###### Abstract
The SRF theory is widely adopted in various applications, including grid-connected inverters, motor drives, and active power filters, where the precise control of PQ and system dynamics is crucial [14; 15]. Instantaneous reactive power (IRP) theory is another important approach. In this theory, the DSTATCOM alters its current to match the desired waveform's peak harmonic magnitude by measuring the source voltage and load currents, which are then transformed using the Clarke transformation. This conversion translates the three-phase quantities into two-phase orthogonal coordinates. This transformation is essential for accurately calculating the instantaneous active and reactive power components. This enables the DSTATCOM to effectively regulate reactive power, thus enhancing the system PQ and overall performance. In the realm of control algorithms, the Proportional-Integral (PI) control method and the Fractional-Order PI controller are widely embraced for their simplicity and effectiveness in minimizing steady-state errors. Proportional-resonant control is highly regarded for its capability to eliminate steady-state errors when tracking sinusoidal signals, making it especially advantageous in grid-connected applications. Hysteresis control, known for its fast dynamic response and straightforward implementation, is also notable, though it has the drawback of producing inconsistent switching frequencies. Moreover, control methods based on optimization algorithms utilize evolutionary strategies to fine-tune control parameters, thereby boosting system efficiency and performance. These advanced control algorithms work together to enhance the stability, responsiveness, and overall effectiveness of DSTATCOM systems in maintaining power quality and voltage regulation. Recent advancements in DSTATCOM control strategies have introduced a range of innovative approaches to enhance system performance. A notable development is the proposal of a Type-2 Fuzzy Logic Controller (FLC) with a recursive least square filter designed to improve control precision [16]. Additionally, a conjugate gradient backpropagation method based on the \(\mathrm{icos}(\phi)\) neural network has been applied, resulting in significant gains in system accuracy [17]. The introduction of a generalized neural network (NN) algorithm, which combines Gaussian, sigmoidal, and linear transfer functions, has further broadened the versatility of DSTATCOM control [18]. The adoption of an enhanced model predictive control (MPC)-based state-space model, along with the application of MPC to a newly developed four-level inverter-based DSTATCOM, has led to marked improvements in dynamic response and stability [19; 20]. Furthermore, an adaptive neuro-fuzzy inference system (ANFIS) utilizing least-mean-square algorithms has proven effective in compensating for current disturbances [21]. Other advancements include the development of an improved Widrow-Hoff algorithm-based adaptive control [22], as well as the implementation of an adaptive reweighted zero-attracting control for a DSTATCOM-based photovoltaic source [23]. Finally, significant research has focused on the tuning of PI controllers, employing methods such as the Differential Search Algorithm and Wind-Driven Optimization [24], as well as the integration of particle swarm and ant colony optimization, both of which have substantially enhanced the performance of DSTATCOM systems [25]. The PI controller, Fractional-Order PI (FOPI) controller, and cascading controllers are extensively utilized to enhance power quality and maintain voltage stability. The PI controller effectively minimizes steady-state errors by integrating past control actions, ensuring rapid correction of voltage deviations. However, system nonlinearities and dynamic changes can adversely affect its performance, leading to oscillations and extended settling times. While FOPI controllers can offer improved system performance, they are often more sensitive to disturbances and noise, which can result in instability if not carefully tuned [26; 27; 28].