Short-Term Optimal Scheduling of Power Grids Containing Pumped-Storage Power Station Based on Security Quantification

Abstract

In order to improve grid security while pursuing a grid operation economy and new energy consumption rates, this paper proposes a short-term optimal scheduling method based on security quantification for the grid containing a pumped-storage power plant. The method first establishes a grid security evaluation model to evaluate grid security from the perspective of grid resilience. Then, a short-term optimal dispatch model of the grid based on security quantification is constructed with the new energy consumption rate and grid loss as the objectives. In addition, an efficient intelligent optimization algorithm, Dung Beetle Optimization, is introduced to solve the scheduling model, dynamically updating the evaluation intervals during the iterative solution process and evaluating the grid security level and selecting the best result after the iterative solution. Finally, the improvement in the term IEEE 30-bus grid connected to a pumped-storage power plant is used as an example to verify the effectiveness of the proposed method and model.

1. Introduction

With the “dual-carbon” goal and the construction of new power systems, China’s installed capacity of new energy has been increasing, and by the end of 2023, China’s cumulative installed new energy capacity will exceed 800 GW, with the installed new energy capacity reaching more than 30% of China’s total installed capacity [1,2,3]. Under the high proportion of new energy access, it brings a great challenge to the stable operation of the power grid [4,5,6], and pumped storage is one of the effective ways to cope with the challenge [7,8]. With the addition of new energy power stations, pumped-storage power stations, and other modules, the grid structure has become more complex; therefore, how to improve the security of the grid while pursuing the new energy consumption rate and economy is the current grid scheduling research question that urgently needs to be addressed [9,10].

Ensuring power system security has long been a critical focus in the planning, design, and operational phases of power grids. As power systems become more complex, traditional security assessment methods face challenges in accurately evaluating grid stability and reliability. Established security indices—such as the frequency safety value [11], voltage margin [12], stability of power supply capacity [13], and failure rate [14]—have been widely used in real-time monitoring. However, these approaches fall short when applied to pre-scheduled evaluations, where predicting grid resilience becomes vital. Recent advancements have attempted to address this issue. For example, research has explored the use of hierarchical analysis and entropy weighting methods to evaluate distributed energy systems [15], while multi-criteria assessment systems have been developed to better quantify security indicators [16]. Additionally, efforts have been made to integrate subjective and objective weighting methods, such as combining hierarchical analysis with the CRITIC method, to improve the accuracy of security assessments [17,18]. Despite these efforts, current evaluation models often rely on extensive data and involve complex calculations, making them less practical for real-time application. These limitations highlight the need for more efficient and effective methods to assess grid security in the context of short-term scheduling, particularly for systems that include pumped-storage power stations. The study addresses these gaps by proposing a novel approach to short-term optimal scheduling that enhances grid security through more streamlined and practical security quantification methods. By building on existing research while introducing new methodologies, this work aims to contribute to more resilient and secure power grid operations.

The above grid security scheduling sets security factors as constraints [19,20], and it is sufficient to satisfy the range of constraints when formulating the scheduling plan, ignoring the resilience of the grid to face uncertainties. Incorporating security into grid scheduling operations has been an important focus in several studies. These studies span various aspects of power system operations, including optimal tidal flow [19,20], economic dispatch [21,22,23], market design [24,25], and electric vehicles [26,27]. For instance, economic dispatch models have been developed to integrate preventive safety constraints with scenario stochasticity [21], while stochastic models have been proposed for coordinating long-term maintenance schedules and short-term security-constrained unit commitments [22]. Additionally, efforts have been made to incorporate frequency stability constraints into economic dispatch models, optimizing the generation costs while ensuring operational and frequency stability [23]. In the realm of market design, approaches have been formulated to improve the transmission grid flexibility by coordinating operators to integrate more wind energy without compromising system security [24]. Similarly, strategies have been developed to enhance the transmission capacity through wind power investments, thereby strengthening the existing transmission network [25]. The rise of electric vehicles and active distribution networks has introduced new uncertainties into the power system. To address these challenges, distributed dispatch co-optimization models have been proposed, leveraging blockchain consensus mechanisms to reduce the generation costs, decrease the daily load variance, and improve system security [26]. Other methodologies have focused on assessing the impact of electric vehicles on transmission grids, such as in the Costa Rican power system [27]. While these studies have successfully incorporated security factors as constraints within their scheduling models [19,20], they often treat security as a static requirement, one that can be satisfied by ensuring the system operates within predefined constraints. However, this approach overlooks the resilience of the grid when faced with uncertainties. As power systems evolve and become more dynamic, there is a growing need for models that not only meet security constraints but also enhance the grid’s ability to withstand and recover from unexpected disruptions. This research aims to address these limitations by proposing a short-term optimal scheduling approach that integrates security quantification with grid resilience, providing a more comprehensive solution to the challenges posed by uncertainties in modern power systems.

The growing share of new energy installations presents significant challenges to the stable operation of power grids. Integrating pumped-storage power plants (PSPPs) offers a promising solution by enhancing grid security and stability. Various studies have explored different aspects of PSPP integration. For example, a day-ahead scheduling model based on price arbitrage has been proposed [28], while another study developed a cost-minimization model that can be solved using a quasi-opposite, fast-converging real-coded genetic algorithm [29]. Research has also focused on optimizing hydrothermal generation scheduling, incorporating both pumped-storage and solar power systems, using a new quasi-contrastive turbulent flow optimization method [30]. Additionally, mixed-integer linear programming has been applied to maximize profits in pumped-storage operations [31]. Further advancements include optimal hourly management models for grid-connected photovoltaic and wind power plants integrated with reversible turbine units [32] and a risk-averse short-term scheduling model that employs a hybrid African vulture optimization algorithm to address multi-layer constraints [33]. Integrated energy systems that combine PSPPs with greenhouse gas emission considerations have also been explored, using meta-heuristic algorithms such as whale optimization to solve both single- and multi-objective functions [34]. Other approaches consider the demand response [35], minimize the supply–demand discrepancies and maintenance costs [36], and model the seasonal dispatch of pumping units [37]. A multi-objective operation model that balances economic, environmental, and stability factors in multi-energy cogeneration systems has also been developed [38]. Despite these efforts, the operation of pumped-storage power plants remains complex, particularly due to the flexibility required for their effective integration into power grids. Current studies have not fully addressed the challenges associated with the frequent switching of operating conditions during PSPP scheduling, which can lead to significant losses in unit efficiency and longevity [37,38]. Therefore, there is an urgent need to explore more efficient and reasonable operation modes for PSPPs to minimize these losses and optimize their contributions to grid stability.

