Oscillation Mechanism and Suppression of Variable-Speed Pumped Storage Unit with Full-Size Converter Based on the Measured Single-Input and Single-Output Impedances

Abstract

As the penetration rate of clean energy gradually increases, the demand for flexible regulation resources in the power grid is increasing accordingly. The variable-speed pumped storage unit with a full-size converter (FSC-VSPSU) can provide fast and flexible regulation resources for the power grid, which assists in the stable operation of the clean-energy-dominated power systems. Thus, its application is gradually becoming widespread. FSC-VSPSU relies on the power electronic converter for grid connection. When the impedance mismatch between FSC-VSPSU and the power grid occurs, the grid-connected system will experience oscillations, which seriously threatens its safe and stable operation. Aiming at this, this article firstly relies on the SISO impedance measurement and an equivalent impedance analysis to obtain the stability analysis criterion. Furthermore, applying the impedance matching analysis with the Bode diagram, the influence rules of the parameters of the grid-connected FSC-VSPSU on oscillation are obtained. In addition, with the summarized oscillation analysis results, this study delves into an exploration of pertinent strategies for oscillation suppression. Finally, a grid-connected FSC-VSPSU simulation model is built in MATLAB/SIMULINK, and the simulation results verify the correctness of the oscillation analysis results and the effectiveness of the proposed oscillation suppression strategy.

1. Introduction

In response to the progressive exhaustion of fossil fuels and the degradation of the environment, the development of renewable and clean energy sources has accelerated, with a particular emphasis on wind power and photovoltaic technologies [1,2]. Nevertheless, while these energy sources present novel opportunities for the power grid, their inherent volatility, unpredictability, and intermittency pose significant challenges to the stability of the electrical network [3]. To solve this problem, it is urgent to improve the flexible adjustment ability of power grids relying on energy storage devices [4]. Currently, the prevalent energy storage technologies encompass pumped storage, lithium batteries, supercapacitors, and flywheel energy storage. Notably, pumped storage technology has garnered increasing preference within the power grid sector due to its substantial storage capacity [4,5,6].

In the domain of pumped storage technology, systems can be categorized into variable-speed pumped storage and constant-speed pumped storage configurations [7]. Variable-speed pumped storage units (VSPSUs) offer a higher degree of agility in regulating the power grid, thereby providing more expeditious support for the stable operation of electrical networks [8]. Moreover, depending on the role of the integrated power electronic converter, VSPSUs can be further classified into two distinct types: the full-size converter type (FSC-VSPSU) and the doubly-fed induction machine type (DFIM-VSPSU) [9,10]. The converter in an FSC-VSPSU is responsible for grid connectivity and performs full-power conversion [11], rendering it more appropriate for applications with smaller capacity requirements. In contrast, the converter of a DFIM-VSPSU is solely dedicated to the conversion of excitation power, making it more advantageous for large-capacity applications [12]. It is pertinent to note that the focus of the present study is on the FSC-VSPSU.

FSC-VSPSU comprises a full-size power converter, an electric motor, a pump turbine, upper/lower reservoirs, etc. [13]. The converter, which is directly interfaced with the power grid, facilitates grid-connected electric power conversion [9]. However, a mismatch between the converter-based FSC-VSPSU and the power grid can result in an oscillation phenomenon [14]. Nowadays, extensive research has been conducted on oscillation issues in converter-based grid-connected systems, including those associated with wind power, photovoltaics, and high-speed railways [14,15].

To address these oscillations, it is imperative to first develop a mathematical analysis model for the grid-connected system, such as an impedance model or a state–space model [16]. Then, combined with the impedance matching analysis and the eigenvalue analysis methods, the underlying oscillation mechanisms can be investigated [17,18,19,20]. However, for actual on-site systems, the establishment of precise mathematical analysis models is often impractical due to their “black box” characteristics. In response to this challenge, impedance measurement technology has rapidly advanced, offering a solution that is independent of the system’s actual topology and parameters. This advancement makes impedance measurement particularly suitable for the analysis of oscillations in such black box systems [21].

