Optimization and Stability Research of Control Strategies for Multienergy Complementary AC–DC Hybrid Power Grids

Abstract

The randomness of power grid has been greatly increased as the new energy power proportion increases due to the uncertainty of wind turbine (WT) and photovoltaic (PV) power, posing significant challenges to grid security and economic efficiency. In this paper, the typical‐day WT and PV power outputs were obtained by the Latin hypercube sampling method. A multiobjective dual‐layer optimization model has the goal of reducing network loss and voltage deviation. The Whale Optimization Algorithm (WOA) was employed to solve the model. Based on the optimization results, the dispatch schemes for reactive power compensation devices, energy storage systems, and on‐load voltage regulation devices are formulated to improve system stability and smooth the output fluctuations of new energy sources. Finally, the proposed method is verified in the improved AC/DC hybrid grid based on IEEE 39‐notes system. The results indicated that the method can effectively reduce the network loss and smooth voltage fluctuations. It provides a theoretical basis for the stable and economical of grids with a high proportion of new energy power.

1. Introduction

With the advancement of the “dual carbon” goal, the integration of new energy into power grids has surged. However, the uncertainty of wind turbine (WT) and photovoltaic (PV) power severely impacts grid security and stability. It is of great significance to study the control strategies for power grid stability in addressing the high proportion of WT and PV power.

The WT and PV output is determined by meteorological conditions and has strong randomness. Extracting typical WT and PV output curves is the basis for studying grid connection strategies. Liu et al. employed Latin hypercube sampling for initial scenario generation and Euclidean distance for scenario reduction [1]. Zheng et al. proposed a scenario analysis method combining quantile regression and t-SNE dimensionality reduction [2]. Wang et al. employed Wasserstein distance for optimal quantile selection and improved K-medoids clustering for scenario reduction [3]. Voltage fluctuations and transmission losses directly determine the stability and economy of power grid operation, and researchers have conducted extensive research on various power grid models. As early as 1994, Yokoyama et al. proposed a multiobjective optimization algorithm for AC/DC hybrid power grids to address the problem of wind and solar random output [4]. Yin et al. considered wind uncertainty in reactive power optimization with objectives of loss, voltage deviation, and stability margin [5]. Liu et al. proposed a dual-strategy particle swarm optimization (PSO) for reactive power optimization in distribution grids [6]. Nie and Zhang proposed an improved PSO (IPSO) algorithm that incorporates chaos and simulated annealing mechanisms, with the economic operation index of the power grid as the optimization objective, to enhance the optimization capability of the system [7]. A. I. V. et al. proposed a multiobjective particle swarm optimization (MOPSO) algorithm for microgrid regulation of new energy access [8]. Liu et al. combined PSO with K-means clustering for regionalized optimization [9]. Genetic algorithm (GA) has advantages such as strong global search capability, good robustness, low requirements for the mathematical model of the problem, and ease of parallel computing, thus having potential application value in multiobjective optimization of power systems [10, 11]. Researchers have introduced a novel intelligent heuristic global optimization algorithm inspired by the hunting patterns of humpback whales named Whale Optimization Algorithm (WOA), which include the guidance strategies of group encircling search and spiral bubble attack to make up for the deficiencies existing in the iterative update of the PSO algorithm [11, 12]. Hasanien introduced the WOA into the multiobjective optimization of power systems that has improved the convergence speed and optimization efficiency [13]. Baradar and Ghandhari formulated a multiobjective model for VSC-HVDC grids [14]. Fu et al. developed a day-ahead scheduling model integrating ESS for peak shaving [15].

Previous researches have validated the accuracy of the proposed model and algorithm, effectively reducing grid system loss and improving system stability when considering new energy. In AC/DC power grids with new energy and EES, variable types and regulation strategies are more complex, and previous research algorithms are insufficient to cope with these situations. Based on previous research, a dual-layer optimization model for AC/DC grids was proposed, incorporating ESS and reactive power compensation to enhance stability and efficiency. The WOA was employed to solve the model. Switching schemes for reactive power compensation devices (SVC) and EES were developed to improve system voltage stability and smooth out fluctuations in new energy output. The improved 39-node standard system was employed for verification, and the results showed that the optimization algorithm demonstrates strong performance in reducing line losses and voltage fluctuations, achieving the stable and economic operation of the power grids.