In the field of production scheduling, multiple objectives have to be optimized simultaneously, and the objectives cannot reach the optimal state at the same time, which are collectively known as multi-objective optimization problems [39,40]. The traditional solution method is to convert a complex multi-objective optimization problem into a single-objective problem, and it is difficult to obtain a set of ideal solutions when the problem is complex, high-dimensional, dynamic, multi-modal, or encounters a complex multi-objective problem with constraints [41]. Therefore, it is of great significance to explore new ways and methods to solve high-dimensional and complex optimization problems. Swarm intelligence has also been proposed for solving optimization problems, and the ant colony algorithm inspired by the foraging behavior of ants is the first successful example of swarm intelligence [42,43]. Subsequently, the particle swarm algorithm that evolved from bird foraging was also proposed by researchers [44], which is one of the most popular optimization algorithms nowadays and is able to converge quickly in complex spaces through the exchange of information between individuals. Immediately after, Yan X, She D and Xu Y (2023) [45] used the grey wolf algorithm for selecting optimal wavelet parameters. For model solving, this paper proposes to use the DBO algorithm [46], which takes into account both global exploration and local exploitation and is characterized by a fast convergence speed and high solution accuracy. It is very competitive with state-of-the-art optimization methods in terms of convergence speed, solution accuracy, and stability.

From the analysis of the above literature, it can be seen that there are still deficiencies in the existing literature in the optimal short-term scheduling of power grids. To address the shortcomings, this paper proposes a short-term optimal dispatch method for power grids containing pumped-storage plants based on security quantification, and the main contributions are summarized as follows:

• The existing grid security evaluation index system is constructed based on instantaneous quantities [11,12,13,14] and evaluates grid security in real time by obtaining the index values through monitoring; it is not applicable to the evaluation of grid security at the stage of prior scheduling plan development. Based on this, this study considers the grid security margin, and we construct a security evaluation index system with a flexibility resource capacity index, flexibility resource response capability index, and branch load balance degree index, which is favorable for the grid security evaluation in the ex ante stage.
• The existing grid security scheduling sets the security factors as constraints [19,20], and it is sufficient to satisfy the constraint range when formulating the scheduling plan, which ignores the anti-disturbance ability of the grid facing uncertainty. In this paper, the proposed grid security evaluation method is combined with optimal scheduling to establish a short-term optimal scheduling model of the grid based on security quantification, which is conducive to the formulation of reasonable scheduling plans, improving the security margin of the grid and enhancing the anti-interference capability.
• Existing pumped-storage power plants undergo frequent switching of operating conditions during dispatch [37,38], which causes large losses to the units. This paper explores the differences between the new energy consumption, network loss, and security levels of the power grid under different pumped-storage power plant operation modes, selects the optimal operation mode for pumped-storage power plant scheduling, which is conducive to reducing the switching frequency of the working conditions, and provides a reference for the economic operation of pumped-storage power plants.

The rest of the paper is structured as follows: Section 2 introduces the grid security evaluation model, Section 3 introduces the short-term optimal dispatch model of the grid based on security quantification, Section 4 presents the case study and analyzes the results from multiple perspectives, and Section 5 summarizes the conclusions of the paper.

2. Grid Security Evaluation Model

In order to evaluate the safety of the grid before the stage of scheduling the plan development, this paper constructs a safety evaluation index system with a flexibility resource capacity index, flexibility resource responsiveness index, and branch circuit load balance index from the grid toughness. In view of the fact that conventional evaluation methods are only applicable to evaluating the security status of the grid at a certain moment, the weights of the scheduling time periods are included in the construction of the hierarchical structure to enhance the applicability of the evaluation model to the scheduling program.

2.1. Grid Security Evaluation Index System

Grid security is multi-faceted and complex, and its security level cannot be characterized by a single indicator only; it needs to be described by multiple indexes simultaneously to reflect its overall level in a more comprehensive way. Therefore, this paper constructs a security evaluation index system with a flexibility resource capacity index, flexibility resource response capability index, and branch load balance index to qualitatively and quantitatively reflect the security of the power grid.

(1)

The flexibility resource capacity is calculated as follows:

$$SM={\displaystyle \frac{TSC-{\displaystyle \sum P_i}}{TSC}}$$

(1)

where $SM$ is the flexibility resource capacity; $TSC$ is the installed capacity of the flexibility resources; and ${\displaystyle \sum P_i}$ is the actual generation power at each node.

(2)

The flexibility resource response capability is calculated as follows:

$$\left\{\begin{array}{l}FR={\displaystyle \sum _{j=m}^{m}SM\ast r_j\ast v_j}\\ {\displaystyle \sum _{j=m}^m{r}_j=1}\end{array}\right.$$

(2)

where $FR$ is the flexibility resource response capability; $r_j$ is the percentage of different types of flexibility resources remaining; and $v_j$ is the speed of response of different types of flexibility resources.

(3)

The branch load balance is calculated as follows:

$$SU={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(f_i-\frac{{\displaystyle \sum _{i=1}^n{f}_i}}{n}\right)}^2}$$

(3)

where $SU$ is the branch load balance; and $f_i$ is the branch load ratio (actual branch transmission power/maximum branch transmission power).

2.2. Methodology for Calculating Evaluation Factor Weights

The weight calculation method belongs to the top-priority components in the construction of evaluation models, and the commonly used methods include the entropy weighting method, principal component analysis method, factor analysis method, combination assignment method, hierarchical analysis method, and so on. This paper applies the hierarchical analysis method to decompose the complex problem into several levels and a number of factors and conducts a simple comparison and calculation between the factors to derive the weights of different indexes.

(1)

Constructing a recursive hierarchy:

Applying the hierarchical analysis method to analyze a decision-making problem, it is first necessary to decompose the problem to form a number of levels, according to the inter-relationships between the factors at each level, to form a recursive hierarchical structure that expresses the decision-making problem. The grid security level is located at the target layer, the scheduling time period is located at the guideline layer, and the indexes mentioned in Section 2.1 are located at the indicator layer.

(2)

Creating a judgment matrix:

After establishing the recursive hierarchical structure of the indicator system, starting from the top layer, the judgment matrix is established by comparing the elements in each layer two by two, based on the elements in the previous layer in order from the top to the bottom. The judgment matrix can be described as:

$$B_{m\times m}=\left[B_{ij}\right]$$

(4)

where $B_{ij}$ is the proportional scale of importance of indicator $i$ and indicator $j$ relative to the upper element; $m$ is the total number of indexes for the layer. The judgment matrix $B$ has the following three properties: each element of the matrix is positive; the diagonal elements of the matrix are all 1; and the non-diagonal elements of the matrix are reciprocals of each other.

Regarding the assignment of $B_{ij}$, the widely used method is the scale method, taking the 1–9 scale method as an example, and the specific meanings are shown in

Table 1. Proportional scaling of materiality.

${\mathit{B}}_{\mathit{i}\mathit{j}}$’s Assignment	Mean	${\mathit{B}}_{\mathit{i}\mathit{j}}$’s Assignment	Mean
1	i and j are of equal importance
3	i is slightly more important than j	1/3	i is slightly more unimportant than j
5	i is clearly more important than j	1/5	i is clearly more unimportant than j
7	i is highly important compared to j	1/7	i has a higher unimportance than j
9	i is extremely important compared to j	1/9	i has an extreme unimportance compared to j
2, 4, 6, 8	Between {1, 3, 5, 7, 9}	1/2, 1/4, 1/6, 1/8	Between {1, 1/3, 1/5, 1/7, 1/9}

.

A judgement matrix is formed using a two-by-two comparison between elements.