Initially, to fully detect the impedance of the converter-based, grid-connected system, techniques employing dq- and sequence–domain impedance measurement are highly regarded [22]. When coupled with the generalized Nyquist criterion, these methods facilitate an accurate investigation into the oscillation mechanisms [23]. Nevertheless, these impedance measurement technologies are categorized as multi-input and multi-output (MIMO) approaches, necessitating the injection of two linearly independent harmonic disturbances at the same target frequency. Subsequently, voltage and current response data for each phase must be individually recorded. Following this, the corresponding dq- and sequence–domain response data are derived through coordinate transformation. Thereafter, the impedance is calculated using the appropriate MIMO impedance computation methods [24].

Nonetheless, in the context of actual on-site systems, the operational state is subject to continuous fluctuations, precluding the assurance of consistent operating conditions under the two injected harmonic disturbances. Additionally, MIMO impedance measurement necessitates a greater number of data acquisition sensors and involves a more intricate measurement process [23]. Considering these challenges, the single-input and single-output (SISO) impedance measurement approach, which exhibits marginally reduced measurement precision, has garnered increased attention in recent times [25,26]. This method simplifies the process by requiring only a single injection of the harmonic disturbance at the target frequency. Furthermore, it obviates the need for extensive data collection by requiring the acquisition of response data from just one phase, thereby circumventing the requirement for additional coordinate transformation. Consequently, the SISO method offers a more streamlined and efficacious approach for practical application.

This study delves into the oscillation mechanism of the grid-connected FSC-VSPSU utilizing the SISO impedance measurement technique, and it investigates the pertinent strategies for oscillation mitigation. The principal innovations and contributions of this work are summarized as follows.

(1)

This is the first instance where SISO impedance matching analysis is employed to examine the oscillation mechanism of the grid-connected FSC-VSPSU, yielding insights into the parameter influence rules;

(2)

A novel oscillation suppression strategy based on grid network impedance compensation is introduced for the first time, characterized by its simplicity in principle and its ease of implementation.

The organization of the article is as follows. Section 1 provides the introduction. Section 2, Section 3 and Section 4 delineate the proposed methods. In detail, Section 2 presents the SISO impedance measurement and oscillation analysis methodologies for the FSC-VSPSU. Section 3 delves into the exploration of the oscillation mechanism. Section 4 outlines the proposed oscillation suppression technique. Section 5 presents the simulation results, and, finally, Section 6 and Section 7 concludes the article.

2. SISO Impedance Measurement and Oscillation Analysis of FSC-VSPSU

The SISO impedance measurement approach is more readily applicable in practical engineering due to its streamlined measurement process and reduced requirement for data acquisition sensors. To elucidate the SISO impedance measurement and oscillation analysis methods for the grid-connected FSC-VSPSU, the subsequent sections are structured as follows. Section 2.1 delineates the structure of the FSC-VSPSU, encompassing its control systems. Subsequently, Section 2.2 delineates the fundamental SISO impedance measurement technique. Section 2.3 will investigate the oscillation analysis method based on the measured SISO impedances.

2.1. Structure of the FSC-VSPSU

Figure 1 presents the detailed structure of the FSC-VSPSU, which mainly consists of upper/lower reservoirs, a pump turbine, a motor, and a power electronic converter. In addition, the control systems are mainly composed of a turbine governor, an excitation system, and a converter controller. The upper and lower reservoirs store water resources, and the pump turbine is a mechanical transmission part. These two components can collaborate to facilitate the reciprocal transformation between potential energy and mechanical kinetic energy. Furthermore, the pump turbine drives the motor to rotate to generate the electric energy, and the power electronic converter can achieve the controllable energy exchange with the power grid. By coordinating the turbine governor, the excitation system, and the converter controller, the FSC-VSPSU can operate efficiently [13].

(1) For the excitation system, it regulates the voltage at the motor terminal, with the corresponding structure depicted in Figure 2. In detail, H₁(s) represents the voltage sampling link; H₂(s) is the series compensation link; H₃(s) represents the power amplification link; and H₄(s) is the parallel correction link [11]. Among them, H₂(s) is crucial for the voltage control performance. Additionally, the limiter is designed to restrict occurrences of over-excitation and under-excitation.