2. Stochastic Models for WT and PV Generation

2.1. Correlation Models With Meteorological Parameters

The output power of PV can be approximated by the following formula based on the principle of PV: 1 $\begin{array}{}{P}_{\text{pv}}=\left\{\begin{array}{cc}{P}_{\text{pv},r}\frac{I}{I_{\max }},& I\le I_{\max },\\ P_{\text{pv},r}& I>I_{\max },\end{array}\right.\end{array}$ where P_pv is the output power of the PV module, which is a function of light intensity, P_pv,r refers to the rated power of a single PV module, and I and I_max are the actual and maximum light intensities during a certain period of time, respectively. Studies showed that PV power follows Beta distribution model [14], and its probability density function is in equation (2). 2 $\begin{array}{}f\left(I\right)=\frac{I}{I_{\max }}\frac{\mathrm{\Gamma }\left(\sigma +\theta \right)}{\mathrm{\Gamma }\left(\sigma \right)\mathrm{\Gamma }\left(\theta \right)}{\left(\frac{I}{I_{\max }}\right)}^{\sigma -1}{\left(1-\frac{I}{I_{\max }}\right)}^{\theta -1},\end{array}$ where Γ is the gamma function, and both σ and θ are parameters of the Bate distribution function.

The output power of WT depends on the real-time wind speed at the WT height, and its functional relationship is as follows: 3 $\begin{array}{}{P}_{\text{WT}}=\left\{\begin{array}{cc}0,& 0<v<v_{\text{in}}\text{\hspace{0.17em}or\hspace{0.17em}}v>v_{\text{off}},\\ P_n\frac{v-v_{\text{in}}}{v_n-v_{\text{in}}},& v_{\text{in}}\le v<v_n,\\ P_n,& v_n\le v\le v_{\text{off}},\end{array}\right.\end{array}$ where P_WT and P_n are the actual and rated output powers of the WT, respectively, v_n is the rated wind speed of the WT, and v_in and v_off are the cutting-in and cutting-off wind speeds of the WT, respectively. The v refers to the average wind speed during a certain period of time, with a probability density close to the Weibull distribution model, and its functional relationship can be expressed as follows [15]: 4 $\begin{array}{}f\left(v\right)=\frac{k}{c}{\left(\frac{v}{c}\right)}^{k-1}{e}^{-{\left(v/c\right)}^k},\end{array}$ where k and c are both parameters of the Weibull distribution coefficient which can be obtained by fitting in accordance with statistical laws.

2.2. Scenery Sampling Scene Generation

Due to the strong randomness and intermittency of meteorological parameters, as well as the time-varying nature of wind and PV power output, in order to ensure high-precision results at a small sampling scale, this paper took advantage of the Latin hypercube stratified sampling method to establish an original scene set of wind and PV output containing 1000 samples, as shown in Figure 1(a), and the generated scene conforms to objective laws [16]. This scene set includes similar scenes, highly correlated scenes, and scenes with low probability of occurrence. The Kantorovich distance reduction algorithm was employed in this paper to reduce the original scene and extract the most probable output curve of WT and PV [17, 18]. Combined with the random probabilities of each scene, the most probable output curve was selected as the actual output scene for wind and solar power.

[IMAGE OMITTED. SEE PDF]

3. Dual-Layer Optimization Model for Power Coordination Control

Due to the uncertainty and randomness of the new energy power output, the system losses and voltage fluctuations will exhibit new characteristics in the AC/DC hybrid power grid with the increase of new energy power proportion in the power grid. Therefore, it is one of the core issues to achieving power grid decarbonization of researching stability control strategies for power grids with high proportion of new energy. In response to these issues, Liu et al. integrated the two-beta method and the RoCoF method to study the impact of stochastic power source disturbances on power grid operation [19]. In the face of the characteristics of multiple target parameters, strong randomness, and nonlinearity in power grid regulation with new energy, researchers have developed applications for multiobjective parameter optimization based on the PSO algorithm [6, 20]. To address the issues of AC/DC hybrid power grids with new energy integration, Cao et al. established a two-layer model for active and reactive power optimization and solved it using the WOA [21]. An AC/DC power grid with new energy integration is taken as the research object in this paper. A dual-layer active and reactive power optimization model was established with power loss and voltage fluctuation as its optimization objectives.

3.1. Upper-Level Optimization Model

The system power loss is relatively sensitive to changes in active power. In the upper model, the minimization of network loss was adopted as the target parameter for active power regulation. The reactive power injection in the upper model was obtained through the lower model which takes the reactive power as its optimization target [18]. The two models undergo an iterative process, with cyclic updates performed after each iteration.

