## 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.