The expressions of H₁(s), H₂(s), H₃(s), and H₄(s) are listed as

$$\left\{\begin{array}{l}{H}_1(\mathrm{s})={\displaystyle \frac{1}{1+s{T}_{\mathrm{c}}}}\hfill \\ H_2(\mathrm{s})=K{\displaystyle \frac{1+\mathrm{s}{T}_1}{K_{\mathrm{v}}+s{T}_2}}\cdot {\displaystyle \frac{1+\mathrm{s}{T}_3}{1+\mathrm{s}{T}_4}}\hfill \\ H_3(\mathrm{s})={\displaystyle \frac{K_{\mathrm{a}}}{1+s{T}_{\mathrm{a}}}}\hfill \\ H_4(\mathrm{s})={\displaystyle \frac{s{K}_{\mathrm{f}}}{1+s{T}_{\mathrm{f}}}}\hfill \end{array}\right.$$

(1)

where T_c is the time constant of the sampling link; T₁, T₂, T₃, and T₄ are the time constants of the series compensation link; T_a is the time constant of the power amplification link; T_f is the time constant of the parallel correction link; K is the DC gain of the series correction link; K_V is the integration correction selection factor; K_a is the gain of the power amplification link; and K_f is the gain of the parallel correction link.

(2) For the turbine governor, it realizes the speed/power regulation of the pump turbine, and the specific structure is shown in Figure 3. In detail, H₅(s) represents the speed/power sampling link; H₆(s) is the delay of the hydraulic system; H₇(s) is the transfer function to describe the water hammer effect; and T_c/T_o are the hydraulic servo motor’s closing/opening times [11]. Furthermore, the PI control in the turbine governor is crucial to the control performance of the pump turbine.

The expressions of H₅(s), H₆(s), and H₇(s) are listed as

$$\left\{\begin{array}{l}{H}_5(\mathrm{s})={\displaystyle \frac{1}{1+s{T}_{\mathrm{R}}}}\hfill \\ H_6(\mathrm{s})={\displaystyle \frac{1}{1+s{T}_{\mathrm{P}}}}\hfill \\ H_7(\mathrm{s})={\displaystyle \frac{1-s{T}_{\mathrm{w}}}{1+0.5s{T}_{\mathrm{w}}}}\hfill \end{array}\right.$$

(2)

where T_R is the time constant of the collection link; T_P is the time constant of the power delay of the hydraulic system; and T_w is the time constant of the water hammer effect of the pump turbine.

(3) For the converter controller, it can control the grid-connected power or the motor speed quickly. Taking the rapid control of the motor speed as an example, its structure diagram is presented in Figure 4. In detail, the grid-side converter facilitates the control of DC voltage through a dual-loop control strategy, wherein the inner loop governs the current, while the outer loop regulates the DC voltage. The machine-side converter controls the motor speed, which also adopts the double closed loop control, but with the rotation speed loop as the outer control loop [13].

2.2. SISO Impedance Measurement Method

As for the FSC-VSPSU, the impedance measurement procedures are shown in Figure 5, which can be divided into four steps: (1) inject the controllable harmonic disturbance into the grid-connected point; (2) collect the voltage/current responses of the FSC-VSPSU; (3) extract the spectrum of the collected response data; (4) calculate the impedance with the extracted spectrum data. Specifically, to achieve more precise impedance measurement results, this study employs a frequency-sweeping disturbance method targeting a frequency band up to 100 Hz [22]. Additionally, for the collection of response data, the data buffer size is determined based on the quantity of data to be sampled (the product of the sampling rate and the sampling duration). The sampling rate is required only to comply with the Nyquist sampling theorem. The measurement period is defined as the reciprocal of the desired frequency resolution.

For a simpler impedance measurement procedure of the FSC-VSPSU, the SISO impedance can be calculated by

$${\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )=\overrightarrow{U}(\mathrm{j}\omega )/\overrightarrow{I}(\mathrm{j}\omega )$$

(3)

where ${\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )$ is the SISO impedance of the FSC-VSPSU and $\overrightarrow{U}(\mathrm{j}\omega )$ and $\overrightarrow{I}(\mathrm{j}\omega )$ are the voltage and current spectrums of the collected response data, respectively.

2.3. Oscillation Analysis Method Based on the Measured SISO Impedances

In the analysis of grid-connected FSC-VSPSUs, stability is contingent upon an adequate phase margin at the point of intersection between the magnitude curves of the grid impedance and the FSC-VSPSU impedance, as determined by measured impedances. Otherwise, the system may experience harmonic amplitude amplification and even oscillation or instability.

