathrm{U}}\\ {\omega }_2\le S_{\mathrm{ps}}+u_{i,t}^{\mathrm{psp}}{S}_{\mathrm{ps}}^{\mathrm{L}}-S_{\mathrm{ps}}^{\mathrm{L}}\\ {\omega }_2\le u_{i,t}^{\mathrm{psp}}{S}_{\mathrm{ps}}^{\mathrm{U}}\\ {\rho }_i^{\mathrm{psp}}{\omega }_2\le P_{i,t}^{\mathrm{psp}}\le {\omega }_2\end{array}$$

(38)

In the above equations, ${\omega }_1$ and ${\omega }_2$ are the auxiliary linear variables.

2.4.3. Full-Scenario Optimization Model

As we obtained one year of load data, wind, photovoltaic, and water inflow data are used, which are too large in volume. Twelve typical scenarios with their corresponding scenario probabilities are obtained through K-means clustering, and the expectation values are calculated. Therefore, by clustering and reducing historical data from one year into 12 typical scenarios, a full-scenario optimization model is employed to simulate the operational states throughout the year [24]. By modeling the seasonal characteristics of wind, photovoltaic, and water inflow, the single-scenario problem established in Section 2 can be transformed into a comprehensive scenario optimization problem. For scenario s, the objective function of the single-scenario wind and photovoltaic power configuration problem is shown in Equations (1)–(4). After transforming the single-scenario problem into a comprehensive scenario optimization problem, the wind and photovoltaic power configurations should comprehensively consider the characteristics of wind, photovoltaic, and water inflow across all scenarios. Consequently, the objective function is transformed into Equations (39) and (40). Therefore, it reduces the computational scale, enhancing the model’s efficiency. Simultaneously, obtaining the expected values helps determine the optimal capacity configuration for the entire year.

$$F_1\left(\mathit{x}\right)={\displaystyle \sum _{s=1}^{\mathrm{S}}{p}_s{f}_1\left({\mathit{x}}_s\right)}$$

(39)

$$F_2\left(\mathit{x}\right)={\displaystyle \sum _{s=1}^{\mathrm{S}}{p}_s{f}_2\left({\mathit{x}}_s\right)}$$

(40)

In the above equations, ${\mathit{x}}_s$ is a matrix composed of variables in scenario $s$; and $F_1$ and $F_2$ are the total mathematical expectations of $f_1$ and $f_2$, respectively.

3. Model Solution

3.1. Solution Method

The scenario-based modeling method is utilized in this study, where several representative scenarios are generated based on the assumed distributional information. Each scenario is associated with a set of parameters and a model, along with its respective probability. By substituting different scenarios for random variables, the problem is transformed into a linear format. To address larger-scale problems, techniques to reduce the scale of the scenario are essential for obtaining solutions.

The model formulated to optimize the combined capacity of wind power, photovoltaic power, and pumped storage for the hybrid cascade hydropower plant is converted into a mixed-integer linear programming (MILP) model. This model can be implemented by using mature commercial solvers. YALMIP is employed to invoke the GUROBI solver in this research. Due to conflicting objective functions within the multi-objective planning model, direct optimization presents significant challenges. To streamline the model-solving process, this study employs the normal boundary intersection (NBI) method [28]. This method reduces the degrees of freedom in the multi-objective optimization problem by transforming it into a single-objective optimization problem [29]. The aim of this transformation is to maximize the distance between multiple utopian lines and the Pareto front, resulting in a uniformly distributed Pareto solution set. The algorithm-solving procedure is presented in Figure 2, and the algorithmic analyses are detailed in Steps 1–4 below.

