Complementary Analysis and Performance Improvement of a Hydro-Wind Hybrid Power System

Abstract

Hydropower as a flexible regulation resource is a rare choice to suppress the ever-increasing penetration of wind power in electrical power systems. The complementary characteristics and performance improvement of a hydro–wind hybrid power system based on a mathematical model of the hybrid power system is studied in this paper. This established model takes into account the stochastic variation in wind speeds in the wind power subsystem and the hydraulic–mechanical–electrical coupling characteristics of the hydropower subsystem. The complementary analysis is conducted based on the evaluation variables outputted by the established model, such as the wind power, hydro-regulation power, hydraulic power, and frequency. To make full use of the regulation capability of the hydropower system, the optimization of parameter settings is also carried out to improve complementary performances of the hybrid power system. The results from the complementary analysis show the detailed characteristics of hydro–wind coordinated operation under different types of real wind speeds. Here, 95% of installed hydro-capacity is used to complement the power shortage of the intermittent wind energy under the low wind speed. Alternatively, only around 66% of the installed hydro-capacity can be utilized to cope with the fluctuation in wind power under the medium and high wind speeds before the optimization of parameter settings. The recommended values and change rules of the control, hydraulic, and electrical parameters for the hydropower system are subsequently revealed from the analysis of parameter settings to contribute to a stable and safe hybrid power system. The results show that the optimized parameter can increase the maximal regulating capacity of the hydropower system by nearly 9 MW, approximately a sixth of the total installed hydropower capacity. The method and results obtained in this paper provide theoretical and technical guidance for the safe and economical operation of power stations.

1. Introduction

To cope with the challenge of climate change and the crisis of energy shortage, global energy generation is gradually tending towards clean renewable energy such as water energy, solar photovoltaic energy, wind energy, biomass energy, geothermal energy, and tidal energy [1]. These renewable energy resources have been applied in various sectors, such as active filters and railways, especially in the power generation industry [2,3].

Among the various energy resources, wind power has become the most rapidly developing form of renewable energy in the world owing to its easy access, non-pollution, and suitability for large-scale development [4]. However, the characteristics of volatility and intermittency of wind power have adverse impacts on the power production, operational regulation, and load tracking of hybrid power systems [5]. One way to cope with this problem is to develop different advanced control of wind approaches, such as the direct power control [6] and fuzzy control [7]. Another way is to complement the flexibility energy resources to balance the large fluctuation of power outputs. Hydropower, as the most mature clean energy in the power system, has flexible regulation ability and stable power supply, which is the best choice of complementary power sources with the advantages of storage, dispatching, quick startup, and rapid closing down [8]. As such, the hydro–wind hybrid power system becomes the most effective way to solve the current problem of the large fluctuations in wind power, since the hydraulic power of hydropower system can continuously regulate and flexibly control the stochastic wind power and finally form the continuous, stable, adjustable, and controllable power output.

To achieve a more stable and reliable hybrid power system and improve the complementary characteristics, recent studies have committed to the model of multiple energy power systems and the improvement of complementarity. Regarding the model of hybrid power systems, Xie et al. (2021) [9] proposed the hydro–wind power model that pays more attention to effectively utilizing reservoir storage. Xiong et al. (2021) [10] proposed a hybrid power model to study the regulation impact of the hydropower system on the stochastic wind power. Wang et al. (2024) [11] presented a model of the hydro–wind-based power system considering the hedging law and complementary dispatching. Liu et al. (2023) [12] established a model of a hybrid power system based on the method of multi-stage nesting and chance constraint to ensure the reliability of power generation. Zhou et al. (2023) [13] proposed a model of a grid-connected hydro–wind-based energy system by effectively using the flexible reserve. Sukah et al. (2024) [14] presented a model of a hybrid power system to search for the minimal cost under various objective functions and constraints. Lin et al. (2024) [15] proposed a multi-layer optimization model of a hybrid power system to help increase energy generation. Regarding the improvement of complementarity, the impact of system parameters on complementary performances is usually investigated in the literature since it is the simplest and the most economical way to enhance the coordinated operation quality of multiple energy power systems. For instance, He et al. (2023) [16] improved the complementary performances by optimizing the installed capacities of multiple renewable energy resources. Guo et al. (2022) [17] proposed a methodology for improving complementary performance that considers the advantages of battery storage. Wang et al. (2024) [18] aimed to optimize the system parameters of the hybrid power system by using the advanced genetic algorithm. Jiang et al. (2023) [19] investigated the effect of system parameters in hybrid power systems on complementarities based on deep network methods. Shi et al. (2024) [20] used a method of linear programming optimization to find the optimal complementary parameters. Kumar et al. (2024) [21] utilized a predictive control method to adjust the changes in power frequency and voltage to further improve the complementarities of hybrid systems. Based on these findings, there are two gaps in the studies. First, the existing models of hydro–wind hybrid systems are generally presented in terms of the objective functions and constraint conditions, while they lack the mathematical and simulation models that can reflect the hydraulic–mechanical–electrical coupling characteristics of hydropower system and the coupling characteristics of hydro and wind subsystems, especially for models in the timescale of seconds. Second, the variation impacts of the typical system parameters on the complementary performances are difficult to demonstrate due to the complex change rules of the hydraulic, mechanical, and electrical parameters along with the operating time.