The equivalent impedance model of the grid-connected FSC-VSPSU is shown in Figure 6. ${\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )$ denote the equivalent grid power supply voltage; ${\overrightarrow{U}}_{\mathrm{p}}(\mathrm{j}\omega )$ denote the FSC-VSPSU port voltage; ${\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )$ represents the grid network impedance; and ${\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )$ represents the FSC-VSPSU impedance. Thus, ${\overrightarrow{U}}_{\mathrm{p}}(\mathrm{j}\omega )$ can be expressed in (4).

$$\begin{array}{l}{\overrightarrow{U}}_{\mathrm{P}}(\mathrm{j}\omega )={\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )\times {\displaystyle \frac{{\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )}{{\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )+{\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )}}\\ \hspace{1em}={\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )\times {\displaystyle \frac{1\angle 0°}{1\angle 0°+\left|{\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )/{\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right|\angle \left[{\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )/{\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right]}}\\ \hspace{1em}={\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )\times {\displaystyle \frac{1\angle 0°}{1\angle 0°+\left[\left|{\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )\right|/\left|{\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right|\right]\left[\angle {\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )-\angle {\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right]}}\end{array}$$

(4)

At the amplitude curve intersection of the grid impedance and the FSC-VSPSU impedance, $\left|{\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )\right|$ equals $\left|{\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right|$, thus making $\left|{\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )\right|/\left|{\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right|=1$. In this case, the amplitude of ${\overrightarrow{U}}_{\mathrm{p}}(\mathrm{j}\omega )$ can be derived in (5).

$$\begin{array}{l}\left|{\overrightarrow{U}}_{\mathrm{p}}(\mathrm{j}\omega )\right|=\left|{\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )\right|\times {\displaystyle \frac{\left| 1\angle 0° \right|}{\left|1\angle 0°+1\left[\angle {\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )-\angle {\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right]\right|}}\\ \hspace{1em}\hspace{1em}=\left|{\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )\right|\times {\displaystyle \frac{1}{\left|1\angle 0°+1\left[\angle {\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )-\angle {\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right]\right|}}\end{array}$$

(5)

Thus, if $\left|1\angle 0°+1\left[\angle {\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )-\angle {\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right]\right|>1$, the phase difference $\left|\angle {\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )-\angle {\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right|<120°$. In this case, ${\overrightarrow{U}}_{\mathrm{p}}(\mathrm{j}\omega )$ will not be larger than ${\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )$, which indicates that no harmonics are amplified and that this system will be stable. Furthermore, when $\left|1\angle 0°+1\left[\angle {\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )-\angle {\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right]\right|<1$, the phase difference $\left|\angle {\overrightarrow{Z}}_{\mathrm{net}}(\mathrm{j}\omega )-\angle {\overrightarrow{Z}}_{\mathrm{pump}}(\mathrm{j}\omega )\right|>120°$, and ${\overrightarrow{U}}_{\mathrm{p}}(\mathrm{j}\omega )$ will be larger compared to ${\overrightarrow{U}}_{\mathrm{g}}(\mathrm{j}\omega )$, which may cause the corresponding harmonics to be amplified. An insufficient phase margin of the system leads to the risk of oscillation. Furthermore, a phase difference exceeding 180° signifies a phase margin that falls below 0°, a condition that is indicative of pronounced harmonic amplification and that has the potential to precipitate system instability.

Based on the above analysis, the obtained oscillation criterion is shown in Figure 7. It is evident that within the green/stable region, the phase difference is less than 120°. A phase margin that is adequately robust ensures the maintenance of system stability. As the phase difference increases, the phase margin will decrease. However, the phase difference located in the grey/critical region with a weak phase margin may cause the corresponding harmonics to be amplified, and the system has a risk of oscillation. Moreover, when the phase difference is in the red/instable region, a negative phase margin will cause the system to oscillate severely, or it may even be unstable.

3. Oscillation Analysis of FSC-VSPSU

The above-mentioned SISO impedance measurement and oscillation analysis methods are employed to investigate the oscillation in the grid-connected FSC-VSPSU. Subsequently, the principles of parameter influence are elucidated in this section as follows. Section 3.1 discusses the influence rules of the DC voltage and the current loops of the grid-side converter; Section 3.2 addresses the rules of the rotational speed and the current loops of the machine-side converter; Section 3.3 explores the parameter rules related to the excitation system and the turbine governor; and Section 3.4 analyzes the influence rules of the equivalent impedance parameters of the grid network.

