Correction: System frequency response model and droop coefficient setting considering renewable energy participation in frequency regulation

Compared to traditional synchronous systems, the extensive integration of high-proportion electronic RES has substituted for some SG, resulting in a gradual reduction in system inertia and relatively weaker frequency regulation capability due to the decoupling characteristics of renewable energy power electronics and their maximum power tracking mode. In addition, the application of UHV large-capacity cross-regional DC transmission has blocked the cross-regional inertia support and power response under disturbances, seriously deteriorating the system frequency stability under large disturbances [1-4]. In interconnected power systems, frequency stability is an important indicator reflecting power quality, mainly representing the balance state of active power in power systems [5-8]. In traditional power systems, frequency control is primarily achieved by regulating the active power output of generator sets, enabling the system's generation power to follow changes in system load power, thereby achieving active power balance across the entire system. This function is commonly referred to as LFC (Load Frequency Control) [9]. However, in power systems with a high penetration of renewable energy, the uncertainty of renewable energy output becomes a critical factor affecting the active power balance of the system [10]. Compared to traditional load disturbances, renewable energy output disturbances are more severe and highly unpredictable, posing challenges to the current load frequency control techniques, which lack suitable representation and handling of this uncertainty. The integration of high proportions of renewable energy inevitably has adverse effects on the quality and stability of frequency control [11]. Furthermore, renewable energy units exhibit significantly different frequency response characteristics from traditional energy units. Their replacement of traditional units leads to uncertain changes in system structure, parameters, and frequency response characteristics, further complicating frequency control [12]. In response to the aforementioned issues regarding frequency response characteristics arising from the high integration of renewable energy, extensive research has been conducted by scholars both domestically and internationally. In Reference [13], the study of the system's frequency dynamic response through the ASF (Average System Frequency) is proposed. This model equates all generators in the system to a single-machine model while retaining the original turbine-governor systems of each unit. However, as the number of generators continues to increase, the proliferation of turbine-governor systems limits the applicability of this method. Building upon the ASF model, Reference [14] further simplifies the turbine-governor systems through equivalent aggregation, thereby approximating the entire power grid as a single-machine model with a centralized load model. The SFR model significantly reduces the order of the frequency response analysis model, enabling the calculation of analytical solutions for maximum frequency deviations and corresponding times under given disturbances. It is currently the most commonly used model for frequency response analysis. Reference [15] established a two-stage distributionally robust unit commitment model for power systems with wind farms, based on the ASF model and its simplified SFR model, considering virtual inertia control and droop control of wind farms. Reference [16] employed the system SFR model to analyze the impact of key frequency control parameters, including inertia time constant, frequency regulation deadband, and governor droop, on system frequency response characteristics. Reference [17] developed an SFR model incorporating wind turbine integration, derived dynamic frequency quantification metrics, and constructed a unit commitment optimization model for wind-integrated systems considering dynamic frequency constraints. Reference [18] integrated wind power virtual inertia control into the traditional SFR model and analyzed its effect on system frequency response. Reference [19] proposed a power system frequency dynamic analysis method based on the DC power flow method, which ignores the impact of reactive power-voltage variations on frequency dynamics and uses the DC power flow method to describe the system network flow equations, considering only generator motion equations and turbine-governor dynamics, with iterative integration methods to calculate post-disturbance system frequency dynamics. Reference [20] established equivalent models for SG, wind farms, and loads, using wind power fluctuations and frequency deviations as input and output variables, respectively, thereby simplifying a multi-machine system to a single-machine system. This enabled the establishment of a frequency-domain transfer function between system power fluctuations and frequency deviations, which was then used to analyze system frequency dynamics with the SFR model. Reference [21] quantitatively analyzed the impact of wind power integration on system equivalent inertia and damping constants. Through the modification of traditional SFR model parameters, it proposed an SFR model that considers wind power integration and derived the corresponding time-domain expression for maximum frequency deviation. Reference [22] introduced an analytical method to aggregate a multi-machine SFR model into a single-machine model. Validation studies demonstrated that the proposed aggregated SFR model accurately represents the multi-machine SFR model. This paper based on the mechanism of traditional thermal power unit inertia and primary frequency regulation (PFR) for system frequency adjustment, employs the SFR method to analyze the impact of various factors on system frequency dynamic characteristics after the participation of renewable energy units in frequency regulation. Considering the involvement of renewable energy units in frequency regulation, the SFR model is improved to derive expressions and correlations for the initial rate of frequency change, maximum frequency deviation, and steady-state frequency deviation. Through theoretical analysis, the mechanism of operating conditions influencing the frequency regulation capability of renewable energy units and system frequency dynamic behavior is revealed. The effectiveness of this improved SFR model is verified through simulations on the modified WCSS 4-machine 10-bus system.