Therefore, this work is committed to studying the complementary characteristics of hydro–wind hybrid power systems on the basis of a simulation model that considers the hydraulic–mechanical–electrical coupling characteristics of hydropower system and coupling characteristics of hydropower and wind subsystems. Under three types of real wind speeds, the complementary analysis is conducted to evaluate the hydro-regulation effects on adjusting fluctuations in the wind power outputs. The complementary characteristics are also revealed in this analysis to point out the non-ideal complementary operating condition and the most unfavorable type of wind speed. To improve such complementary performances, the impacts of system parameters on the complementarity are conducted to reflect the sensitivity of typical hydraulic, control, and electrical parameters to stable outputs of wind power and the reduction in the demand gap of hydro-regulation power. The recommended system parameters are also obtained in this investigation. The main contributions of this paper include the following two aspects. (i) The coordinated operating scenario regarding the lowest utilization rate of the installed hydro-capacity is identified in order to further improve the complementary performances through the optimization of parameter settings, which helps take full use of the hydropower energy and improve the power generation in power stations. (ii) The methodology of this work for improving complementary performances of hydro–wind power systems can be applied to other renewable energy power systems that use hydropower as a flexible energy source. This brings necessary knowledge to the field of the efficient use of energy.

The overall framework of this paper is as follows. A hydro–wind hybrid power model is given in Section 2. The complementary analysis is conducted in Section 3. The impacts of system parameters on the complementary characteristics are conducted in Section 4. Section 5 concludes with the main findings.

2. Hydro–Wind Hybrid Power Model

In this section, a model of the hydro–wind hybrid power system is established which considers the wind power system and hydropower system. It mainly utilizes hydropower to regulate the fluctuation of wind power. The hydropower system consists of the hydro-turbine, diversion pipeline, governor, and synchronous generator. The wind power system is made up of the doubly fed induction generator (DFIG), wind turbine, converter, and transmission system. The detailed modeling procedure is shown as follows.

2.1. Hydropower System

Figure 1 [22] describes the working mechanism of the hydro-turbine and diversion pipeline.

The dynamic characteristic of the diversion pipeline refers to the variation of turbine head caused by the change in turbine flow, represented by the flow–head transfer function. This transfer function is from the flow change Δq to the turbine transient head Δh_q, and it is expressed by the following elastic water-hammer equation [23,24]:

$$\Delta h_q\left(s\right)=2h_{\omega }{\displaystyle \frac{\frac{1}{48}{T_r}^3{s}^3+\frac{1}{2}{T}_{r}s}{\frac{1}{8}{T_r}^2{s}^2+1}}\Delta q\left(s\right)$$

(1)

If set:

$$R\left(s\right)={\displaystyle \frac{1}{\frac{1}{8}{T_r}^2{s}^2+1}}\Delta q\left(s\right)$$

(2)