• Step 1: For the multi-objective optimization problem required in this paper,

  $$\{\begin{array}{l}{g}_1(\mathit{x})=-F_1(\mathit{x})\\ g_2(\mathit{x})=F_2(\mathit{x})\end{array}$$

  (41)

  $$\min \mathit{F}=\min [g_1(\mathit{x}),g_2(\mathit{x})]$$

  (42)

  where $g_1(\mathit{x})$ is the opposite value of the utilization of outgoing channels; $g_2(\mathit{x})$ is the peak-to-valley difference for the residual system loads; and $\mathit{F}$ is a matrix constructed from $g_1(\mathit{x})$ and $g_2(\mathit{x})$.
• Step 2: Solve two single-objective optimization problems individually to construct the utopian line:

  $$\{\begin{array}{lll}{g}_1(x_1^{*})& =\hfill & \min g_1(x_1)\hfill \\ g_2(x_2^{*})\hfill & =\hfill & \min g_2(x_2)\hfill \end{array}$$

  (43)

  where $g_1(x_1^{*})$ and $g_2(x_1^{*})$ are the optimal solutions when the two objective functions are optimized separately. As shown in Figure 3, the solution set of the multi-objective optimization problem is essentially represented by the points on the Pareto front. We can connect points A and B in the figure to obtain line segment AB, which is the utopia line.
  Demarcation process:

  $$\{\begin{array}{l}{\overline{g}}_1(\mathit{x})={\displaystyle \frac{g_1(\mathit{x})-g_1(x_1^{*})}{g_1(x_2^{*})-g_1(x_1^{*})}}\\ {\overline{g}}_2(\mathit{x})={\displaystyle \frac{g_2(\mathit{x})-g_2(x_2^{*})}{g_2(x_1^{*})-g_2(x_2^{*})}}\end{array}$$

  (44)

  $$\mathit{P}=\left[\begin{array}{cc}{\overline{g}}_1(x_1^{*})& {\overline{g}}_1(x_2^{*})\\ {\overline{g}}_2(x_1^{*})& {\overline{g}}_2(x_2^{*})\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$$

  (45)
• Step 3: After specification of the objective function, let $m={[\begin{array}{cc}-1& 1\end{array}]}^T$ represent the unit normal from the utopia line pointing to the origin. Any point on the utopia line can be described as $\mathit{P}\beta ={[\begin{array}{cc}{\beta }_1& {\beta }_2\end{array}]}^T$, where ${\beta }_1$ and ${\beta }_2$ denote the weight coefficients in the range of [0, 1], and ${\beta }_1+{\beta }_2=1$. Thus, the set of points in the objective function space can be expressed as $\overline{\mathit{\Phi }}\beta +\lambda \overrightarrow{n}$, $\lambda \in R$.
• Step 4: Solving single-objective optimization problems

When the point denoted as $\overline{\mathit{\Phi }}\beta +\lambda \overrightarrow{n}$ is in the feasible domain shown in Figure 3, we have:

$$\overline{\mathit{\Phi }}\beta +\lambda \overrightarrow{n}=\overline{G}(\mathit{x})$$

(46)

In other words,

$$\left[\begin{array}{l}{\beta }_1\\ {\beta }_2\end{array}\right]+\lambda \left[\begin{array}{l}-1\\ -1\end{array}\right]=\left[\begin{array}{l}{\overline{f}}_1(\mathit{x})\\ {\overline{f}}_2(\mathit{x})\end{array}\right]$$

(47)

As shown in Figure 3, when the intersection point of the normal nears the origin and the boundary of the feasible domain of the optimization problem, i.e., $\lambda$, takes the maximum value, we obtain the Pareto optimal solution of the multi-objective problem. The original multi-objective optimization problem is transformed into a series of single-objective optimization problems when changing ${\beta }_1$ or ${\beta }_2$ causes the intersection of the normal $n$ and the utopia line to move, i.e.,

$$\begin{array}{l}\max \lambda \\ \{\begin{array}{l}{\beta }_1-\lambda ={\overline{f}}_1(\mathit{x})\\ 1-{\beta }_1-\lambda ={\overline{f}}_2(\mathit{x})\\ 0\le {\beta }_1\le 1\end{array}\end{array}$$

(48)

This results in a series of single-objective solution problems to obtain a uniformly distributed Pareto curve, known as the Pareto front.