3.1.1. Objective Function

The system power loss is mainly caused by the Ohmic loss of equipment in the power grid. This part of energy not only causes the equipment temperature to rise which threatens insulation but also significantly affects the transmission efficiency and economic operation of the power grid. To minimize the total active power loss of the AC/DC hybrid system, the optimization target in the upper-level model mainly includes AC and DC parts, as shown in equation (5). 5 $\begin{array}{}\min f\left(x,u\right)=\frac{1}{T}{\displaystyle \sum }_{t=0}^T{P}_{\text{loss},t}=\frac{1}{T}{\displaystyle \sum }_{t=0}^T\left(P_{\text{acloss},t}+P_{\text{dcloss},t}\right),\end{array}$ where the subscript t represents the circuit parameters at a certain moment, T is the calculation time period, and P_loss,t is the total active power loss of the system at time t, which includes active power losses both of the AC (P_acloss,t) and DC (P_dcloss,t) systems. The active power losses of the AC and DC systems are as shown in equation (6), respectively. 6 $\begin{array}{}\left\{\begin{array}{c}{P}_{\text{acloss},t}={\displaystyle \sum }_{i,j}^{N_c}{G}_{ij}\left(U_i^2+U_j^2+2U_i{U}_j\cos {\theta }_{ij}\right),\\ P_{\text{dcloss},t}={\displaystyle \sum }_k^{N_d}{I}_k^2{R}_k,\end{array}\right.\end{array}$ where N_c and N_d are the total number of nodes in AC and DC systems, respectively. The main symbol G stands for admittance, and U represents voltage, the subscript i and j are both node numbers in AC system, and θ_ij is the phase difference between nodes i and j of voltage. The main symbols I and R represent the current and resistance in the DC system, respectively, and the subscript k indicates the DC node number.

3.1.2. Constraint Conditions

The constraints of the upper model should include power flow constraints, grid security boundary limits (GSBL) constraints, and the constraint of ESS.

3.1.2.1. Trend Constraints

Power flow constraints include active power constraints and reactive power constraints as shown in equation (7). 7 $\begin{array}{}\left\{\begin{array}{c}{P}_{\text{Gi},t}+P_{\text{WTi},t}+P_{\text{PVi},\text{t}}+P_{\text{ESSi},t}^{\mathrm{\ast }}-P_{\text{Li},t}-P_{\text{ti}\left(\text{dc}\right),t}=U_i{\displaystyle \sum }_{j=1}^N{U}_j\left(G_{ij}\cos {\theta }_{ij}+B_{ij}\sin {\theta }_{ij}\right),\\ Q_{\text{Gi},t}+Q_{\text{WTi},t}+Q_{\text{PVi},t}+Q_{C\text{i}}-Q_{\text{Li},t}-Q_{\text{ti}\left(\text{dc}\right),t}=U_i{\displaystyle \sum }_{j=1}^N{U}_j\left(G_{ij}\sin {\theta }_{ij}-B_{ij}\cos {\theta }_{ij}\right),\end{array}\right.\end{array}$ where the main symbols P and Q represent active and reactive power, respectively, and the subscripts G, WT, PV, and L represent the output power of generators, WT, PV, and load, respectively. The main symbols G and B represent conductance and susceptance, respectively. The subscript ti(dc) represents the power exchange between the AC and DC systems. The $P_{\text{ESS}}^{\mathrm{\ast }}$ represents the active power output of the ESS, which is the parameter to be optimized in this level. The Q_ci represents the reactive power injected at node i, which can be provided by two types of reactive power sources: Static Var Generator (SVC) and capacitor bank (CB). 8 $\begin{array}{}{Q}_{C\text{i}}=Q_{S\text{VCi},t}+{\eta }_{\text{Ci},t}{Q}_{C0},\end{array}$ where η_C is the number of switched CB and Q_C0 is the reactive power output by a single capacitor. The η_C and Q_SVC are the variables to be controlled in the lower level model, with an initial value of 0 in the first solution, and then iteratively updated based on the optimization results of the lower-level model.

3.1.2.2. System Operation Security Constraints

The system safety constraints should include the safe operation constraints of power sources and lines, as shown in equations (9) and (10). 9 $\begin{array}{}\left.\begin{array}{c}{P}_{\text{Gi},\min }\le P_{\text{Gi},\min }\le P_{\text{Gi},\max },\\ P_{\text{WTi},\min }\le P_{\text{WTi},\min }\le P_{\text{WTi},\max },\\ P_{\text{PVi},\min }\le P_{\text{PVi},\min }\le P_{\text{PVi},\max },\end{array}\right|\left.\begin{array}{c}{Q}_{\text{Gi},\min }\le Q_{\text{Gi},\min }\le Q_{\text{Gi},\max },\\ Q_{\text{WTi},\min }\le Q_{\text{WTi},\min }\le Q_{\text{WTi},\max },\\ Q_{\text{PVi},\min }\le Q_{\text{PVi},\min }\le Q_{\text{PVi},\max },\end{array}\right|,\end{array}$ 10 $\begin{array}{}{h}_{m\min }\le G_{ij}{U}_i^2-U_i{U}_j\left(G_{ij}\cos {\theta }_{ij,t}+B_{ij}\sin {\theta }_{ij,t}\right)\le h_{m\min },\end{array}$ where h_mmin and h_mmax are the upper and lower limits of the power flow of branch m, respectively, and i and j are the two endpoints of branch m.