Equation (1) is rewritten as:

$$\Delta h_q\left(s\right)={\displaystyle \frac{{T_r}^3{h}_{\omega }}{24}}R\left(s\right)s^3+T_r{h}_{\omega }R\left(s\right)s$$

(3)

On the basis of the Laplace transform initial value theorem:

$$\underset{t\to 0^{+}}{\lim }r\left(t\right)=\underset{s\to +\infty }{\lim }sR\left(s\right)$$

(4)

The initial value of r(t) is set at 0. When the Laplace inverse transformation is performed for Equations (2) and (3), they are obtained as:

$$q=q_0+r\left(t\right)+{\displaystyle \frac{1}{8}}{T_r}^2{r}^{"}\left(t\right)$$

(5)

and

$$\Delta h_q=T_r{h}_{\omega }{r}^{\prime }\left(t\right)+{\displaystyle \frac{{T_r}^3{h}_{\omega }}{24}}{r}^{‴}\left(t\right)$$

(6)

Define x₁ = r(t), x₂ = r′(t), and x₃ = r″(t). Equation (6) is further converted into the flowing state-space equation [25]:

$$\left\{\begin{array}{c}{x_1}^{\prime }=x_2\\ {x_2}^{\prime }=x_3\\ {x_3}^{\prime }=-{\displaystyle \frac{24}{{T_r}^2}}{x}_2+{\displaystyle \frac{24}{{T_r}^3{h}_{\omega }}}\Delta h_q\end{array}\right.$$

(7)

and it is also obtained as:

$$\Delta h_q=h_0-f_p{q}^2-{\displaystyle \frac{q^2}{y^2}}{y_r}^2$$

(8)

Meanwhile, the output power of hydro-turbine [26] is:

$$P_m=A_t{\displaystyle \frac{q^2}{y^2}}{y_r}^2\left(q-q_{nl}\right)$$

(9)

This paper uses a fifth-order synchronous generator model [27], and the corresponding equation is:

$$\left\{\begin{array}{l}{U}_d=X_q{I}_q\hfill \\ U_q={E_q}^{\prime }-{X_d}^{\prime }{I}_d\hfill \\ {\displaystyle \frac{d\delta }{dt}}=\omega -1\hfill \\ {\displaystyle \frac{d\omega }{dt}}={\displaystyle \frac{1}{T_{ab}}}\left[m_t-m_e-D\left(\omega -1\right)\right]\hfill \\ {\displaystyle \frac{{d{E}_q}^{\prime }}{dt}}={\displaystyle \frac{1}{{T_{d0}}^{\prime }}}\left[E_f-{E_q}^{\prime }-\left(X_d-{X_d}^{\prime }\right)I_d\right]\hfill \end{array}\right.$$

(10)

2.2. Model of Control System

The hydropower system mainly uses the parallel PID controller to adjust the variation in the hydraulic frequency. The parallel PID controller adopts the proportional–integral–differential (PID) control law. Correspondingly, the tuning parameters of the PID control system include the proportional, integral, and differential adjustment coefficients K_p, K_i, and K_d, respectively. The mathematical model of the PID control system [28] is:

$$Y_{PID}=Y_P+Y_I+Y_D$$

(11)

$$\left\{\begin{array}{l}{Y}_p=K_p\Delta F\hfill \\ Y_I={\displaystyle \frac{K_i}{S}}\Delta I={\displaystyle \frac{K_i}{S}}\left[\Delta F+b_p\left(Y_c-Y_{PID}\right)\right]\hfill \\ Y_D={\displaystyle \frac{K_{d}S}{1+T_{1V}S}}\Delta F\hfill \end{array}\right.$$

(12)

If the coefficient of the permanent state difference bp = 0, the transfer function of the PID controller between the guide vane opening Y_PID(s) and input frequency ΔF(s) is:

$$G\left(S\right)={\displaystyle \frac{Y_{PID}\left(s\right)}{\Delta F\left(s\right)}}=\left(K_p+K_i{\displaystyle \frac{1}{S}}+{\displaystyle \frac{K_{d}S}{1+T_{1V}S}}\right)$$

(13)

and

$$G\left(S\right)={\displaystyle \frac{Y_{PID}\left(s\right)}{\Delta F\left(s\right)}}=\left(K_p+K_i{\displaystyle \frac{1}{S}}+K_{d}S\right),\left(T_{1V}=0\right)$$

(14)

Based on the above considerations, the PID governor is modeled in Figure 2.