3.2. Optimization Model

The main information encompassed in the capacity optimization model presented in this paper is depicted in Figure 4. The input data include the parameters of the HPP units, wind power units, and photovoltaic units, typical scenario data obtained by clustering, and output coefficients. The decision variables of the proposed model are the capacity of pumped storage units, wind power units, and photovoltaic units, as well as operation-related variables such as the power outputs of wind power, photovoltaic, hydropower, and pumped storage units. As previously mentioned, the objective function comprises utilization of the outgoing channel and peak-to-valley difference for residual system loads, while the constraints include operational constraints of each unit, electricity balance constraints, water balance constraints, and on–off time constraints. Subsequently, the nonlinear parts mentioned were linearized and transformed into a MILP model for resolution, and then the capacity optimization model was solved by the NBI method.

3.3. Case Study

This study examines the wind and photovoltaic power stations surrounding cascade hydropower plants in the Xiao Jin Chuan River in Sichuan, China. The aim of integrating hybrid pumped storage stations to transform these conventional hydropower plants is to achieve an optimized configuration of a coordinated and complementary integrated pumped–hydro–wind–photovoltaic multi-energy generation system within the region. By building upon existing cascade hydropower plants and incorporating an indeterminate capacity of pumped storage units, along with an indeterminate capacity of wind and photovoltaic power stations, efforts have been made to enhance the utilization of outgoing channels, bundle outgoing channels, and decrease residual load peak-to-valley differences by complementing multiple energy sources. The aim of leveraging the adjustability of cascade hydropower and pumped storage units is to reduce the rate of renewable energy abandonment, absorb more output from wind and photovoltaic power sources, and stabilize fluctuations in wind and photovoltaic power output. The basic parameters of the cascade hydropower plant are set as shown in

Table 1. Basic parameter settings of a cascade hydropower plant.

Parameters	Primary Hydropower Station	Secondary Hydropower Station	Tertiary Hydropower Station
Initial reservoir capacity/104 m3	36	48	-
Terminal reservoir capacity/104 m3	36	48	-
Maximum reservoir capacity/104 m3	90	120	0
Time lag of water flow/h	1	2	-
Maximum generating power of hydropower unit/MW	45	60	36
Minimum generating power of hydropower unit/MW	10	13	9
Generation efficiency of hydropower unit	1.1582	1.7786	0.7677

and

Table 2. Cascade hydropower unit parameter settings.

Parameters	Pumped Storage Unit
Generation efficiency	0.9
Pumping efficiency	1.2

.

The maximum installed capacity of the wind power station is set at 500 MW, the maximum installed capacity of the photovoltaic station is set at 500 MW, and the upper limit of the outgoing channels is 350 MW.

4. Results Analysis

4.1. The Generation of Typical Scenarios

A 24-hour scheduling cycle served as the basis for condensing load, wind power, photovoltaic power, and water inflow data collected over a year into 12 typical days using the K-means clustering method. These representative days were utilized as 12 distinct scenarios for the subsequent analysis. The datasets for each typical scenario are outlined in Figure 5, Figure 6, Figure 7 and Figure 8, and the corresponding probability distributions are listed in

Table 3. Probability of twelve typical scenarios occurring.

Scenario	Scenario Probability
Scenario 1	0.1014
Scenario 2	0.1342
Scenario 3	0.0247
Scenario 4	0.0932
Scenario 5	0.0712
Scenario 6	0.1616
Scenario 7	0.0575
Scenario 8	0.0849
Scenario 9	0.0137
Scenario 10	0.0356
Scenario 11	0.1425
Scenario 12	0.0795

.

Regarding the consideration of water inflow for the cascade hydropower plants, three distinct periods are taken into account: the dry, normal, and wet seasons. Throughout the dry season, the water inflow remains at 10 (10⁴ m³/h) for 24 h per day. During the normal season, the water inflow remains constant at 15 (10⁴ m³/h) for 24 h per day. Conversely, the wet season was characterized by a steady water inflow rate of 20 (10⁴ m³/h) throughout the entire day. In the southern regions of China, the typical seasonal patterns encompass the normal season in May and November, dry season from January to April and December, and wet season from June to October. The water periods corresponding to the twelve typical scenarios obtained by clustering are shown in

Table 4. The water periods corresponding to the twelve typical scenarios.