3.1.2.3. EES Constraints

The EES has two operating modes: charging and discharging. Its state of charge (SOC) at any moment is determined by remaining energy and the charging/discharging power. Its SOC is determined by the base remaining energy at the previous moment and the amount of charge or discharge power, and its specific model can be expressed as equation (11). 11 $\begin{array}{}\left\{\begin{array}{c}\text{SO}{\text{C}}_{\text{ESS},i}\left(t+\mathrm{\Delta }t\right)=\text{SO}{\text{C}}_{\text{ESS},i}\left(t\right)+\left(P_{\text{ch},i}\left(t\right)\mathrm{·}{\eta }_{\text{ch}}\mathrm{·}{D}_{\text{ch}}-P_{\text{dis},i}\left(t\right)/{\eta }_{\text{dis}}\mathrm{·}{D}_{\text{dis}}\right)\mathrm{\Delta }t,\\ 0\le P_{\text{c}\text{hi}}\left(t\right)\le P_{\text{c}\text{hi},\max },\\ 0\le P_{\text{d}\text{isi}}\left(t\right)\le P_{\text{d}\text{isi},\max },\\ t=t_0,t_0+\mathrm{\Delta }t,\cdots ,T,\end{array}\right.\end{array}$ where SOC_ESS,i(t) is the SOC of the ith EES at time t. The subscripts ch and dis denote the parameters in the charging and discharging states, respectively. The superscript η denotes the energy conversion efficiency of the EES; Δt and T represent the time step and research period, respectively; D_ch and D_dis are the working state indicator variable of the EES, which belong to switch variables. When the EES is in a charging state, D_ch is 1, and the corresponding value of D_dis will be 1 at the discharging state. In light of the operating characteristics of the EES, the values of D_ch and D_dis are mutually exclusive at a given moment, satisfying the relationship in equation (12). 12 $\begin{array}{}\left\{\begin{array}{c}{D}_{\text{ch}}+D_{\text{dis}}\le 1,\\ D_{\text{ch}}-D_{\text{dis}}\in \left(01,\right).\end{array}\right.\end{array}$

In addition, EES also needs to meet SOC constraints. 13 $\begin{array}{}01\le \text{SO}{\text{C}}_{\text{ESSi}}\left(t\right)\le .\end{array}$

3.2. Lower-Level Optimization Model

The optimization objective in the lower level model is minimization network loss and voltage fluctuation. The active power injection in the lower model is optimized from the upper model, and it is no longer a fixed value as the upper- and lower-level models iterate repeatedly.

3.2.1. Objective Function

Due to the significant impact of reactive power regulation on both system loss and voltage, a multiobjective optimization model taking the minimization of network loss and voltage deviation as its optimization objectives is established in the lower level model, as shown in equation (13). 14 $\begin{array}{}\left\{\begin{array}{c}\min f_1\left(x,u\right)=\frac{1}{T}{\displaystyle \sum }_{t=0}^T{P}_{\text{loss},t}=\frac{1}{T}{\displaystyle \sum }_{t=0}^T\left(P_{\text{acloss},t}+P_{\text{dcloss},t}\right),\\ \min f_2=\min \frac{1}{T}{\displaystyle \sum }_{t=0}^T\mathrm{\Delta }{U}_t=\min \frac{1}{T}{\displaystyle \sum }_{t=0}^T{\displaystyle \sum }_{\text{i}=1}^n\frac{\left|U_{i,t}-U_{p.u.}\right|}{\mathrm{\Delta }{U}_{i\max }}.\end{array}\right.\end{array}$

3.2.2. Constraint Conditions

The lower model also includes power flow constraints, system security boundary, and equipment operation boundary of reactive power source.

3.2.2.1. Power Flow Constraint

15 $\begin{array}{}\left\{\begin{array}{c}{P}_{\text{Gi},t}+P_{\text{WTi},t}+P_{\text{PVi},t}+P_{\text{ESSi},t}^{\mathrm{\ast }}-P_{\text{Li},t}-P_{\text{ti}\left(\text{dc}\right),t}=U_i{\displaystyle \sum }_{j=1}^N{U}_j\left(G_{ij}\cos {\theta }_{ij}+B_{ij}\sin {\theta }_{ij}\right),\\ Q_{\text{Gi},t}+Q_{\text{WTi},t}+Q_{\text{PVi},t}+Q_{C\text{i}}^{\mathrm{\ast }}-Q_{\text{Li},t}-Q_{\text{ti}\left(\text{dc}\right),t}=U_i{\displaystyle \sum }_{j=1}^N{U}_j\left(G_{ij}\sin {\theta }_{ij}-B_{ij}\cos {\theta }_{ij}\right).\end{array}\right.\end{array}$

The active power $P_{\text{ESS}}^{\mathrm{\ast }}$ supplied by EES is the control variable in the upper model. In the optimization process, the results of the upper model will be transmitted to the lower model as known variables, and automatically updated as the lower-level model is solved.