Finally, the hydropower system considering the hydro-turbine, diversion pipeline, governor, and synchronous generator is modeled in Figure 3.

2.3. Wind Power System

Kinetic energy is converted into mechanical energy through wind turbines. The wind speed through the blade cannot be fully converted by the wind turbine. The DFIG ceases to function when the wind speed surpasses the thresholds for cut-in and cut-out wind speeds. When the wind speed exceeds the cut-in threshold but remains below the cut-out threshold, the wind power system operates in maximum power tracking mode. When the wind speed exceeds the cut-out wind speed, the wind generator maintains operation at its rated power. Accordingly, the expression of output power is as follows:

$${P_{i,t}}^W=\left\{\begin{array}{c}0\\ {\displaystyle \frac{1}{2}}\rho A{C}_P{V_{i,t}}^3,\\ 1.5\end{array}\right.\begin{array}{c}when\\ when\\ when\end{array}\begin{array}{l}{V}_{i,t}\le V_{cut-in}\hfill \\ V_{cut-in}\le V_{i,t}<V_{cut-out}\hfill \\ V_{cut-out}\le V_{it}\hfill \end{array}$$

(15)

The DFIG uses the conventional back-to-back converter. The converter control includes the grid-side controller and rotor-side controller. The rotor-side controller adopts vector control to realize active and reactive decoupling control. The expression of the rotor-side controller [29,30,31] is:

$$\left\{\begin{array}{l}{\displaystyle \frac{d{x}_1}{dt}}=P_{ref}-P_s=\Delta P\hfill \\ i_{qr\_ref}=K_{p1}\left(P_{ref}-P_s\right)+K_{i1}{x}_1\hfill \\ {\displaystyle \frac{d{x}_2}{dt}}=i_{qr\_ref}-i_{qr}\hfill \end{array}\right.$$

(16)

and

$$\left\{\begin{array}{l}{\displaystyle \frac{d{x}_3}{dt}}=u_{s\_ref}-u_s=\Delta u\hfill \\ i_{dr\_ref}=K_{p3}\left(u_{s\_ref}-u_s\right)+K_{i3}{x}_3\hfill \\ {\displaystyle \frac{d{x}_4}{dt}}=i_{dr\_ref}-i_{dr}\hfill \end{array}\right.$$

(17)

and

$$\left\{\begin{array}{c}{u}_{dr}=K_{p2}\left(K_{p3}\Delta u+K_{i2}{x}_3-i_{dr}\right)+K_{i2}{x}_4-s{\omega }_s{L}_m{i}_{qs}-s{\omega }_s{L}_{rr}{i}_{dr}\\ u_{qr}=K_{p2}\left(K_{p1}\Delta P+K_{i1}{x}_1-i_{qr}\right)+K_{i2}{x}_2-s{\omega }_s{L}_m{i}_{ds}-s{\omega }_s{L}_{rr}{i}_{qr}\end{array}\right.$$

(18)

The grid-side controller adjusts the constant DC-side capacitor voltage of the back-to-back converter and the output of reactive power of converter. The voltage of the capacitor is controlled by the d-axis component of the grid side converter current, and the reactive power is controlled by the q-axis component of the grid-side converter current. The control equation is expressed as:

$$\left\{\begin{array}{l}{\displaystyle \frac{d{x}_5}{dt}}=u_{dc\_ref}-u_{dc}=\Delta u_{dc}\hfill \\ i_{dg\_ref}=-K_{p4}\Delta u_{dc}+K_{i4}{x}_5\hfill \\ {\displaystyle \frac{d{x}_6}{dt}}=i_{dg\_ref}-i_{dg}\hfill \end{array}\right.$$