Scenario	Water Period
Scenario 1	normal season
Scenario 2	dry season
Scenario 3	wet season
Scenario 4	dry season
Scenario 5	wet season
Scenario 6	normal season
Scenario 7	dry season
Scenario 8	dry season
Scenario 9	normal season
Scenario 10	normal season
Scenario 11	dry season
Scenario 12	dry season

.

Firstly, using the K-means clustering method, the nominal values of twelve typical scenarios can be obtained. Then, by selecting a suitable base value, the nominal values of the load, wind power, and photovoltaic power can be normalized.

4.2. The Optimization Results and the Pareto Frontier Curve

Twelve typical scenarios were subjected to stochastic optimization for case analysis to determine the expected value of the objective function. Since this is a multi-objective mixed-integer linearized model, the YALMIP toolkit and the commercial solver GUROBI were used to obtain the multi-objective optimization solution, and the Pareto frontier curve was obtained using the NBI algorithm. The results of the solution are shown in

Table 5. Channel utilization and residual load peak-to-valley difference for twelve typical scenarios.

Scenario	Channel Utilization	Peak-To-Valley Difference for Load/MW	Residual Load Peak-To-Valley Difference/MW
Scenario 1	0.3889	367.5000	149.9124
Scenario 2	0.5778	264.9000	198.1139
Scenario 3	0.4318	413.4000	168.7307
Scenario 4	0.6034	318.6000	45.5740
Scenario 5	0.5359	429.1500	148.8437
Scenario 6	0.6798	343.2000	322.1566
Scenario 7	0.7999	327.0000	172.5000
Scenario 8	0.4016	345.0000	138.6687
Scenario 9	0.7402	367.5000	116.2777
Scenario 10	0.4882	389.7000	138.9926
Scenario 11	0.7719	283.6500	173.6756
Scenario 12	0.3395	345.1500	147.9577

, and the Pareto curve is shown in Figure 9.

The red curve in Figure 9 is the Pareto frontier curve, and the blue arrow in Figure 10 is the normal line. In Figure 9, the horizontal coordinate is the value of the utilization rate of the outgoing channel, and the vertical coordinate is the peak-to-valley difference for the residual load of the system. It can be seen that when the delivery channel utilization rate increases, the system residual load peak–valley difference increases, which is consistent with the trend in the Pareto frontier curve in Figure 9. When the utilization rate of the delivery channel and the system residual load peak-to-valley difference reach the corresponding weighting relationship, the residual load peak–valley difference reaches its lowest, the delivery channel utilization rate reaches its highest, and the normal line reaches its longest length, as shown in Figure 10. Then, $\lambda =0.305$, and at this time, ${\beta }_1$ = 0.5 (for the weighting coefficient of the first objective).

After clustering 365 historical scenario data using K-means clustering, 12 typical scenarios are obtained. Consequently, for the annual planning of wind and photovoltaic power installation capacities, only one optimal solution exists among the twelve typical scenarios. At this optimum, the wind power installation capacity is 362 MW, the photovoltaic installation capacity is 325 MW, and the pumped storage capacity is 34 MW.

4.3. Comparative Analysis of Scenario

From Table 5, it can be observed that scenarios 7, 9, and 11 rank among the top three in terms of outgoing channel utilization. As a result, a detailed analysis is conducted for these three scenarios regarding the specific combined system’s output, wind and photovoltaic power unit output, hydropower unit output, and pumped storage unit output. The output of each unit, the working conditions of the pumped storage unit and the residual load curves of each scenario are shown in following Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19. The optimization results corresponding to the three scenarios are shown in

Table 6. Optimization results corresponding to the three scenarios.

Scenario	Capacity Configuration			Channel Utilization	Residual Load Peak-To-Valley Difference/MW
	Pumped Storage Unit	Wind Power Unit	Photovoltaic Unit
Scenario 7	34	362	325	0.7999	172.5000
Scenario 9	34	362	325	0.7402	116.2777
Scenario 11	34	362	325	0.7719	173.6756

.