3.2.2.2. System Security Boundary

System security boundary includes constraints of both AC and DC systems. The AC system constraints include the allowable range of node voltage, the on-load tap changer (OLTC) regulation range of transformers, the number of groups of switched CB, and the input capacity of reactive power source, as shown in equation (16) 16 $\begin{array}{}\left\{\begin{array}{c}{U}_{i,\min }\le U_{i,t}\le U_{i,\max },\\ T_{k,\min }\le T_{k,t}^{\mathrm{\ast }}\le T_{k,\max },\\ {\eta }_{i,\min }\le {\eta }_{i,t}^{\mathrm{\ast }}\le {\eta }_{i,\max },\\ Q_{\text{SVCi},\min }\le Q_{\text{SVCi},t}^{\mathrm{\ast }}\le Q_{\text{SVCi},\max }.\end{array}\right.\end{array}$

The operational constraints of the DC system include the constraints on the current, voltage, and control angle of the converter. The constraint equation is shown in equation (17). 17 $\begin{array}{}\left\{\begin{array}{c}{I}_{\text{di},\min }\le I_{i,t}^{\mathrm{\ast }}\le I_{\text{di},\max },\\ U_{\text{di},\min }\le U_{\text{di},t}\le U_{\text{di},\max },\\ {\delta }_{\text{di},\min }\le {\delta }_{i,t}^{\mathrm{\ast }}\le {\delta }_{\text{di},\max },\\ i\in N_d.\end{array}\right.\end{array}$

The variables with “^∗” in the equations are the variables to be optimized.

3.2.2.3. The Coupling Relationship Between the Dual-Layer Model

In the established optimization model, the upper model took the operating state of the EES at each time as the control variable to be optimized. The tap ratio of the OLTC, reactive power output, and DC system control parameters are transmitted from the lower model to the upper-layer model as known quantities. With the solution of the upper model, the output of EES will be transferred to the lower model as known parameters to solve the reactive power variables. And then, the reactive power in the upper model is updated for the next iteration. The variables transfer relationship between the two models is shown in Table 1.

Table 1 Variables transfer relationship between the two models.

	Variables to be optimized	Variable to be updated
Upper model	$P_{\text{ESSi},t}^{\mathrm{\ast }}$	ηi,t, QSVCi,t, Tk,t, DC parameters
Lower model	${\eta }_{i,t}^{\mathrm{\ast }}$, $Q_{\text{SVCi},t}^{\mathrm{\ast }}$, $T_{k,t}^{\mathrm{\ast }}$, DC parameters	PEESi,t

4. Three Case Studies for Verification and Result Analysis

4.1. Example Parameter Settings

This article employed an improved AC/DC hybrid system based on IEEE 39-bus for verification and analysis. The system topology is shown in Figure 2.

[IMAGE OMITTED. SEE PDF]

The details of topology change are shown in Table 2. The scale of energy exchange per cycle of ESS is 60 MW with the SOC range between 0.1 p.u and 0.9 p.u. SVC is connected with a capacity of 100 Mvar to node 6. The hybrid reactive power compensation device containing SVC of 100Mvar and the compensation CB with a single-group capacity of 20 Mvar and the maximum switching group of 5 were connected to nodes 21 and 25, respectively. Each OLTC devices is equipped with 8 tap positions, with a regulation step size of 0.025 p.u. The boundary values of the control parameters for each device in the system are presented in Table 3.

Table 2 Details of topology change in IEEE 39-bus system.

Type	Name	Node number	Capacity
PV	PV1	4	70 MW
PV2	29	100 MW
WT	WT1	7	120 MW
WT2	26	100 MW
EES	EES1	3	500 MW·h
EES2	24	500 MW·h
SVC	SVC1	6	100 Mvar
SVC2	21	100 Mvar + 5 ∗ 20 Mvar
SVC3	26	100 Mvar + 5 ∗ 20 Mvar
DC line	DC1	14–18	—
DC2	15–16
DC3	16–28
OLTC	OLTC1	2–30	—
OLTC2	11–12
OLTC3	22–35
OLTC4	29–38

Table 3 Boundary limits for control variables.

Control variable	Upper limit	Lower limit	Control variable	Upper limit	Lower limit
Tk (p.u)	1.1	0.9	Id3−4 (p.u.)	1.0	0.2
QCB (group)	5	0	Id15−16 (p.u.)	2.0	0.8
QSVC (MW)	100	0	Id21−22 (p.u.)	8.0	4.0
pee (MW)	60	−60	α (°)	18	8
SOC (p.u.)	0.9	0.1	γ (°)	25	15

4.2. Result Analysis

Based on the dual-layer optimization model established in this article, the Pareto optimal solution obtained through the WOA, PSO, and GA methods is shown in Figure 3. Compared with the other two algorithms, the Pareto frontier of the WOA algorithm was closer to the coordinate axes of voltage deviation and network loss, with a wider distribution of solutions and higher quality. The optimal solutions obtained under different objectives were all the lowest, which verified that the algorithm shows good optimization performance.