(19)

and

$${\displaystyle \frac{d{x}_7}{dt}}=i_{qg\_ref}-i_{qg}$$

(20)

and

$$\left\{\begin{array}{l}{u}_{dg}=K_{p5}\left(-K_{p4}\Delta u_{dc}+K_{i4}{x}_5-i_{dg}\right)+K_{i5}{x}_6+X_{Tg}{i}_{qg}\hfill \\ u_{qg}=K_{p5}\left(i_{qg\_ref}-i_{qg}\right)+K_{i5}{x}_7-X_{Tg}{i}_{dg}\hfill \end{array}\right.$$

(21)

The transmission system connects the blade to the generator. The transmission is made up of the transmission shaft and hub, and it is linked with generator rotor through the gearbox and drive shaft. This study considers a rigid shaft that reflects the flexibility and damping characteristics. The transmission system is expressed as:

$$\left\{\begin{array}{l}{\displaystyle \frac{d{\omega }_t}{dt}}={\displaystyle \frac{1}{2H}}\left(T_{wm}-T_{sh}\right)\hfill \\ {\displaystyle \frac{d{\theta }_{tw}}{dt}}={\omega }_t-{\omega }_r\hfill \\ T_{sh}=K_{sh}{\theta }_{tw}+D_{sh}\left({\omega }_t-{\omega }_r\right)\hfill \\ T_{wm}={\displaystyle \frac{P_m}{{\omega }_t}}\hfill \\ T_m=K_{sh}{T}_{sh}\hfill \end{array}\right.$$

(22)

Based on the above considerations, Figure 4 shows the model of wind power system.

2.4. Model of Hybrid System

According to the hydro- and wind power models, the hybrid power system is finally modeled in Figure 5. The established model is validated in Appendix A and Appendix B.

3. Methodology

The improvement of the complementary performances of the hybrid power system is based on the various outputs of the established model. These outputs can form four complementary evaluation criteria, including (i) complementary trends of wind power and hydraulic power, (ii) the difference in power demand and total hydro–wind power, (iii) the fluctuation features of wind power with operating time, and (iv) the stability of the hydraulic frequency. Based on these evaluation criteria, the scenario with the lowest utilization rate of installed hydro-capacity is recognized to further study the optimization of parameter settings. Note that the complementary evaluation criteria are the same so as to optimize the system parameters. The details of the methodology in this work are shown in Figure 6.

4. Complementary Analysis

This section aims to study the complementarity of hybrid systems under low, medium, and high wind speeds, and the data of these three types of real wind speeds are from National Renewable Energy Laboratory (NREL, Golden, CO, USA) [32]. The analysis is simulated based on the software of Matlab/Simulink 2023b. The variation in the low, medium, and high wind speeds is shown in Figure 7, and the results of the complementary characteristics are shown in Figure 8 and Figure 9.

In Figure 7, the three types of real wind speeds are obtained by using the Signal Builder module in the software Matlab/Simulink (Matlab 2023b). The variation ranges of low, medium, and high wind speeds are [2.68 m/s, 8.23 m/s], [6.22 m/s, 17.03 m/s], and [8.46 m/s, 21.68 m/s], respectively. All of three types of real wind speeds show similar characteristics of volatility and intermittency. The use of real wind speeds as the input variable enables the newly established mathematical model to output the variables of complementary characteristics, including wind power, hydraulic power, demand for hydro-regulation power, and hydraulic frequency.

Figure 8 clearly shows the differences in the complementarity of the hybrid power system under different real wind speeds. For the condition of low wind speed in Figure 8a, wind power and hydraulic power show opposite variation trends, meaning that the hydropower system is able to complement the fluctuation in wind power. However, hydraulic power cannot meet the demand for hydro-regulation power. This is due to the considerably low output of wind power under the low wind speed. The mean wind power is roughly below 20 MW, which is significantly less than the installed capacity of wind power of 84 MW. In comparison to the condition of low wind speed, there are larger fluctuations in wind power for the medium and high wind speeds in Figure 8b,c. In addition to this, hydraulic power is able to track the change in the demand for the hydro-regulation power. As such, the complementary characteristics of the system are better suited to medium and high wind speeds than to the condition of low wind speed.