In Figure 11, the combined system’s output under typical scenario 7 is depicted. In this scenario, there is a larger output of photovoltaic (PV) power between 11:00 and 17:00, which aligns with the characteristic curve of the PV output. Between 11:00 and 12:00 and between 15:00 and 16:00, due to substantial wind and PV power generation and a comparatively low load, water is pumped from the lower reservoir to the upper reservoir by the pumped storage unit to accumulate energy. This action enables surplus wind and photovoltaic energy storage in the upper reservoir. During these periods, surplus electricity needs to be accommodated, as there are specific requirements that must be met to accommodate wind power and photovoltaic power curtailment. Hence, the pumping operations of the pumped storage unit are activated to reduce the abandonment of these resources.

Between 13:00 and 14:00, hydropower units do not generate mass electricity. Consequently, the pumped storage unit discharges water to meet peak demand and simultaneously supplements the lower reservoir’s capacity by releasing water from the upper reservoir.

During the early morning and nighttime, the PV units do not produce electricity, leaving only the wind power unit’s output. However, relying solely on wind power is inadequate to fulfill the peak load demand due to its inherent output fluctuations. Therefore, during these times, the third-stage hydropower units in the cascade hydropower plant release water for power generation. Upon comparing the final load and residual load curves in Figure 13, it is evident that the pumped–hydro–wind–photovoltaic co-generation system, coupled with external grid-connected bundled output resources, effectively regulates the remaining load on the network interconnection line. This system plays a significant role in load balance, reducing the residual load peak–valley difference while concurrently maintaining a high utilization rate of external grid transmission channels.

Figure 14 shows the combined system’s output for scenario 9, which shows that the load is higher and the PV resource is lower in this scenario, suggesting that the hydropower units of the cascade hydropower group have been discharging water to generate electricity. Between 1:00 and 8:00, the combined system’s output is lower, mainly relying on wind power and hydropower generation.

In order to meet the peak load demand to the greatest extent possible, from 9:00 to 11:00, when the wind power, PV power, and three cascade hydropower units generating power at the same time are not enough to maximize the peak effect, the pumped storage unit discharges water from the reservoirs of the first-stage hydropower station to the reservoirs of the second-stage hydropower station to generate power. In Figure 15, it can be seen that, at this time, the pumped storage units under the power generation condition can be incorporated with the upper reservoir’s water discharge to supplement the lower reservoir’s capacity. The conditions of the pumped storage units are presented in Figure 15. Simultaneously, at 13:00 and 17:00, the excess power is pumped and stored owing to the regulation ability of pumped storage.

Photovoltaic power is higher from 11:00 a.m. to 16:00 a.m., which conforms to the characteristic curve of photovoltaic power. Moreover, during the period from 18:00 a.m. to 24:00 a.m., when there is still a certain demand for load peaking, the photovoltaic power drops significantly. At this time, it is necessary to rely on the power generation of the three-stage hydropower units of the cascade hydropower plant to achieve a peak throughout the entire day. At least one one-stage hydropower unit is usually on, which could indicate that the load is high in this scenario, and the combined system needs to generate electricity at all times to enable peak shifting and achieve a better peak shifting effect.

It can be seen in Figure 16 that the combined pumped–hydro–wind–photovoltaic hybrid system in this scenario has a better peak-to-valley regulation effect for the outgoing load because the adjustable output characteristics of the cascade hydropower and pumped storage units can generate power and energy storage, enabling a variety of renewable energy sources to play a multi-energy complementary role and reducing the abandonment rate of renewable energy sources, such as wind power, photovoltaic power, and hydropower. At the same time, the channel utilization in this scenario reaches 74.02%. Under the multi-objective optimization of maximizing the utilization rate of the outgoing channel and minimizing the peak-to-valley difference for the residual load, this co-generation system co-optimized operation shows a better optimization effect.