(3)

Consistency check:

In order to ensure that the application of hierarchical analysis leads to logical conclusions, it is necessary to test the judgment matrix for consistency. The consistency test indicator is described as:

$$CI={\displaystyle \frac{{\lambda }_{\max }-m}{m-1}}$$

(5)

where $CI$ is the consistency test index; ${\lambda }_{\max }$ is the maximum eigenvalue of the judgment matrix; and $m$ is the order of the judgment matrix. The greater the deviation of $CI$ from 0, the worse the consistency of the judgment matrix.

As the order of the judgment matrix increases, it becomes more difficult for the judgment matrix to maintain perfect consistency. In order to measure whether the judgment matrices of different orders are satisfactorily consistent, a stochastic consistency ratio is introduced, described as:

$$CR={\displaystyle \frac{CI}{RI}}$$

(6)

where $CR$ is the stochastic consistency ratio; $CI$ is the consistency test index; and $RI$ is the same-order average stochastic consistency ratio in

Table A1. Randomized consistency RI table.

n order	1	2	3	4	5	6
RI	0	0	0.52	0.89	1.12	1.26
n order	7	8	9	10	11	12
RI	1.36	1.41	1.46	1.49	1.52	1.54
n order	13	14	15	16	17	18
RI	1.56	1.58	1.59	1.5943	1.6064	1.6133
n order	19	20	21	22	23	24
RI	1.6207	1.6292	1.6358	1.6403	1.6462	1.6497

in Appendix A. When $CR\le 0.1$, the consistency of the judgment matrix is considered acceptable; when $CR>0.1$, the judgment matrix is considered to need an adjustment.

(4)

Computing the weight vector:

For a general judgment matrix $B$, there exists $B\cdot W={\lambda }_{\max }W$, where ${\lambda }_{\max }$ is the largest eigenvalue of $B$, and $W$ is the corresponding eigenvector of ${\lambda }_{\max }$. $W$ is normalized and can be approximated as a weight vector for $B$. The component of $W$ is $w_i$, which is the weight value of element $i$ with respect to the upper element.

2.3. Fuzzy Evaluation Method for Power Grid Security

Using the fuzzy comprehensive evaluation method to evaluate power grid security, first of all, the fuzzy evaluation subset needs to be scaled and defined, and the data set to be evaluated should be divided into a number of grades, and a reasonable grade interval should be constructed. The division of the fuzzy evaluation subset should fully consider the actual situation and the characteristics of the evaluation object, and it cannot be divided simply by equal proportion. Therefore, this paper selects the k-mean clustering algorithm for grade division, and the process is as follows:

4.

Import the sample set $D=\left\{x_1,x_2,\dots ,x_m\right\}$, number of clusters clustered $K$, and maximum iterations $N$.

5.

Select the initial center of mass: The smallest sample is selected as the first center of mass ${\mu }_1$ from the data set $D$. Iterate through all the samples to select the sample with the largest distance $d(x,{\mu }_1)$ from A as the second center of mass ${\mu }_1$. Iterate through all the samples again to select the sample with the largest sum of distance $d(x,{\mu }_1)$ from ${\mu }_1$ and distance $d(x,{\mu }_2)$ from ${\mu }_2$ as the third center of mass ${\mu }_3$ and so on; $K$ initial centers of mass $\left\{{\mu }_1,{\mu }_2,\dots ,{\mu }_K\right\}$ are selected.

6.

Start the $n$ iteration:

① Calculate the distance from the sample point $x_i$ to each center of mass ${\mu }_j(j=1,2,\dots ,K)$, classifying the sample points $x_i$ into clusters corresponding to the minimum distance. Repeat this operation until the division of all sample points is completed, generating the cluster division $\left\{C_1^n,C_2^n,\dots ,C_K^n\right\}$ for the $n$ iteration.

② Calculate the new center of mass ${\mu }_j={\displaystyle \frac{1}{\left|C_j\right|}}{\displaystyle {\sum }_{x\in C_j}x}$ for the $n+1$ iteration based on all the sample points in the $j$ cluster. Repeat this operation until all cluster centers are updated to generate the center of mass $\left\{{\mu }_1^{n+1},{\mu }_2^{n+1},\dots ,{\mu }_m^{n+1}\right\}$ for the $n+1$ iteration.

③ If $N$ iterations have been completed or none of the $k$ centers of mass have changed after the update is completed, proceed to step (4); otherwise, go back to step (3) ①, and start the next iteration.

7.

Output the cluster division $C=\left\{C_1,C_2,\dots ,C_K\right\}$.

According to the basic theory of the fuzzy comprehensive evaluation method, the evaluation set includes four fuzzy evaluation subsets, namely Distinction, Merit, Intermediate, and Pass, and the set is denoted by $v=\left(v_1,v_2,v_3,v_4\right)=\left(\mathrm{Pass},\mathrm{Intermediate},\mathrm{Merit},\mathrm{Distinction}\right)$.

For indicator $x$, its affiliation degree for each fuzzy evaluation subset forms an affiliation vector $r=\left(r_1,r_2,r_3,r_4\right)$. Each element $r_i$ of $r$ takes values in the range [0,1]. Combine the fuzzy evaluation subset interval division method to obtain five fuzzy evaluation subset interval demarcation points, $h_1,h_2,h_3,h_4,h_5$, and calculate the affiliation degree of $x$.

(1)

The degree of affiliation to the fuzzy subset $\left\{v_4=\mathrm{Distinction}\right\}$ is:

$$r_4=\left\{\begin{array}{cc}1& {\mathrm{h}}_4\le x\\ {\displaystyle \frac{x-{\mathrm{h}}_3}{{\mathrm{h}}_4-{\mathrm{h}}_3}}& {\mathrm{h}}_3<x\le {\mathrm{h}}_4\\ 0& x<{\mathrm{h}}_3\end{array}\right.$$

(7)

(2)

The degree of affiliation to the fuzzy subset $\left\{v_3=\mathrm{Merit}\right\}$ is:

$$r_3=\left\{\begin{array}{cc}1& {\mathrm{h}}_3\le x<{\mathrm{h}}_4\\ {\displaystyle \frac{x-{\mathrm{h}}_2}{{\mathrm{h}}_3-{\mathrm{h}}_2}}& {\mathrm{h}}_2\le x<{\mathrm{h}}_3\\ {\displaystyle \frac{{\mathrm{h}}_5-x}{{\mathrm{h}}_5-{\mathrm{h}}_4}}& {\mathrm{h}}_4\le x<{\mathrm{h}}_5\\ 0& x<{\mathrm{h}}_2,x\ge {\mathrm{h}}_5\end{array}\right.$$

(8)

(3)

The degree of affiliation to the fuzzy subset $\left\{v_2=\mathrm{Intermediate}\right\}$ is:

$$r_2=\left\{\begin{array}{cc}1& {\mathrm{h}}_2\le x<{\mathrm{h}}_3\\ {\displaystyle \frac{x-{\mathrm{h}}_1}{{\mathrm{h}}_2-{\mathrm{h}}_1}}& {\mathrm{h}}_1\le x<{\mathrm{h}}_2\\ {\displaystyle \frac{{\mathrm{h}}_4-x}{{\mathrm{h}}_4-{\mathrm{h}}_3}}& {\mathrm{h}}_3\le x<{\mathrm{h}}_4\\ 0& x<{\mathrm{h}}_1,x\ge {\mathrm{h}}_4\end{array}\right.$$