Figure 9 shows the variation in hydraulic frequencies under the three types of high wind speed, medium wind speed, and low wind speed. It is found that the fluctuation in hydraulic frequency under the three types of real wind speeds is largely less than the acceptable range of ±0.5 Hz. This means that the hydropower system can suppress the large fluctuation in wind power through its regulation capabilities.

The utilization rate of the installed hydro-capacity reaches 95% under the low wind speed. Conversely, the hydraulic power is significantly less than the rated power under the medium and high wind speeds, and its maximum is roughly 66% of the installed hydro-capacity. Here, the utilization rate of installed hydro-capacity is the ratio of the average output of hydraulic power along the operating time for the installed hydro-capacity. Moreover, the maximal difference responding to the demand for hydro-regulation power is larger for the condition of medium wind speed as compared to the condition of high wind speed. Meanwhile, for the actual operation of power stations, wind power systems frequently operate in the medium wind speed. For these reasons, the following section selects the condition of medium wind speed to further study the optimization of parameter settings of a hydropower system.

5. Impact of Parameter Setting on Complementary Performances

Due to the instability of wind energy caused by the characteristics of intermittence and volatility, the hybrid system uses hydro-regulation capabilities to realize stable operation. Different system parameters of the hydropower system influence the complementarity by adjusting the outputs of hydraulic power and wind power. As such, this section concentrates on analyzing the impact of parameter setting on complementary characteristics, and also on quantifying the impacts of parameter variation on complementary performances. The system parameters mainly involve three subsystems, including the control subsystem, hydraulic subsystem, and electrical subsystem. The parameters for the control subsystem include K_p, K_i, and K_d which are the proportional, integral, and differential adjustment coefficients, respectively. The parameters for the hydraulic subsystem include the head loss coefficient f_p, the relative value of on-load flow of the hydro-turbine q_nl, and the elastic water-hammer time constant T_r. The parameters of electrical subsystem include the d-axis and q-axis synchronous reactances x_d and x_q, respectively. Based on the references [23,25,33], the recommended ranges of control parameters are K_p = (0.1, 12), K_i = (0.1, 12), and K_d = (0.1, 8). The recommended ranges of hydraulic parameters are f_p = (0.002, 0.03), q_n1 = (0.1, 0.4), and T_r = (0.27, 0.87). The recommended ranges of electrical parameters are x_d = (0.5, 1.1), and x_q = (0.2, 1).

The quantified results are estimated by the maximal difference between the hydraulic power and the demand for hydro-regulation power. The analysis results are shown in Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14.

Figure 10 shows the difference in the demand and actual output for hydraulic power with the PID control parameters K_p, K_i, and K_d. The power difference decreases slightly and then increases with the increase in K_p, and it reaches the minimum power difference at K_p = 0.2. The power difference grows as K_d increases, and it gradually decreases as K_i increases. This means that the complementarity of the hybrid power system is enhanced when properly increasing K_i and decreasing K_d and K_p. Compared with these three control parameters, the parameter K_i has the greatest influence on the complementary characteristics, while the parameter K_p has the lowest influence on the complementarity.Moreover, Appendix C describes the contradictions in the choice of control parameters.

In Figure 11, there are similar variation trends for the differences in demand and actual output for hydraulic power under different hydraulic parameters, and all power differences demonstrate increase trends with the changes in the head loss coefficient f_p, relative value of on-load flow of hydro-turbine q_nl, and elastic water-hammer time constant T_r. This reveals that properly decreasing the hydraulic parameters of f_p, T_r, and q_nl can improve the system stability. It is noticed that the variations in q_nl and T_r have significant influences on the complementarity in comparison with the parameter setting of f_p. Correspondingly, the regulation capacity of the system is able to increase 9 MW if the parameters of q_nl and T_r are properly set.

Figure 12 shows the difference in the demand and actual output for hydraulic power with the electrical parameters x_d and x_q. The power difference first decrease and then increase as the parameter x_d gradually increases, reaching the minimum at x_d = 0.8. Differently, the power difference continuously decreases as the parameter x_q gradually increases. Compared to the parameter x_d, the parameter x_q has relatively greater impacts on the complementary characteristics of the hybrid system.