3.1. DC Voltage Loop and Current Loop Parameters of the Grid-Side Converter

When changing the proportional parameter of the DC voltage loop of the grid-side converter (K_pv), the relevant Bode diagram of the impedance matching analysis is shown in Figure 8. Specifically, the red and blue lines depicted in the figure correspond to the impedances of the grid network and the FSC-VSPSU, respectively. Additionally, the pink line denotes the phase margin curve. It is to be noted that the line designations are consistently applied across subsequent figures, and thus they will not be reiterated in their descriptions. As it can be seen, at the intersections of the impedance amplitude curves, the corresponding phase margins are relatively small at around 0°, which indicates that the system will experience oscillation.

The specific analyses are as follows. (1) When K_pv is set to 0.5, the phase margin is approximately negative, which indicates that the system may experience oscillation. (2) When K_pv is increased to 1, the phase margin is slightly increased and higher than 0°, and thus the oscillation will be suppressed. (3) When K_pv is further increased to 2, the phase margin slightly increases, and the oscillation will be further weakened.

When changing the integration parameter of the DC voltage loop of the grid-side converter (K_iv), the relevant Bode diagram of the impedance matching analysis is shown in Figure 9. As it can be seen, at the intersections of the impedance amplitude curves, there is a relatively significant increase in the phase margin when K_iv is reduced. When K_iv is set to 80, the phase margin is weak and close to 0; hence, this system has a risk of oscillation. Furthermore, when K_iv is decreased to 40, the phase margin increases to around 15°, and the oscillation phenomenon that occurs in the system will be weakened to some extent. At last, when K_iv is decreased to 20, the phase margin further increases accordingly, and the oscillation will be further weakened.

When changing the proportional parameter of the current loop of the grid-side converter (K_pc1), the relevant Bode diagram of the impedance matching analysis is shown in Figure 10. As it can be seen, when K_pc1 is set to 2, the phase margin is relatively minimal and close to 0°, which indicates that the system will oscillate. Furthermore, when K_pc1 is increased to 4, the phase margin is increased, and thus the oscillation will be suppressed. However, when K_pc1 is further increased to 8, the phase margin decreases, and the oscillation will reappear. Therefore, the regularity of the influence of K_pc1 on oscillation is not significant.

When changing the integration parameter of the current loop of the grid-side converter (K_ic1), the relevant Bode diagram of the impedance matching analysis is shown in Figure 11. As it can be seen, when K_ic1 is set to 50, the phase margin is weak and close to 0; thus, this system has a risk of oscillation. Furthermore, when K_ic1 is decreased to 25, the phase margin is increased, and the oscillation phenomenon that occurs in the system will be suppressed.

3.2. Rotation Speed Loop and Current Loop Parameters of the Machine-Side Converter

Upon adjustment of the parameters associated with the rotation speed loop and the current loop of the machine-side converter, the pertinent single-input–single-output (SISO) impedances of the FSC-VSPSU are illustrated in Figure 12. In detail, the red line represents the initial FSC-VSPSU impedance, and “○”, “□”, “◇”, and “✩” represent the measured SISO impedances when changing K_pw, K_iw, K_pc2, and K_ic2, respectively. K_pw and K_iw are the proportional and integration parameters of the rotation speed loop, respectively, and K_pc2 and K_ic2 are the proportional and integration parameters of the current loop of the machine-side converter, respectively. As it can be seen, when changing K_pw, K_iw, K_pc2, and K_ic2, the SISO impedance of FSC-VSPSU remains almost unchanged. Therefore, the corresponding control parameters of the machine-side converter have a weak impact on oscillation occurring in the grid-connected point.

Thus, the oscillation suppression performances of the control parameters are shown in Table 1. In detail, “↓” represents that reducing the relevant parameter can suppress the oscillation, and “×” represents poor or irregular suppression of oscillation by adjusting the relevant parameter.