(9)

(4)

The degree of affiliation to the fuzzy subset $\left\{v_1=\mathrm{Pass}\right\}$ is:

$$r_1=\left\{\begin{array}{cc}1& x<{\mathrm{h}}_2\\ {\displaystyle \frac{{\mathrm{h}}_3-x}{{\mathrm{h}}_3-{\mathrm{h}}_2}}& {\mathrm{h}}_2\le x<{\mathrm{h}}_3\\ 0& {\mathrm{h}}_3\le x\end{array}\right.$$

(10)

Finally, the affiliation matrix under the indicator system can be formed after the affiliation vector is calculated using the affiliation formulas for all evaluation indexes; according to the weight vector (calculated through the hierarchical analysis in Section 2.2) and affiliation matrix, the fuzzy synthesis operator is used to obtain the fuzzy comprehensive evaluation vector, and the evaluation results of the indicator system as a whole can be determined according to the principle of maximum affiliation.

3. Short-Term Optimal Dispatch Model for Power Grid Based on Security Quantification

A conventional grid security scheduling model ignores the anti-disturbance ability of the grid facing uncertainty. Therefore, this paper constructs a short-term optimal scheduling model based on security quantification for power grids containing pumped-storage plants, combines the security evaluation method with scheduling, and develops a reasonable scheduling plan to improve the security margin of the power grid and enhance the anti-interference capability.

3.1. Objective Function

New energy consumption is an important index to assess the operation of the power grid, and at the same time, it is necessary to coordinate the power generation of new energy, thermal power, and hydropower with the impedance of each branch of the power grid and the conventional power loads at each node as far as possible in the formulation of the scheduling plan to minimize the network loss and improve the operation economy. Therefore, this paper takes the maximum rate of new energy consumption and the minimum network loss as the optimization objectives.

Objective 1: Maximum new energy consumption rate:

$$\max f_1={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T\left(\frac{P_t^w}{P_t^{w^{\prime }}}\ast 0.5+\frac{P_t^{pv}}{P_t^{p{v}^{\prime }}}\ast 0.5\right)}\ast 100\%$$

(11)

Here, $P_t^w$ is the actual grid-connected power of wind power at $t$; $P_t^{pv}$ is the actual grid-connected power of photovoltaic power at $t$; $P_t^{w^{\prime }}$ is the forecasted wind power at $t$; and $P_t^{p{v}^{\prime }}$ is the forecasted photovoltaic power at $t$.

Objective 2: Minimum grid loss:

$$\min f_2={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{(i,k)\in n}\frac{{\left(P_{i,t}\right)}^2+{\left(Q_{i,t}\right)}^2}{{\left(V_{i,t}\right)}^2}{R}_{ik}}}$$

(12)

Here, $P_{i,t}$ is the active power of node $i$ at $t$; $Q_{i,t}$ is the reactive power of node $i$ at $t$; $V_{i,t}$ is the voltage of node $i$ at $t$; and $R_{ik}$ is the line resistance between node $i$ and node $k$.

3.2. Constraint

(1)

New energy power plant output constraints are as follows:

$$\left\{\begin{array}{l}0\le P_t^w\le P_t^{w^{\prime }}\\ 0\le P_t^{pv}\le P_t^{p{v}^{\prime }}\end{array}\right.$$

(13)

where $P_t^w$ is the actual grid-connected power of wind power at $t$; $P_t^{pv}$ is the actual grid-connected power of photovoltaic power at $t$; $P_t^{w^{\prime }}$ is the forecasted wind power at $t$; and $P_t^{p{v}^{\prime }}$ is the forecasted photovoltaic power at $t$.

(2)

Thermal power plant output constraints are as follows:

$$S^{th}\cdot \eta \le P_t^{th}\le S^{th}$$

(14)

where $P_t^{th}$ is the actual grid-connected power of thermal power at $t$; $S^{th}$ is installed thermal power capacity; and $\eta$ is the minimum thermal power output technical indicator.

(3)

Hydroelectric power plant output constraints are as follows:

$$\left\{\begin{array}{l}{N}_t^{h\cdot \min }\le N_t^h\le N_t^{h\cdot \max }\\ N_t^h=k\ast Q{E}_t\ast \Delta H_t\\ \Delta H_t=\overline{Zu{p}_t}-Ztai{l}_t\\ Zu{p}_t=f^{ZV}\left(V_t\right)\\ Ztai{l}_t=f^{ZQ}\left(Q{O}_t\right)\end{array}\right.$$

(15)

where $N_t^{h\cdot \min }$, $N_t^h$, and $N_t^{h\cdot \max }$ are the lower limit of generating power, generating power, and the upper limit of generating power at $t$ of a hydroelectric power plant; $k$ is the coefficient of power generation in hydroelectric power plants; $Q{E}_t$ is the flow rate quoted for hydroelectric power generation at $t$; $\Delta H_t$ is the water head at $t$; $\overline{Zu{p}_t}$ is the average pre-dam level at $t$; $Zu{p}_t$ and $Ztai{l}_t$ are the pre-dam level and the post-dam level at $t$; $f^{ZV}$ is the water level–capacity relationship of the hydroelectric power plant; $f^{ZQ}$ is the discharge flow–tail water level relationship of a hydroelectric power plant; $V_t$ is the reservoir capacity of the hydroelectric power station at $t$; and $Q{O}_t$ is the discharge flow from the hydroelectric power plant at $t$.

(4)

Pumped-storage plant output constraints are as follows:

$$\left\{\begin{array}{l}0\le \left|P_t^{gen}\right|\le S^{gp}\\ 0\le \left|P_t^{pump}\right|\le S^{gp}\\ P_t^{gen}\times P_t^{pump}=0\end{array}\right.$$

(16)

where $P_t^{gen}$ is the power generation from pumped-storage plants at $t$; $P_t^{pump}$ is the pumping power from pumped-storage plants at $t$; and $S^{gp}$ is the installed capacity of pumped-storage power plants. At any given moment, the plant cannot have simultaneous pumping and generation, and the generation and pumping states are mutually exclusive.

(5)

Network power balance constraints are as follows:

$$\left\{\begin{array}{c}{P}_j=U_j{\displaystyle \sum _{k\in A(j)}}{U}_k(G_{jk}\cos {\delta }_{jk}+B_{jk}\sin {\delta }_{jk})\\ Q_j=U_j{\displaystyle \sum _{k\in A(j)}}{U}_k(G_{jk}\sin {\delta }_{jk}-B_{jk}\cos {\delta }_{jk})\end{array}\right.$$

(17)

where $P_j$ is the active power of node $j$; $Q_j$ is the reactive power of node $j$; ${\delta }_{jk}$ is the voltage phase angle difference; $G_{jk}$ and $B_{jk}$ are electrical conductance and susceptance; and $A\left(j\right)$ is the set of nodes to which node $j$ is connected.

(6)

Branch circuit capacity constraints are as follows:

$$0\le L\le \overline{L}$$

(18)

where $\overline{L}$ is the branch limit transmission capacity.