When comparing all of the selected system parameters, it is found that the hydraulic parameters have the greatest influence on the complementary characteristics as compared to the parameters from the control and electrical subsystems. The hydraulic parameters q_nl and T_r have the greatest influences among all system parameters. For this reason, Figure 13 and Figure 14 are plotted to further study the change rule of the hydraulic parameters q_nl and T_r.

In Figure 13a, the output of hydraulic power obviously increases when the parameter q_nl decreases from 0.4 to 0.1. Owing to the increase in hydraulic power, the gap in the demand for hydro-regulation power reduces, as shown in Figure 13b. When parameter q_nl = 0.4, the hydro-regulation power cannot meet the demand of stable operation during the whole regulation time. In contrast, the actual hydraulic power exceeds the demand during 70% of the regulation time. It is worth noting that a slight vibration occurs in the hydropower generation unit during the initial operating time due to the decrease in parameter q_nl, but such a vibration cannot influence the total trend of power complementation.

In Figure 14a, the variation in parameter T_r mainly influences the fluctuation of the output of hydraulic power. When the parameter T_r increases from 0.27 to 0.87, the fluctuation in hydraulic power not only becomes large, but its fluctuating time also lasts for a long period. In this state, the hydropower system generates a relatively large vibration, which threatens the stability of the system. In Figure 14b, it is clear that the difference changes between the demand and actual power due to the occurrence of a large fluctuation in terms of the hydraulic power. Moreover, the hybrid power system has an excellent complementary characteristic at T_r = 0.27, since the actual hydraulic power can roughly meet the demand for hydro-regulation power. Simultaneously, no vibration occurs in the hydropower system under this condition.

6. Conclusions and Discussion

To improve the operating performance of the hydro–wind hybrid power system, this work investigates the complementary characteristics between those different energy sources and also utilizes the optimization of the typical system parameters of the hydropower system to reduce the gap in power demand. These analyses are carried out based on an established simulation model of the hybrid power system that considers the hydraulic–mechanical–electrical coupling characteristics of the hydropower system and the interaction between hydraulic power and wind power. The complementary characteristics are reflected by the model outputs in the timescale of seconds, like the hydro-regulation power, the wind power, and the hydraulic frequency. By summarizing the laws of complementarity, the investigation of parameter settings is applied to the most significant power shortage scenario to maximize the use of the hydropower capacity. The main findings are performed as follows:

• Complementary characteristics: The utilization rate of the installed capacity for a hydropower generation unit approaches 95% under the low wind speed operating scenario, although the total power from the hybrid system is far below the power demand. As a result, there is little capacity space for improvement under the low wind speed in comparison with the operating scenarios in both the medium and high wind speeds.
• Enhanced system performance: The complementary characteristics of the hybrid power system are closely related to the typical system parameters of the hydropower system, especially for the hydraulic parameters, such as the on-load flow of hydro-turbine and the elastic water-hammer time constant. The proper setting of such hydraulic parameters can increase the regulating capacity by nearly 9 MW.
• Suggestions for parameter setting: The hybrid power system shows an excellent complementary performance and also maintains stable operation when the typical system parameters (K_p, K_i, K_d, f_p, T_r, q_nl, x_d, and x_q) are appropriately set at the values of (2, 12, 0.1, 0.002, 0.27, 0.1, 0.8, 1), respectively.

This work focuses on studying typical system parameters related to the control, hydraulic, and electrical subsystems. The operators in the hydropower station generally change these typical system parameters to achieve a stabler and safer system. However, except for the selected typical system parameters, the dynamic performances of the system are also related to other residual system parameters, such as the characteristic coefficient of the pipe and the inertia time constant of the generator. As such, future work will involve the most of the system parameters to better investigate the effect of coupling characteristics of multiple subsystems in a hydropower system on the hybrid power system. Modern intelligent algorithms, such as deep neural networks [34,35], may be used to find the sensitive parameters to ensure the stable operation of the hybrid power system. Meanwhile, some advanced correlational analysis methods, like information entropy [36] and regression analysis [37], may be employed to investigate the coupling relationship among the system parameters.