3.3. Excitation System and Turbine Governor Parameters

In the event of modifying the parameters of the excitation system and the turbine governor, the corresponding single-input–single-output (SISO) impedances of the FSC-VSPSU are depicted in Figure 13. In detail, the red line represents the initial FSC-VSPSU impedance, and “○”, “□”, and “◇” represent the measured SISO impedances when changing K_pg, K_ig, and K, respectively. K_pg and K_ig are the proportional and integration parameters of the turbine governor, respectively, and K is the DC gain of the series correction link of the excitation system. As it can be seen, when changing K_pg, K_ig, and K, the SISO impedance of FSC-VSPSU also remains almost unchanged. Therefore, the corresponding excitation system and turbine governor parameters also have weak impacts on oscillation occurring in the grid-connected point.

3.4. Equivalent Impedance Parameters of the Grid Network

When changing the equivalent inductance of the grid network (L_g), the relevant Bode diagram of the impedance matching analysis is shown in Figure 14. As it can be seen, when L_g is set to 0.8 mH, the phase margin is negative, which indicates that the system may experience instability. Furthermore, when L_g is decreased to 0.6 mH, the phase margin is slightly increased to 5°, and the weak phase margin indicates that the system will experience oscillation. When L_g is further decreased to 0.4 mH, the phase margin is enhanced, and the oscillation will be weakened. At last, when L_g is further decreased to 0.1 mH, the impedance amplitude curves have no intersection, and so the sufficient phase margin makes the system extremely stable.

When changing the equivalent resistance of the grid network (R_g), the relevant Bode diagram of the impedance matching analysis is shown in Figure 15. As it can be seen, when R_g is appropriately increased, the intersections of the impedance amplitude curves almost have no movements, and the corresponding phase margin is improved, which can suppress the oscillation phenomenon that occurs in the system.

3.5. Summary of the Oscillation Analysis

To sum up, the oscillation analysis results are shown in Table 1. In detail, “↓” represents that reducing the relevant parameter can suppress the oscillation; “↑” represents that increasing the relevant parameter can suppress the oscillation; and “×” represents poor or irregular suppression of the oscillation by adjusting the relevant parameter.

Table 1. Summary of the oscillation analysis results.

Control parameters of the grid-side converter	Kpv	Kiv	Kpc1	Kic1
	×	↓	×	↓
Control parameters of the machine-side converter	Kpw	Kiw	Kpc2	Kic2
	×	×	×	×
Excitation system and turbine governor parameters	Kpg		Kig	K
	×		×	×
Equivalent impedance parameters of the grid network	Lg		Rg
	↓		↑

Table 1. Summary of the oscillation analysis results.

Control parameters of the grid-side converter	Kpv	Kiv	Kpc1	Kic1
	×	↓	×	↓
Control parameters of the machine-side converter	Kpw	Kiw	Kpc2	Kic2
	×	×	×	×
Excitation system and turbine governor parameters	Kpg		Kig	K
	×		×	×
Equivalent impedance parameters of the grid network	Lg		Rg
	↓		↑

4. Oscillation Suppressions of FSC-VSPSU

Based on the oscillation suppression performances presented in Table 1, this section formulates targeted strategies for mitigating oscillations focusing on two key optimization points: (1) the control parameters of FSC-VSPSU; (2) the grid network impedance. Specifically, the oscillation suppression strategy related to control parameters targets the black box controller, wherein the in situ modification of controller parameters is impractical in real-world applications. Consequently, this section introduces an oscillation suppression approach grounded in the optimization of grid network impedance, characterized by its straightforward principle and ease of implementation.

From Table 1, reducing L_g or appropriately increasing R_g can suppress the oscillation of the grid-connected FSC-VSPSU. However, for the actual operating grid network, reducing its equivalent inductance is difficult to achieve. Therefore, the following will study the oscillation suppression strategy by increasing the equivalent resistance of the grid network, and the corresponding schematic diagram is shown in Figure 16. When the system operates stably, the bypass switch is closed, causing the compensation resistor (R_c0) to be short-circuited. Furthermore, when the system experiences oscillation, the bypass switch is opened, and the R_c0 is connected to the system in series, which increases the equivalent resistance of the grid network to suppress the occurring oscillation.