In Figure 17, the combined system’s output under scenario 11 is presented. It is evident that in this scenario, there is an ample supply of wind power. Between 1:00 and 3:00, relying solely on wind power does not adequately meet the peak load demand. Consequently, the pumped storage units and the three-stage hydropower units in the cascade hydropower plant operate at different times. However, from 4:00 to 5:00, the wind power resources gradually increase. During this time, the adjustable capabilities of wind power generation and the pumped storage unit are utilized to discharge water for power generation or to store energy by pumping water; notably, at 4:00, the pumped storage unit pumps water from the reservoir of the second-stage hydropower station to the reservoir of the first-stage hydropower station to store energy, as depicted in Figure 18.

The photovoltaic output is significant from 10:00 to 15:00. Following the characteristic curve of the photovoltaic output, especially at 12:00, the photovoltaic output is too high; therefore, pumped storage units are needed for energy storage. The load curve represented in Figure 19 demonstrates a high demand between 18:00 and 22:00. At this time, both the wind and PV power outputs have significantly decreased. Hence, the three hydropower units of the cascade hydropower plant operate to meet the continuous peak load demand, as shown in Figure 17, especially after 18:00.

However, at 21:00, relying solely on the three hydropower units and wind–photovoltaic output does not achieve the optimal effect on the load peak–valley difference. Therefore, the pumped storage unit is utilized to discharge water for power generation to supplement the electricity demand, further reducing the residual load peak–valley difference. Figure 17 demonstrates that the co-generation system performs well in terms of multiple energy complementation in this scenario.

Additionally, Figure 19 indicates notable regulation effects on the load peak–valley difference, achieving an external transmission channel utilization rate of 77.19%, thereby optimizing both objectives effectively while minimizing renewable energy wastage.

4.4. Comparative Analysis with and without Pumped Storage Units

Considering the optimization results of both the hybrid pumped storage station combined with the wind–photovoltaic power system and the conventional cascade hydropower plant combined with the wind–photovoltaic power system, the utilization rates of the channels and the residual load peak–valley differences for the twelve typical scenarios are shown in

Table 7. The channel utilization of twelve typical scenarios with and without pumped storage units.

Scenario	Channel Utilization (With Pumped Storage)	Channel Utilization (Without Pumped Storage)
Scenario 1	0.3889	0.3825
Scenario 2	0.5778	0.5629
Scenario 3	0.4318	0.4257
Scenario 4	0.6034	0.5847
Scenario 5	0.5359	0.5271
Scenario 6	0.6798	0.6656
Scenario 7	0.7999	0.7719
Scenario 8	0.4016	0.4004
Scenario 9	0.7402	0.7151
Scenario 10	0.4882	0.4824
Scenario 11	0.7719	0.7408
Scenario 12	0.3395	0.3332

and

Table 8. The residual load peak-to-valley difference for twelve typical scenarios with and without pumped storage units.

Scenario	Peak-To-Valley Difference for Load/MW	Residual Load Peak-To-Valley Difference (With Pumped Storage)/MW	Residual Load Peak-To-Valley Difference (Without Pumped Storage)/MW
Scenario 1	367.5000	149.9124	161.3718
Scenario 2	264.9000	198.1139	203.5166
Scenario 3	413.4000	168.7307	187.9693
Scenario 4	318.6000	45.5740	79.7703
Scenario 5	429.1500	148.8437	166.1520
Scenario 6	343.2000	322.1566	333.7397
Scenario 7	327.0000	172.5000	131.2122
Scenario 8	345.0000	138.6687	177.5925
Scenario 9	367.5000	116.2777	106.4320
Scenario 10	389.7000	138.9926	153.8073
Scenario 11	283.6500	173.6756	173.1723
Scenario 12	345.1500	147.9577	156.8472

, respectively.

From Table 7, it can be observed that without the transformation of the pumped storage units into the cascade hydropower plant, the utilization rates of the channels in the 12 typical scenarios are all reduced to varying degrees. Due to the loss of the flexible regulation ability of the pumped storage units for outgoing power, the outbound utilization rate of the integrated power generation system is reduced.