[IMAGE OMITTED. SEE PDF]

The network loss of AC/DC hybrid system shown in Figure 2 was calculated employing three methods, WOA proposed in this paper, PSO, and GA; their convergence curves are presented in Figure 4. It can be observed from Figure 4 that the WOA method exhibits a faster convergence rate and a lower final network loss value compared with the other two algorithms. The DC system control parameters are shown in Table 4.

[IMAGE OMITTED. SEE PDF]

Table 4 Optimization results of DC system control parameters.

	DC line 14–18	DC line 15–16	DC line 16–28
Rectification angle α (°)	13.24	12.80	8.76
Turn-off angle γ (°)	17.18	17.22	15.46
DC current I (p.u.)	0.78	1.45	5.32

The final solution result of the optimization model is shown in Figure 5; the output of each SVCs and the ratio of OLTCs were all within the adjustable ranges.

[IMAGE OMITTED. SEE PDF]

In order to study the effectiveness of the dual-layer coordinated optimization model, this article compares and analyzes the network loss and voltage fluctuations before and after optimization, taking 24 h a day as the time unit. The comparison of system loss and minimum voltage at each time before and after optimization is shown in Figure 6. As shown in the figure, the optimized system has a significant decrease in network loss at every moment compared with the original power flow. The average daily network loss power of the system was 74.26 MW without reactive power compensation, and it will decrease to 63.42 MW after introducing EES and SVC devices, with a loss reduction rate of 14.59%. At the same time, the voltage has been improved by adjusting the output of the SVC to improve the power flow. As shown in Figure 6, the overall voltage amplitude is relatively low and the minimum voltage at several nodes has exceeded the safe range of the system before optimization. The system voltage has been raised to a reasonable level, which is conducive to suppressing network losses and maintaining voltage stability. The output of new energy is relatively sufficient during daytime and insufficient during night (17:00–07:00). Through the regulation of active power by the EES, the new energy output and local load achieve a high degree of matching, which effectively reduces the system network loss. The effect is even more significant during night compared with daytime, due to the insufficient output of new energy. The discharge of EES to supply the local load can effectively avoid long-distance power transmission under the condition of insufficient new energy output.

[IMAGE OMITTED. SEE PDF]

The charge states and power curves of two optimized energy storage systems within 24 h are shown in Figure 7. By adjusting the energy storage actions, the output fluctuation of new energy power sources can be alleviated. During daytime, the EES charges and absorbs excess energy to increase the grid’s consumption capacity during daytime, reduces the new energy curtailment, and smooths out the power fluctuations in the grid. During this period, the SOC of ESS shows an upward trend, while the SOC curve of EES results in a downward trend during the period from afternoon to night (16:00–08:00) when the output of new energy decreases in the peak load period. During this period, the EES discharges to meet the local load to avoid long-distance power transmission and alleviate grid pressure.

[IMAGE OMITTED. SEE PDF]

The following three types of optimization were developed for comparative analysis to demonstrate the superiority and effectiveness of the optimization model proposed in this article:

Type 1: A reactive power optimization model with EES and ratio of OTCL as its optimization variables.

Type 2: An active power optimization model, with the SVC and EES as its optimization variables.

Type 3: An active and reactive power coordination optimization model with the SVC, ratio of OTCL, and EES as its optimization variables.

The optimization results of the three types for voltage deviation and network loss are shown in Table 5. The single reactive power optimization type 1 has a network loss of 65.78 MW and an average voltage deviation of 7.24 p.u., with a loss reduction rate of 9.74% and 22.16%, respectively, compared to the initial system without optimization. The single active power optimization type 2 has a network loss of 68.82 MW and an average voltage deviation of 7.24 p.u., with reduction of 5.57% and 20.12%, respectively, compared to initial value. With optimization type 3 proposed in this article, the network loss and average voltage deviation are 61.5 MW and 6.13 p.u., respectively, with corresponding loss reduction rates of 16.23% and 34.36% compared to the initial value before optimization, much smaller than those of type 1 and type 2.

Table 5 Statistics results of the three scenarios.

Tape	System network loss (MW)	Voltage deviation (p.u.)
Original	72.88	9.34
Type 1	65.78	7.24
Type 2	68.82	7.46
Type 3	61.05	6.13

Figures 8(a) and 8(b) show the average voltage deviations of all nodes at each moment and the network loss in the original system without optimization and under the three scenarios, respectively. Compared to the original system, all the three optimization strategies can effectively improve the voltage deviation and reduce network losses, and have stronger adaptability to the volatility of new energy. Among them, the effect of type 2 (active power only optimization model) on improving the system voltage deviation is slightly lower than that of type 1 (reactive power only optimization model), and the voltage deviation in type 3 (coordinated optimization of active and reactive power) shows a significant decrease compared with the previous two types. It can be seen from Figure 8(b) that the effect of network loss suppression of the type 1 was lower than that of the other two types. This was due to the limitations of the EES capacity, resulting in an insignificant loss reduction effect during the daytime period (09:00–14:00), In particular, the loss reduction rate was almost 0 between 9:00 and 10:00 during high new energy power generation. This is because the load and EES fail to absorb the excess power, which need long-distance transmission and result in a relatively high level in system network loss.