It is noteworthy that an increased compensation resistance yields a more pronounced effect on the suppression of oscillations. Nevertheless, this enhancement is accompanied by a reduction in the system’s short-circuit ratio (SCR), which poses a threat to its safe operation. Therefore, the compensation resistance has a maximum limitation.

The SCR expression is written as

$$K_{\mathrm{scr}}={\displaystyle \frac{S_{\mathrm{ac}}}{P_{\mathrm{dN}}}}={\displaystyle \frac{U_{\mathrm{N}}^2}{P_{\mathrm{dN}}}}\cdot {\displaystyle \frac{1}{\left|Z\right|}}>K_{\mathrm{scr}\_\min }$$

(6)

where K_scr is the SCR value and K_{scr_min} is its minimum limitation; S_ac is the short-circuit capacity of the grid; P_dN is the rated DC power of the unit; Z is the equivalent impedance of the grid network; and U_N is the rated voltage of the grid.

When R_c0 is connected to the system, the equivalent impedance of the grid network is expressed as

$$Z={\mathrm{R}}_{\mathrm{g}}{+\mathrm{jX}}_{\mathrm{g}}{+\mathrm{R}}_{\mathrm{c}0}$$

(7)

where X_g, written as X_g = 2πfL_g, is the equivalent reactance of the grid network.

Furthermore, by substituting (7) into (6), the maximum limitation of the compensation resistance can be solved as

$${\mathrm{R}}_{\mathrm{c}0}<\sqrt{{\displaystyle \frac{U_{\mathrm{N}}^4}{K_{\mathrm{scr}\_\min }^2·P_{\mathrm{dN}}^2}}-{\mathrm{X}}_{\mathrm{g}}^2}-{\mathrm{R}}_{\mathrm{g}}$$

(8)

Therefore, at the grid-connected point of FSC-VSPSU, X_g and R_g can be obtained through impedance measurement, and the maximum limitation of the compensation resistance can be further calculated through (8).

5. Simulation Results

To ascertain the accuracy of the oscillation analysis presented herein and to evaluate the efficacy of the proposed oscillation suppression measures, a grid-connected FSC-VSPSU simulation model has been developed within the MATLAB/SIMULINK environment (2023b). This model is constructed in accordance with the structural diagram provided in Figure 1.

Table 2. Basic parameters of the simulation system.

Symbol	Parameter	Value
ug	Input voltage of grid-side converter	ug = 2800 V
ud	DC reference voltage	ud = 5200 V
Lg	Equivalent inductance of the grid	Lg = 1 mH
Rg	Equivalent resistance of the grid	Rg = 0.04 Ω
Cd	DC capacitance	Cd = 15 mF
Kpv, Kiv	PI parameters of the DC voltage loop	Kpv = 1, Kiv = 80
Kpc1, Kic1	PI parameters of the current loop of the grid-side converter	Kpc1 = 2, Kic1 = 50
Kpw, Kiw	PI parameters of the rotation speed loop	Kpw = 2, Kiw = 20
Kpc2, Kic2	PI parameters of the current loop of the machine-side converter	Kpc2 = 10, Kic2 = 100
Kpg, Kig	PI parameters of the turbine governor	Kpg = 2, Kig = 5
K	DC gain of the series correction link of the excitation system	K = 200

lists the basic simulation parameters. Furthermore, the oscillation analysis results summarized in Table 1 will be verified separately in Section 5.1, Section 5.2, Section 5.3, Section 5.4, and Section 5.5 will verify the proposed oscillation suppression strategy.

Under the parameters listed in Table 2, the system will experience oscillation, which is shown in Figure 17. As it can be seen, when observing the oscillation of the DC-side voltage, the current on the AC side also oscillates at the same frequency. Notably, the three different colors in Figure 17b represent the three phases in the power system. To prevent the article from being too lengthy, only the DC-side voltage is provided to demonstrate the stability of the system in the following content. Furthermore, to verify the correctness of the oscillation analysis results, the following content will analyze the oscillation changes when adjusting the corresponding parameters.

5.1. Oscillation Analysis Verification When Changing the Control Parameters of the Grid-Side Converter

Figure 18 gives the simulation results when changing the control parameters of the grid-side converter. As it can be seen, when K_pv is changed to 2, the oscillation phenomenon observed in Figure 18a exhibits a noticeable reduction in intensity when contrasted with the curve presented in Figure 17. A similar result can also be seen in Figure 18c when K_pc1 is changed to 8. As a result, these two control parameters have a weak performance in completely suppressing the oscillation. Therefore, “×” is used to label them in Table 1.