(7)

Node voltage constraints are as follows:

$$\underset{¯}{U_j}\le U_j\le \overline{U_j}$$

(19)

where $\overline{U_j}$ and $\underset{¯}{U_j}$ are the node voltage upper and lower limits.

3.3. Solution Algorithm

In this paper, an intelligent optimization algorithm is used to solve the model. The Dung Beetle Optimization (DBO) algorithm is a type of intelligent optimization algorithm that is inspired by the biological behavioral process of dung beetles and has the characteristics of a strong optimization-seeking ability and fast convergence speed. The algorithm simulates the behaviors of dung beetles, such as ball rolling, dancing, foraging, stealing, and reproduction, by designing particles.

(1)

Dung Beetle Roller:

① Accessibility mode:

Dung beetles can use cues from celestial bodies (in particular the sun, moon, and polarized light) to navigate the dung ball along a straight line during rolling; sunlight, for example, affects the trajectory of the movement, which is curved or elliptical; natural factors (e.g., wind and uneven ground) cause the dung beetles to deviate from their original direction. To simulate the rolling behavior, the dung beetle is required to move in a given direction throughout the search space, assuming that only the intensity of the light source affects the dung beetle’s path.

$$\left\{\begin{array}{l}{x}_i(t+1)=x_i(t)+a\ast k\ast x_i(t-1)+b\ast \Delta x\\ \Delta x=\left|x_i(t)-X^{\mathrm{W}}\right|\end{array}\right.$$

(20)

Here, $t$ is the number of iterations; $x_i(t)$ is location information of the $i$ dung beetle at $t$; $a$ is the natural coefficient taken as 1 or −1, where −1 means deviation from the original direction, and 1 means no deviation; $k\in \left(0,0.2\right]$ is a constant indicating the deflection coefficient; $b\in \left(0,1\right)$ is the coefficient of influence of the light intensity change on the position; $\Delta x$ is to simulate changes in the light intensity; and $X^{\mathrm{W}}$ is the worst position.

② Obstacle mode:

When a dung beetle encounters an obstacle and is unable to move forward, it needs to reorient itself by dancing with the aim of obtaining a new route. To simulate the dancing behavior, the tangent function is used to obtain the new rolling direction:

$$x_i(t+1)=x_i(t)+\tan \left(\theta \right)\left|x_i(t)-x_i(t-1)\right|$$

(21)

where $\theta \in \left[0,\pi \right]$ is the deflection angle. When $\theta =0,0.5\pi ,\pi$, the dung beetle’s location is not updated.

(2)

Dung beetle laying eggs:

In nature, dung balls are rolled by dung beetles to a safe hiding place. The selection of suitable spawning sites is crucial for dung beetles in order to provide a safe environment for their offspring. A regional boundary selection strategy for modeling the spawning of female dung beetles is defined as:

$$\left\{\begin{array}{l}L{b}^{\ast }=\max \left(X^{\ast }\times \left(1-R\right),Lb\right)\\ U{b}^{\ast }=\max \left(X^{\ast }\times \left(1+R\right),Ub\right)\\ R=1-{\displaystyle \frac{t}{T_{\max }}}\end{array}\right.$$

(22)

where $L{b}^{\ast }$ and $U{b}^{\ast }$ are the lower and upper boundaries of spawning areas; $Lb$ and $Ub$ are the lower and upper bounds for decision variables; $X^{\ast }$ is the current localized optimal position; and $T_{\max }$ is maximum iterations.

Once the spawning region has been determined, female dung beetles select the egg balls in this region to lay their eggs, with each female dung beetle laying only one egg in each iteration. The boundary range of the spawning region is dynamically changing, and the position of the egg ball is also dynamic during the iteration process, denoted as:

$$B_i\left(t+1\right)=X^{\ast }+b_1\times \left(B_i\left(t\right)-L{b}^{\ast }\right)+b_2\times \left(B_i\left(t\right)-U{b}^{\ast }\right)$$

(23)

where $B_i\left(t\right)$ is the location information of the $i$ dung beetle’s sperm at $t$; and $b_1$ and $b_2$ denote two independent random vectors of size $1\ast D$, where $D$ denotes the dimension of the optimization problem, and the positions of the ovoid spheres are strictly limited.

(3)

Baby dung beetle foraging:

Some dung beetles that have grown to adulthood will burrow out of the ground to forage for food, called baby dung beetles. It is also necessary to establish optimal dung beetle areas to guide the dung beetles to forage for food, and the boundaries of the optimal dung beetle areas are defined as follows:

$$\left\{\begin{array}{l}L{b}^b=\max \left(X^b\times \left(1-R\right),Lb\right)\\ U{b}^b=\max \left(X^b\times \left(1+R\right),Ub\right)\\ R=1-{\displaystyle \frac{t}{T_{\max }}}\end{array}\right.$$

(24)

where $L{b}^b$ and $U{b}^b$ are the lower and upper boundaries of foraging areas; $Lb$ and $Ub$ are the lower and upper bounds for decision variables; $X^b$ is the current best position for foraging in foraging areas; and $T_{\max }$ is the maximum iterations.

$$x_i\left(t+1\right)=x_i\left(t\right)+C_1\times \left(x_i\left(t\right)-L{b}^b\right)+C_2\times \left(x_i\left(t\right)-U{b}^b\right)$$

(25)

Here, $x_i\left(t\right)$ is the location information of the $i$ baby dung beetle at $t$; $C_1$ is a random number obeying a normal distribution; and $C_2$ is a random vector belonging to $\left(0,1\right)$.

(4)

Dung Beetle Stealing:

There are also dung beetles known as stealing dung beetles that will steal dung balls from other dung beetles, which is a very common phenomenon in nature, and the location update information for the stealing dung beetle is defined as follows:

$$x_i\left(t+1\right)=S\times g\times \left(\left|x_i\left(t\right)-X^{\ast }\right|+\left|x_i\left(t\right)-X^b\right|\right)+X^b$$

(26)

where $x_i\left(t\right)$ is the location information of the $i$ stealing dung beetle at $t$; $g$ is the independent random vectors of size $1\ast D$, which follows a normal distribution; and $S$ is a constant value.

3.4. Compromise Solution Selection Method

The entropy weight method is used for selecting the compromise solution in the Pareto solution set, and the process is as follows:

(1)

Un-dimensioned process:

① For a positive index, the larger the value of the indicator, the better. The treatment is as follows:

$${\chi }_{ij}^{\prime }={\displaystyle \frac{x_{ij}-m_j}{M_j-m_j}}$$

(27)

② For a reverse index, the smaller the value of the indicator, the better. The treatment is as follows:

$${\chi }_{ij}^{\prime }={\displaystyle \frac{M_j-x_{ij}}{M_j-m_j}}$$

(28)

where $M_j$ is the maximum value of the target $j$; and $m_j$ is the minimum value of the target $j$.

(2)

Target normalization:

$$p_{ij}={\displaystyle \frac{{\chi }_{ij}^{\prime }}{\sum _{i=1}^n{\chi }_{ij}^{\prime }}}$$

(29)

Here, ${\chi }_{ij}^{\prime }$ is the dimensionless target value; and $p_{ij}$ is the normalized target value. $n$ is the number of solutions in the solution set.