[IMAGE OMITTED. SEE PDF]

Through the above comparison, it can be found that the dual-layer optimization model proposed in this paper has greater advantages suppressing network loss and voltage fluctuations.

5. Application and Analysis of Algorithm Scalability

To verify the practicality and scalability of this method, online tests are conducted using both a simulation system and a digital replica of an actual power system.

5.1. Simulation Verification

First, the topology of the 39-bus system as shown in Figure 2 was modified: the DC line between buses 3 and 4 is moved to buses 6 and 13, the WT on bus 26 is moved to bus 4; and the energy storage module on bus 18 is relocated to bus 3.

The system operating parameters are optimized, with random WT and PV power input. The voltage values of each bus at a certain moment before and after optimization are extracted, as shown in Figure 9. It can be seen that before optimization, the voltages of some buses had seriously exceeded the lower limit of safety and stability. The voltages of all buses are within the range of safe and stable operation after optimization.

[IMAGE OMITTED. SEE PDF]

5.2. Online Verification of the Digital Twin System

An online verification of the optimization method is conducted by employing the digital replica of an actual 30-bus AC/DC hybrid power grid to replace the actual system for operation. The voltage values of each bus at a certain moment before and after optimization are extracted, as shown in Figure 10. After optimization, the overall voltage level is close to 1.0 p.u., which effectively reduces the voltage deviation.

[IMAGE OMITTED. SEE PDF]

In summary, the WOA-based dual-layer optimization model proposed in this paper achieves favorable optimization results in different systems, laying a foundation for its application in actual AC/DC hybrid power grids.

6. Summary and Prospect

Considering the impact of the uncertainty of new energy output on the AC/DC hybrid power grid, this paper constructed the most probable scenarios for WT and PV power model through Latin hypercube sampling scenario generation and Kantorovich distance scenario reduction method. A dual-layer optimization model for active and reactive power coordination was established with a time scale of 24 h. The switching scheme of EESs and SVCs, ratio of OLTCs, and DC system parameters were taken as control variables. The minimization of voltage fluctuations and network loss were taken as the optimization target. The model was solved via the hybrid WOA. Finally, an example verification was conducted in the AC/DC hybrid system improved by IEEE 39-notes. The results indicated that the method proposed in this article can compensate and adjust both active and reactive power simultaneously. Comparing with the single active or reactive power optimization strategy, this optimization algorithm provides control strategy basis for energy-saving operation of high-proportion new energy grids.

It should be noted that the system’s adjustable parameters such as switching power of the ES and reactive power compensation modules and the transformer ratio were treated as continuous adjustable parameters, without considering the influence of the gear of the system’s adjustable parameters. However, in actual systems, the switching units of energy storage systems and dynamic reactive power compensation modules are individual independent units, and their actual switching capacity is an integer multiple of a single module, and the transformer voltage adjustment typically adopts stepwise regulation. These key parameters often affect the convergence performance of the optimization algorithm. In future research, the impact of the above factors on convergence performance should be considered.

Data Availability Statement

The data that support the findings of this study are not openly available because the sci-tech project has not yet been concluded, and the data are in the confidentiality period but can be made available by the authors with appropriate permission.

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

This work was financially supported by Key R&D Special Project of Henan Province, Grant no. 231111240100, and Henan Science and Technology Projects Fund, Grant no. 252102241020.

Acknowledgments

This research was supported by Key R&D Special Project of Henan Province (no. 231111240100) and Henan Science and Technology Projects Fund in 2025 (no. 252102241020).

References

1 Liu M., Qiu X., Zhang K., Zhang H., and Li L., Collaborative Optimization Operation of Power Systems With High Proportion of Renewable Energy Considering Uncertainty of Generation and Load, Electric Power Construction. (2018) 39, no. 12, 55–62.

2 Zheng Y., Zhao J., Song Y. et al., Optimal Operation of Battery Energy Storage System Considering Distribution System Uncertainty, IEEE Transactions on Sustainable Energy. (2018) 9, no. 3, 1051–1060, https://doi.org/10.1109/tste.2017.2762364, 2-s2.0-85031824364.

3 Wang Q., Dong W., and Yang L., A Wind Power/Photovoltaic Typical Scenario Set Generation Algorithm Based on Wasserstein Distance Metric and Revised K-Medoids Cluster, Proceedings of the CSEE. (2015) 35, no. 11, 2654–2661.