Furthermore, when K_iv is decreased to 20, the oscillation is completely suppressed, as shown in Figure 18b, to maintain the system’s stability. Similarly, when K_ic1 is decreased to 25, the oscillation also disappears, which indicates that reducing the relevant parameters can suppress the oscillation. Thus, “↓” being used to label them in Table 1 is verified.

5.2. Oscillation Analysis Verification When Changing the Control Parameters of the Machine-Side Converter

Figure 19 gives the simulation results when changing the control parameters of the machine-side converter. As it can be seen, when changing K_pw, K_iw, K_pc2, and K_ic2, the oscillations are hardly mitigated, and they show almost no changes compared to Figure 17. As a result, the control parameters of the machine-side converter have no ability to suppress the oscillations. Therefore, “×” being used to label them in Table 1 is verified.

5.3. Oscillation Analysis Verification When Changing the Excitation System and the Turbine Governor Parameters

Figure 20 gives the simulation results when changing the excitation system and the turbine governor parameters. As it can be seen, just as in Section 5.2, when changing K_pg, K_ig, and K, the oscillations are also hardly mitigated, and they show almost no changes compared to Figure 17. As a result, the excitation system and the turbine governor parameters have no ability to suppress the oscillations. Therefore, “×” being used to label them in Table 1 is verified.

5.4. Oscillation Analysis Verification When Changing the Equivalent Impedance Parameters of the Grid Network

Figure 21 gives the simulation results when changing the equivalent impedance parameters of the grid network. As it can be seen, when decreasing L_g, or increasing R_g, the oscillations can be suppressed, and the system ultimately returns to a stable operating state. Therefore, “↓” being used to label L_g and “↑” being used to label R_g in Table 1 are verified.

5.5. Oscillation Suppression Strategy

Figure 22 gives the simulation results when applying the oscillation suppression strategy at 1.5 s. As it can be seen, when without the compensation resistor, the system oscillates and gradually diverges. Furthermore, when the compensation resistor is applied at 1.5 s, the oscillation gradually decreases and eventually returns to a stable operating state, which verifies the effectiveness of the proposed suppression strategy.

5.6. Summary of Results

The oscillation analysis results summarized in Table 1 are verified separately in Section 5.1, Section 5.2, Section 5.3 and Section 5.4, which support contribution 1 presented in the introduction. Section 5.5 verifies the proposed oscillation suppression strategy, which supports contribution 2 presented in the introduction.

6. Discussions

The FSC-VSPSU can offer flexible, large-capacity regulation resources to the power grid, facilitating the safe operation of power systems dominated by clean energy sources. However, the impedance mismatch between FSC-VSPSU and the power grid will lead to oscillation phenomena, severely restricting its rapid development. This article explores the oscillation mechanism of the grid-connected FSC-VSPSU and proposes practical oscillation suppression strategies to ensure the safe operation of the unit. Therefore, this study can promote the rapid development of FSC-VSPSU, which brings huge market opportunities and economic benefits to the manufacturers of motors, pump turbines, and converters. Meanwhile, this study has the potential to facilitate the advancement of the pumped storage sector, attenuate the effects of volatility and intermittency associated with renewable energy sources on the electrical power system, and foster the transition toward a more sustainable and clean energy structure.

7. Conclusions

The impedance mismatches between the FSC-VSPSU and the power grid can induce oscillation phenomena, posing risks to the secure and stable operation of the power system. To address this, this article studies the oscillation mechanism and the suppression strategy of the grid-connected FSC-VSPSU. By using the SISO impedance measurement method and the derived oscillation analysis criterion, the oscillation mechanism and the corresponding parameter influence rules of the grid-connected FSC-VSPSU are obtained, which indicates that the power grid network and the grid-side converter of FSC-VSPSU have a greater impact on the grid-connected wideband oscillations compared to the machine-side converter, the excitation system, and the governor. Based on this, the corresponding oscillation suppression strategies are further formulated. Notably, this work introduces for the first time the concept of oscillation suppression through power grid network resistance compensation, which provides guidance for the design of converters capable of mitigating oscillations.