(3)

Calculation of the entropy of target $j$:

$$e_j=-{\displaystyle \frac{1}{\ln n}}\sum _{i=1}^n{p}_{ij}\ln p_{ij},0\le e_j\le 1$$

(30)

Here, $e_j$ is the entropy value of the target $j$.

(4)

Calculation of the coefficient of variation:

$$g_j=1-e_j$$

(31)

Here, $g_j$ is the coefficient value of the target $j$.

(5)

Calculation of the weights of target $j$:

$$w_j={\displaystyle \frac{g_j}{{\displaystyle \sum _{j=1}^m}{g}_j}}$$

(32)

Here, $w_j$ is the weight of the target $j$. The optimal solution is selected in the solution set based on the target weights.

3.5. Short-Term Optimal Dispatch Methodology Process for Pumped-Storage-Containing Power Plant Grid Based on Security Quantification

The flowchart of the short-term optimal dispatch method of the power grid containing a pumped-storage power station based on security quantification is shown in Figure 1, and the specific steps are as follows:

(1)

Construct the grid security evaluation index system by taking the grid security level as the target layer, the scheduling time period as the criterion layer, and the flexibility resource capacity index, flexibility resource responsiveness index, and branch load balance degree index as the index layer.

(2)

Obtain typical load curves, build the judgment matrix according to the load size using the scale method, judge whether the matrix meets the consistency, and if it meets it, calculate the weights of each scheduling period, or else reconstruct the judgment matrix.

(3)

According to the evaluation indexes, use the scale method to establish the judgment matrix, determine whether the matrix meets the consistency, and if the conditions are met, calculate the weights of each index; otherwise, reconstruct the judgment matrix.

(4)

Consider the constraints to initialize the decision variables and algorithm parameters, as different kinds of particles are updated according to their respective updating principles; the objective function values are calculated, while the indexes corresponding to the solutions are calculated and retained as the data set.

With the particle update, the particle type is first determined. If it is the Dung Beetle Roller in accessibility mode, update the position according to Equation (20); if it is the Dung Beetle Roller in obstacle mode, update the position according to Equation (21); if it is the dung beetle laying eggs, determine the spawning area according to the local optimal position using Equation (22), and update the position within the area according to Equation (23); if it is baby dung beetle foraging, determine the foraging area according to the global optimal position using Equation (24), and within the area, update the position according to Equation (25); in the case of Dung Beetle Stealing, obtain the global optimal position and local optimal position, and update the position by combining Equation (26).

(5)

After all particles are updated, one iteration is completed. At this point, according to the data set retained from the last iteration and the data set collected in this iteration, divide the fuzzy evaluation subset using mean clustering, select the half of the data set closest to the center of mass in each interval to be retained, erase the rest of the data set, release the memory, and continue to the next iteration.

(6)

At the end of the iteration, output the Pareto solution set, and calculate the index affiliation according to the latest fuzzy evaluation subset interval.

(7)

Combine the weights to evaluate the grid security level of the corresponding solutions, obtain the Pareto solution sets corresponding to different levels, and select the optimal scheduling plan using the entropy weight method.

4. Example Analysis

4.1. Description of Instances

The improvement in the term IEEE 30-bus grid accessed by a pumped-storage power plant is used as an example to verify the effectiveness of the proposed modeling method, and its basic structure is shown in Figure 2. Nodes 1 and 27 are thermal power plant access nodes with capacities of 80 and 55 MW, respectively; node 2 is a hydroelectric power plant access node with a capacity of 80 MW; node 13 is a pumped-storage power plant access node with a capacity of 40 MW; node 22 is a photovoltaic power plant access node with a capacity of 50 MW; and node 23 is a wind power plant access node with a capacity of 30 MW, and the limit of the transmission capacity of the line is shown in

Table 2. Line limit transmission capacity.

Prime Node	End Node	Maximum Transmission Capacity (MVA)	Prime Node	End Node	Maximum Transmission Capacity (MVA)
1	2	130	15	18	16
1	3	130	18	19	16
2	4	65	19	20	32
3	4	130	10	20	32
2	5	130	10	17	32
2	6	65	10	21	32
4	6	90	10	22	32
5	7	70	21	22	32
6	7	130	15	23	16
6	8	32	22	24	16
6	9	65	23	24	16
6	10	32	24	25	16
9	11	65	25	26	16
9	10	65	25	27	16
4	12	65	28	27	65
12	13	65	27	29	16
12	14	32	27	30	16
12	15	32	29	30	16
12	16	32	8	28	32
14	15	16	6	28	32
16	17	16

.

Typical daily new energy forecasts and load processes are shown in Figure 3.

Pumped-storage power plants operate flexibly, but the frequent switching of operating conditions will cause large losses to the unit and shorten the service life of the unit. Four pumped-storage power plant operation scenarios are proposed for comparative analysis: operation mode 1: one pumping and one generating, which means that the pumped-storage power plant completes one pumping and one generating in one dispatching cycle; operation mode 2: one pumping and two generating; operation mode 3: two pumping and one generating; operation mode 4: two pumping and two generating. It is assumed that there is at least a 1 h interval between the pumping condition and power generation condition.

4.2. Calculation of Scheduling Time Period Weights and Indicator Weights

Load forecasting, according to the load size of the importance of the time period of two–two comparisons, and establish the judgment matrix. The judgment principle is load peak time importance > load trough time importance, and the judgment matrix of scheduling time is shown in Equation (A1) in Appendix A. The weights of the scheduling periods are shown in

Table 3. Weights of scheduling periods.

Scheduling periods	1	2	3	4	5	6
Weights	0.0167	0.0133	0.0200	0.0100	0.0067	0.0033
Scheduling periods	7	8	9	10	11	12
Weights	0.0233	0.0267	0.0300	0.0333	0.0800	0.0367
Scheduling periods	13	14	15	16	17	18
Weights	0.0767	0.0600	0.0500	0.0567	0.0533	0.0667
Scheduling periods	19	20	21	22	23	24
Weights	0.0400	0.0467	0.0633	0.0433	0.0733	0.0700

.

For the index in the security evaluation index system, the importance of the flexibility resource capacity indicator > the importance of the branch load balance degree indicator > the importance of the flexibility resource responsiveness indicator, and the judgment matrix of the security index is:

$$\left[\begin{array}{ccc}1& 0.5& 0.33\\ 2& 1& 0.67\\ 3& 1.5& 1\end{array}\right]$$

The weights of the security index are shown in

Table 4. Weights of security index.

Index	Flexibility Resource Capacity	Branch Load Balance	Flexibility Resource Responsiveness
Weights	0.5	0.33	0.17

.

4.3. Optimized Scheduling Results

The number of populations in the DBO algorithm was set to 200, the number of iterations was set to 200, and both the model and algorithm programs were written in the Matlab platform. The model running environment is set as follows: the CPU is Intel(R)Core(TM)[email protected]; the memory is 16G; the operating system is Windows 10; the software environment is Matlab version 2022a; and the Pareto solution set for solving the optimization model is shown in Figure 4.