4 Yokoyama R., Ito K., and Yuasa Y., Multiobjective Optimal Unit Sizing of Hybrid Power Generation Systems Utilizing Photovoltaic and Wind Energy, Journal of Solar Energy Engineering. (1994) 116, no. 4, 167–173, https://doi.org/10.1115/1.2930078, 2-s2.0-0028546835.

5 Yin Q., Yang H., and Ma X., Probabilistic Optimal Reactive Power Dispatch of Power Grid With Large-Scale Wind Farm Integration, Power System Technology. (2017) 41, no. 02, 514–520.

6 Liu Z., Wei X., and Wu Y., Reactive Power Optimization of Power System Based on Particle Swarm Optimization Algorithm, Highlights in Science, Engineering and Technology. (2023) .

7 Nie Z. and Zhang R., Research on Intelligent Dispatching of Micro-Grid According to Optimized Particle Swarm Algorithm, Advanced Control for Applications. (2023) 6, no. 2, https://doi.org/10.1002/adc2.157.

8 A I. V., B L. R., B S. V., C V. V., Siarry P., and Uden L., Multi-Objective Optimization and Energy Management in Renewable Based AC/DC Microgrid, Computers & Electrical Engineering. (2018) 70, 179–198, https://doi.org/10.1016/j.compeleceng.2018.01.023, 2-s2.0-85041182413.

9 Liu H., Li H., Li J., and Shao L., Distributed Photovoltaic Reactive Power Control Strategy Based on Improved Multiobjective Particle Swarm Algorithm, Energy Science & Engineering. (2024) 12, no. 11, 4904–4917, https://doi.org/10.1002/ese3.1902.

10 Mirjalili S. and Lewis A., The Whale Optimization Algorithm, Advances in Engineering Software. (2016) 95, 51–67, https://doi.org/10.1016/j.advengsoft.2016.01.008, 2-s2.0-84959304045.

11 Yi-Lei G. U., Nuo X. U., and Xi-Tian W., The Difficulties and Improvements of the Genetic Algorithm Utilization in the Power Grid Planning, Power System Technology. (2007) .

12 Medani K. B. O., Sayah S., and Bekrar A., Whale Optimization Algorithm Based Optimal Reactive Power Dispatch: A Case Study of the Algerian Power System, Electric Power Systems Research. (2018) 163, 696–705, https://doi.org/10.1016/j.epsr.2017.09.001, 2-s2.0-85030245316.

13 Hasanien M., Whale Optimisation Algorithm for Automatic Generation Control of Interconnected Modern Power Systems Including Renewable Energy Sources, IET Generation, Transmission & Distribution. (2017) 12, no. 3, 607–614, https://doi.org/10.1049/iet-gtd.2017.1005, 2-s2.0-85041523929.

14 Baradar M. and Ghandhari M., A Multi-Option Unified Power Flow Approach for Hybrid AC/DC Grids Incorporating Multi-Terminal VSC-HVDC, IEEE Transactions on Power Systems. (2013) 28, no. 3, 2376–2383, https://doi.org/10.1109/tpwrs.2012.2236366, 2-s2.0-84880923653.

15 Fan S., Wang W., Han W., Wang W., Zhang P., and Shen X., Second-Order Cone Programming Relaxation-Based Multi-Period Reactive Power Optimization With VSC-Type HVDC and DFIG, IOP Conference Series: Earth and Environmental Science. (2019) .

16 Yang F. U., Jianbo L., Zhenkun L. I., Xiao Q., and Xin T., Day-Ahead Optimal Scheduling and Operating of Active Distribution Network Considering Violation Risk, Proceedings of the CSEE. (2017) 37, no. 21, 6328–6338.

17 Bu S. Q., Du W., Wang H. F., Chen Z., Xiao L. Y., and Li H. F., Probabilistic Analysis of Small-Signal Stability of Large-Scale Power Systems as Affected by Penetration of Wind Generation, IEEE Transactions on Power Systems. (2012) 27, no. 2, 762–770, https://doi.org/10.1109/tpwrs.2011.2170183, 2-s2.0-84860250598.

18 Gupta V. and Radu C., Statistical Approximation Properties of q-Baskakov-Kantorovich Operators, Open Mathematics. (2009) 7, no. 4, 809–818, https://doi.org/10.2478/s11533-009-0055-y, 2-s2.0-70449512308.

19 Liu Q., Zeng C., Li H., Zhang Z., and Liu Y., Data-Driven Enhancement of Power System Disturbance Magnitude Estimation, Integrating Two-Beta and RoCoF Methods. (2024) .

20 Lee J., Asymptotic Comparison of Latin Hypercube Sampling and Its Stratified Version, Journal of the Korean Statistical Society. (1999) no. 2, 135–150.

21 Cao G., Shi H., Dang J., Jia R., Guo Z., and Xue C., A Bi-Level Cooperating Optimization for AC/DC Power Systems Considering Renewable Energy Integration, Energy Reports. (2024) 11, 5556–5574, https://doi.org/10.1016/j.egyr.2024.05.027.