From Table 8, it can be seen that in the absence of the pumped storage unit’s transformation into cascade hydropower, the residual load peak–valley difference increases by 10% compared to the scenario with the transformation. After losing the flexible regulation capability of the pumped storage units for energy generation and storage, the peak-shaving capability of the integrated system decreases to a certain extent.

Furthermore, in the absence of pumped storage units, there is also a difference in the installed capacity between the wind and photovoltaic power stations, as shown in the optimization results in

Table 9. Wind and photovoltaic power capacities with and without pumped storage units.

	With Pumped Storage Units	Without Pumped Storage Units
Wind power installation/MW	362	341
Photovoltaic power installation/MW	325	321
Pumped storage installation/MW	34	0

.

From Table 9, it can be inferred that due to the constraint of the abandonment rate being less than 5% during the operational stage in the model, wind and photovoltaic power generators will reduce their installed capacity in the absence of actions such as energy generation and storage by pumped storage units, in order to ensure compliance with the abandonment rate requirement. Consequently, the peak-shaving capability of the integrated power generation system naturally decreases.

With the inclusion of the pumped storage unit in the co-generation system, the output flexibility of the wind and photovoltaic power systems is enhanced. This improvement arises from the unique adjustable pumping capacity of the pumped storage unit, allowing for the effective accommodation of discarded wind and photovoltaic energy at each time interval. Moreover, the presence of the pumped storage unit results in a lower residual load peak–valley difference, thereby enhancing the peak load regulation effectiveness of the co-generation system.

In general, the results show that retrofitting cascade hydropower plants with pumped storage units to construct HPSPs enhances their ability to accommodate wind and photovoltaic power. The optimization capacity of the wind and photovoltaic power is increased, the utilization rate of the system’s transmission channel is improved, and the peak-to-valley difference for the residual load of the receiving-end power grid is reduced. Our conclusions are presented in the last section, where we state that pumped storage transformation based on traditional cascade hydropower stations is helpful in improving the ability of the multi-energy complementary system to absorb and adjust the output of renewable energy.

5. Conclusions

In this study, the development and construction of a high-penetration clean energy base composed of a pumped–hydro–wind–photovoltaic hybrid power generation system are considered. This model accounts for the co-generated system’s capacity for wind and photovoltaic power, its abandonment of wind and photovoltaic power, and its secure and stable operation. It is built upon a multi-energy complementary cooperative power generation system model composed of a cascade hydropower plant, wind power station, photovoltaic power station, and pumped storage stations. The optimization of the capacity configuration and operation of the complementary power generation system is based on the objectives of maximizing the external transmission channel rate and minimizing the residual load peak–valley difference for the receiving-end grid.

Following an analysis and calculations of twelve typical days at the Xiao Jing Chuan integrated renewable energy base, the following conclusions are drawn:

(1)

From the perspective of regulating capacity, compared with no pumped storage unit, wind power is configured with 341MW, and photovoltaic power is configured with 321MW. After installing 34MW of the pumped storage units, the co-generation system can accommodate a larger capacity of wind, which configures 362 MW capacity, and photovoltaic power, which configures 325 MW capacity, because of its improved capability to consume renewable energy.

(2)

By configuring the pumped storage unit to transform the cascade hydropower, the utilization rate of the outgoing channel can be improved, and the difference between the peak and valley of the residual load can be reduced by about 10%. This reduction significantly enhances the consumption capacity of power and photovoltaic wind improves the utilization efficiency of renewable energy by about 5% and stabilizes the receiving-end power grid.

In this study, by employing clustering methods, we identified twelve typical extreme scenarios that occur throughout the year. It is observed that after the pumped storage unit is configured, the system’s ability to regulate new energy is improved. Additionally, we plan to transform the existing cascade hydropower plants with pumped storage and capacity configuration of wind power, photovoltaic power, and pumped storage. While NBI algorithms effectively determine the Pareto frontier between the two objectives in multi-objective problems, further research will explore the integration of thermal power resources, such as diesel engines, into the entire system and the impact of pumped storage on the deep peak-shaving of thermal power, aiming to reduce carbon emissions through the installation of hybrid pumped storage stations.