As can be seen from Figure 4, there is an obvious competitive relationship between the grid new energy consumption rate and network loss. For the flexibility resource responsiveness index, the flexibility resource response rate is pumped storage > hydropower > thermal power, and the response rate is taken as 3, 2, and 1. K-mean clustering is carried out in the iterative process, and the clustering is completed by setting K = 5. The clusters obtained from clustering are rank ordered from good to bad, i.e., rank one corresponds to good, and rank five corresponds to bad. The ensemble of rank one and rank two is set as excellent in the fuzzy evaluation subset, rank three is set as good in the fuzzy evaluation subset, rank four is set as medium in the fuzzy evaluation subset, and rank five is set as qualified in the fuzzy evaluation subset. The dynamically updated fuzzy evaluation subsets for each scenario are shown in

Table 5. Fuzzy evaluation subsets.

Operating Method	Index	Pass	Intermediate	Merit	Distinction
Pumping once and generating once	Flexibility resource capacity	[112, 124]	[124, 139]	[139, 162]	[162, 169]
	Branch load balance	[0.23, 0.27]	[0.21, 0.23]	[0.20, 0.21]	[0.19, 0.20]
	Flexibility resource responsiveness	[166, 187]	[187, 214]	[214, 240]	[240, 293]
Pumping once and generating twice	Flexibility resource capacity	[109, 127]	[127, 139]	[139, 163]	[163, 171]
	Branch load balance	[0.23, 0.27]	[0.22, 0.23]	[0.21, 0.22]	[0.19, 0.21]
	Flexibility resource responsiveness	[162, 165]	[165, 176]	[176, 208]	[208, 286]
Pumping twice and generating once	Flexibility resource capacity	[113, 123]	[123, 140]	[140, 163]	[163, 167]
	Branch load balance	[0.22, 0.26]	[0.21, 0.22]	[0.20, 0.21]	[0.19, 0.20]
	Flexibility resource responsiveness	[175, 187]	[187, 211]	[211, 231]	[231, 289]
Pumping twice and generating twice	Flexibility resource capacity	[116, 123]	[123, 140]	[140, 161]	[161, 169]
	Branch load balance	[0.24, 0.27]	[0.23, 0.24]	[0.21, 0.23]	[0.19, 0.21]
	Flexibility resource responsiveness	[170, 174]	[174, 179]	[179, 194]	[194, 280]

.

According to the fuzzy evaluation subset of the solutions in the Pareto solution set, to calculate the degree of affiliation, combined with the weight to evaluate the grid security level. According to the grid security level, the solution set is reclassified, and the entropy weight method is used to select the compromise solution; the Pareto solution set under each level is shown in Figure 5, and the range of new energy consumption and the range of network loss of each grid security level under different operation modes are shown in

Table 6. Range of new energy consumption and grid losses.

Operating Method	Grid Security Level	New Energy Consumption Rate Limit (%)	Grid Loss Limit (MW)
Pumping once and generating once	Distinction	94.76–96.94	53.64–55.15
	Merit	95.56–97.05	53.79–55.17
	Intermediate	95.26–97.55	53.72–55.94
	Pass	94.93–97.32	53.35–55.92
Pumping once and generating twice	Distinction	95.21–97.89	54.25–55.28
	Merit	95.93–98.17	54.27–56.00
	Intermediate	95.54–98.42	54.27–56.25
	Pass	95.33–98.51	54.26–56.49
Pumping twice and generating once	Distinction	92.58–96.51	54.75–56.17
	Merit	92.24–97.22	54.67–56.68
	Intermediate	92.34–97.02	54.69–56.41
	Pass	93.02–96.06	54.86–55-94
Pumping twice and generating twice	Distinction	96.24–98.20	55.23–56.73
	Merit	95.65–97.98	55.21–56.63
	Intermediate	95.35–97.86	55.19–56.59
	Pass	95.27–98.29	55.18–56.75

.

From Figure 5 and Table 6, it can be seen that under the operation mode of one pump and one generator, when the grid security level is in the optimal range, compared with the other levels, the guaranteed rate of new energy consumption is the smallest at 94.76%. When the grid security level is good, the maximum guaranteed rate of new energy consumption is 95.56%. If the decision maker favors the new energy consumption rate, the new energy consumption rate can reach 97.55%, and the grid security level is medium; if the decision maker favors the grid loss, the minimum loss is 53.35 MW, and the grid security level is qualified. When the decision maker favors the grid security level, the new energy consumption decreases by 2.79% at most, and the grid loss increases by 3.37% at most.

Under the operation mode of one pump and two generators, when the grid security level is in the optimal range, compared with the other levels, the guaranteed rate of new energy consumption is at least 95.21%. When the grid security level is good, the maximum guaranteed rate of new energy consumption is 95.93%. If the decision maker prefers the new energy consumption rate, the new energy consumption rate can reach 98.51%, and then the grid security grade is qualified; if the decision maker prefers the grid loss, the minimum loss is 54.25 MW, and then the grid security grade is excellent. When the decision maker favors the grid security level, the new energy consumption decreases by 3.3% at most, and the grid loss increases by 1.9% at most.

Under the operation mode of two pumping and one generating, when the grid security level is within the good range, compared with the other levels, the guaranteed rate of new energy consumption is 92.24% at the minimum. When the grid security level is qualified, the maximum guaranteed rate of new energy consumption is 93.02%. If the decision maker prefers the new energy consumption rate, the new energy consumption rate can reach 97.22%, and the grid security grade is good; if the decision maker prefers the network loss, the minimum network loss is 54.67 MW, and the grid security grade is good. When the decision maker favors the grid security level, the new energy consumption decreases by up to 4.64%, and the grid loss increases by up to 2.74%.

Under the operation mode of two pumps and two generators, when the grid security level is within the qualified range, compared with the other levels, the guaranteed rate of new energy consumption is at least 95.27%. When the grid security level is excellent, the maximum guaranteed rate of new energy consumption is 96.24%. If the decision maker favors the new energy consumption rate, the new energy consumption rate can reach 98.29%, and then the grid security level is qualified; if the decision maker favors the grid loss, the minimum loss is 55.18 MW, and then the grid security level is qualified. When the decision maker favors the grid security level, the new energy consumption decreases by 2.05% at most, and the grid loss increases by 2.81% at most.

Table 7. Optimization results of compromise solutions for different operation modes of pumped-storage plant.

Operating Method	New Energy Consumption Rate (%)	Grid Loss (MW)
Pumping once and generating once	96.63	54.527
Pumping once and generating twice	97.65	54.354
Pumping twice and generating once	95.80	55.854
Pumping twice and generating twice	96.38	55.237

shows the optimization results of the compromise solution for different operation modes of the pumped-storage power plant, and provides an analysis of the impact of the change of different operation modes in the pumped-storage power plant through a comparison of different objectives.

From the perspective of new energy consumption, comparing the index of the new energy consumption rate, the operation mode of “pumping once and generating twice” for the pumped-storage power station is better than “pumping once and generating once”, better than “pumping twice and generating twice”, and better than “pumping twice and generating once”. From the economic point of view, comparing the system network loss index, the operation mode of “pumping once and generating twice” for the pumped-storage power station is superior to “pumping once and generating once”, “pumping twice and generating twice”, and “pumping twice and generating once”. Through the above comparison, it can be seen that the operation mode of one pump and two generators of the pumped-storage power station is optimal because the typical load curve shows a double hump shape, and there are two peak hours, the afternoon peak and the evening peak. Arranging two times for power generation in a pumped-storage power station can reduce the pressure of the power supply in the load peak, make the grid current reasonable, reduce the network loss, and make the line capacity abundant. Arranging pumping once in the load valley is conducive to the consumption of wind power at night, which improves the rate of new energy consumption.

The results of the optimization of the power output of the grid for each time period and for each scenario are shown in Figure 6.

When the pumped-storage power station is set in the operation state of “one pumping and one generating”, it is in the pumping condition during the low load period from 1 to 6 h and in the generating condition during the evening peak from 17 to 22 h, during which the load is larger and the photovoltaic power generation capacity is weaker, and the reasonable arrangement of the pumped-storage power station at this time is conducive to reducing the pressure of the power supply. When the pumped-storage power station is set in the “one pumping and two generating” operation state, it is in the pumping condition during the hours 1–6 in the load valley and is in the generating condition during the hours 12–14 in the afternoon peak and 19–22 in the evening peak; compared with “one pumping and one generating”, this kind of operation can take care of two load peak hours at the same time, which is beneficial to the power supply pressure. Compared with “one pumping and one generating”, this operation can simultaneously take care of two load peak hours, which is conducive to the reasonable distribution of the grid current and reduction in network loss. When the pumped-storage power station sets the “two pumping and one generating” operation state, it is in the pumping operation at 1–4 and 7–9 h and is in the generating operation at 17–22 h; this operation mode has a big difference in the load curve, so it divides the load valley time into two parts to meet the conditions; the primary power generation does not take into account the afternoon peak time, so this operation mode is not ideal. However, due to the water balance constraint, the pumped-storage power generation capacity is strong in the evening peak hours compared with the other operation methods. When the pumped-storage power station is set to the “two pumping and two generating” operation, it is in pumping condition from 1 to 4 and 7 to 9 h and is in the generating condition in the afternoon peak from 12 to 14 h and the evening peak from 19 to 22 h, which can better deal with the peak load hours, and the two pumping are slightly redundant.

In order to verify the validity of the proposed model, the model with the objectives of maximum new energy consumption and minimum grid loss of the system is used as a comparison model, which is called the “traditional model”. The operation mode of the pumped-storage plant is selected as “pumping once and generating once”, and the optimization results of the two models are shown in

Table 8. Optimization results of the two models for typical period.

Typical Period	Model	New Energy Consumption Rate (%)	Grid Loss (MW)	Grid Security Level
Dry water period	Traditional model	96.56	54.44	Merit
	Proposed model	96.63	54.53	Distinction
Flood season	Traditional model	89.27	64.40	Intermediate
	Proposed model	87.17	63.58	Distinction

to evaluate the effectiveness of the proposed model through the comparison of different objectives.

In the dry water period, compared with the traditional model, the new energy consumption rate of the proposed model is increased by 0.13%, the grid loss is increased by 0.16%, and the security level is improved. The above analysis shows that although the grid loss in the proposed model is large, the optimization target value of the proposed model incorporates the grid security level, which improves the ability of the optimization results to cope with accidents and makes the grid operation state more secure. In the flood season, compared with the traditional model, the new energy consumption rate of the proposed model is reduced by 2.1%, the grid loss is reduced by 1.3%, and the grid security level is improved. The above analysis shows that the proposed model has a slight loss in the new energy consumption rate and grid loss indicators compared with the traditional model, but the ability to cope with accidents is greatly improved. From the perspective of different periods, during the flood season, the upstream water increases, and the proportion of hydropower generation increases, resulting in a decrease in the new energy consumption rate.

Table 9. Calculation time comparison.

Model	Calculation Time/Min
	Dry Water Period	Flood Season
Proposed model	6.423	6.481
Traditional model	4.058	4.382

shows the results of the calculation time of the two models in different periods. The solution time of the proposed model is slightly larger than that of the traditional model, but both models can complete the solution within a few minutes, which meets the time-sensitive requirements of power generation programming in actual power dispatch.

4.4. Sensitivity Analysis of the Increase in the Installed Capacity of New Energy Sources

A wind and light new energy power station is in the stage of vigorous development, and the future installed new energy capacity is expected to account for 40% of the total installed capacity of the system; at present, the improvement in the term IEEE 30-bus grid in the installed new energy capacity accounted for 24% only. Under the prospect of growing the installed new energy capacity, the large-scale integration of new energy into the grid will inevitably change the operation mode of the existing power structure. The growth rate of the installed new energy capacity is analyzed in different typical periods, taking into account the different operation modes of pumped-storage power plants.

Figure 7 analyzes the sensitivity of the grid’s new energy consumption rate to the growth rate of the installed wind and PV capacities under the existing channel capacity.

As the installed capacities of wind power and photovoltaic (PV) power increase, the grid’s new energy consumption stays the same at first, and then gradually decreases. This is because at the beginning, the installed wind power and photovoltaic capacities accounted for a small proportion of the installed capacity of the grid; the system flexibility resources are sufficient, so the new energy sources can be fully absorbed. When the proportion of the installed capacity of new energy reaches 17%, under the operation mode of pumped-storage power plant with two pumps and one generator, the rate of new energy consumption starts to decrease, considering the system network loss and security level. Upon adjusting the operation mode of the pumped-storage power station, when the proportion of the installed new energy capacity reaches 20%, the new energy consumption can still be fully absorbed.

Figure 8 analyzes the sensitivity of grid network losses to the growth rate of the installed wind and PV capacities given the available channel capacity.

With the increase in the installed capacities of wind power and photovoltaic power, the network loss of the power grid first decreases, and then gradually rises. This is because there is a certain complementary characteristic between new energy and load, which is conducive to the coordination of the power supply and conventional power load at the node, and it reduces the network loss. When the proportion of the installed new energy capacity reaches 22–24%, the system network structure and load remain unchanged, and the network loss gradually increases. When the proportion of the installed new energy capacity reaches 35%, the network loss increases slowly due to the sacrifice of the new energy consumption rate index.

5. Conclusions

In this paper, a short-term optimal scheduling method based on security quantification is proposed for grid security optimization of pumped-storage-containing power plants. Combining the security evaluation method with scheduling, a short-term optimized scheduling model of the grid based on security quantification is constructed according to the grid security evaluation model. The improvement in the term IEEE 30-bus grid accessed by the pumped-storage power station is used as an example for research, and the results show that the method proposed in this paper can improve the security of the power grid while pursuing the new energy consumption rate and economy, and it can provide support for the safe and stable operation of the power system. Regarding pumped-storage power plants, it is recommended to combine the load curve and reasonably select the operation mode according to the number of peak and trough loads. With the increase in the installed capacities of wind power and photovoltaic power, the reasonable selection of the intervention bus and configuration capacity of each power source can reduce the trends of new energy reduction and grid loss increase. In the future, with the continuous acquisition of new information, the practical application can be solved on a rolling time scale, realizing the dynamic update in the power generation plan.