Frequency Regulation of Renewable Energy Plants in Regional Power Grids: A Study Considering the Frequency Regulation Deadband Width

Abstract

With the continuous increase in renewable energy penetration, traditional frequency regulation strategies in power grids struggle to maintain frequency stability under high renewable-share conditions. To address the shortcomings of the current deadband settings in regional grid frequency regulation, this paper proposes an optimized deadband-configuration scheme for renewable energy power plants and evaluates its effectiveness in enhancing the frequency regulation potential of renewable units. By developing frequency response models for thermal power, wind power, photovoltaic generation, and energy storage, the impact of different deadband widths on dynamic frequency response and steady-state deviation is analyzed. Three representative output scenarios for renewable units are constructed, and under each scenario the coordinated control performance of the proposed and the existing deadband configurations is compared. Simulation studies are then conducted based on a typical high renewable penetration scenario. The results show that, compared with the existing regional-grid deadband settings, the proposed configuration more fully exploits the regulation potential of renewable units, improves overall frequency-response capability, significantly reduces frequency deviations, and shortens recovery time. This research provides both theoretical foundations and practical guidance for frequency-support provision by renewable energy power plants under high penetration conditions.

1. Introduction

In recent years, with the continuous rise in renewable energy penetration, the frequency regulation capability of regional power grids has faced unprecedented challenges. By the end of 2024, global additions to installed capacity comprised 117 GW of wind power, 600 GW of photovoltaic power, and 91.3 GW of stand-alone energy storage; renewable energy accounted for 46.4% of the total installed capacity. High renewable penetration significantly weakens the grid’s inertial response and primary frequency regulation capability, severely undermining dynamic frequency stability [1,2]. This is because wind and photovoltaic units—being grid-connected via power converters—cannot inherently respond to system-frequency deviations in the same way as conventional thermal units. Accordingly, both national and regional grid-integration operation codes now require that renewable energy plants provide active frequency-support when operating online [3].

In recent years, numerous studies both domestically and internationally have addressed the provision of frequency support by multiple regulation resources. For wind turbines, the primary frequency regulation strategies chiefly fall into two categories: power reserve control and rotor kinetic energy control. References [4,5,6] propose a method that, based on system-frequency deviation signals, emulates the droop-control loop of synchronous machines to furnish rapid active-power support and thereby improve the frequency characteristics under disturbance. References [7,8] design an auxiliary power loop that harnesses the rotor’s kinetic energy for frequency regulation in response to system-frequency changes. In the case of photovoltaic plants, the main primary frequency regulation approaches include fixed-ratio curtailment reserves and variable-curtailment operation. Reference [9] introduces a fixed-coefficient curtailment-reserve mode for PV units to supply frequency support to a disturbed grid; Reference [10] develops a variable-curtailment control strategy that enhances the frequency-response capability of PV power stations. Regarding stand-alone energy storage, strategies typically encompass SOC (State of Charge)-based feedback adjustment, droop control, and synthetic-inertia control. Reference [11] proposes a coordinated thermal–storage frequency regulation strategy that effectively supplements the system’s primary frequency response capacity; Reference [12] presents a dynamic voltage–frequency composite control method for energy storage to provide power support during disturbances. However, these studies largely focus on individual resource control schemes and do not fully explore the combined influence of multiple frequency regulation resources on the grid’s overall dynamic frequency behavior.

Especially for intermittent energy sources such as wind power and photovoltaic, their regulation capability is more volatile and uncertain than that of traditional thermal power units. The deadband configuration prevents frequent power adjustments due to small frequency deviations in this process, reducing the dynamic fluctuations and equipment burden on the system. However, in practice, although the deadband is usually set narrowly, its potential impact on system performance should not be ignored. Optimizing the deadband configuration can effectively improve the frequency response capability of the renewable energy power generation unit, which in turn enhances the overall frequency regulation performance of the system, avoids unnecessary frequent adjustments, and reduces the wear and tear of the equipment and control difficulties caused by frequency fluctuations.

In a modern power system, multiple types of renewable energy plants—such as wind farms, photovoltaic (PV) installations, and energy-storage systems—must coordinate to provide grid frequency regulation, and their effectiveness critically depends on the proper configuration of frequency regulation deadbands. The deadband determines each type of generator’s activation threshold for frequency support and is thus a key factor in the synergistic performance of frequency regulation resources. Conventional thermal units typically employ fixed deadbands, whereas renewable units offer a wider adjustable range. Different deadband configurations can significantly influence primary frequency regulation performance. Related studies have shown that the design of renewable-unit frequency regulation strategies must account for deadband values; Literature [13] proposed a hybrid energy storage control strategy based on batteries and supercapacitors, focusing on the power distribution of the storage unit, but did not fully consider the dynamic characteristics of multiple frequency regulation resources and system nonlinearities. Literature [14] optimized the virtual synchronization control parameters of wind turbines to meet the physical constraints but did not incorporate the actual operating state and disturbance sensitivity of multiple resources. Literature [15] designed the primary frequency regulation parameters for compressed air energy storage system, which lacks the consideration of the dynamic response under complex operating conditions. In contrast, the control strategy proposed in this paper is based on the deadband configuration method of multiple frequency regulation resources, which fully considers different seasonal load disturbances and resource characteristics, and is validated on Matlab/Simulink 2023a and BPA platforms, effectively improving the frequency stability and system robustness.

To this end, this paper presents a simulation study on the impact of coordinated deadband-configuration schemes under several typical renewable-output scenarios on the grid’s primary frequency regulation characteristics. First, a system frequency response model is developed that incorporates multiple regulating resources—thermal units, wind turbines, photovoltaic units, and stand-alone energy-storage stations—to analyze the dynamic behaviors and regulation capabilities of each unit type. Second, using the system model that includes renewable deadbands, the influence of deadband parameters on frequency stability is examined, revealing how different deadband configurations affect dynamic frequency response and steady-state deviation. Third, a novel deadband-configuration scheme is proposed and validated via simulations in three representative renewable-output scenarios; the proposed and existing configurations are compared in terms of response waveform characteristics and key performance metrics. Finally, the applicability of the proposed scheme under high renewable penetration conditions in the East China Grid is assessed, and feasible recommendations for enhancing frequency stability are provided, offering both theoretical foundations and practical guidance for renewable energy plants’ participation in grid frequency regulation.

2. System Frequency Response Model for Multiple Frequency-Regulating Resources

Taking into account the effect of the frequency regulation deadband, the system frequency response model shown in Figure 1 is constructed to include thermal units, wind farms, photovoltaic plants, and stand-alone energy-storage stations. In this figure, $\rho$ denotes the system’s renewable energy penetration rate; $H_{\mathrm{s}}$ is the system’s equivalent inertia time constant; $R$ represents the primary frequency regulation droop coefficient of synchronous units; and $D_{\mathrm{s}}$ is the load’s damping coefficient. Symbols appearing in the relevant schematic diagrams in Section 2 are described in Appendix A,

Table A1. Description of relevant symbols.

Symbols	Meaning
ΔPd	disturbed active power
ΔPE	energy storage response output power
e0	initial SOC error
E0	current storage capacity
Erated	rated storage capacity
$\eta$	charge/discharge efficiency
TA	wind turbine inertia time constant
ΔPm	wind turbine response power
Δ$\omega$	wind turbine rotor speed deviation
T1	photovoltaic inertial response time constant
b	damping parameters of the frequency response of a photovoltaic converter
e	current frequency error signal or its derivative
ρ	the proportion of installed renewable generation capacity to the total installed capacity

.

2.1. Mathematical Models of Thermal Power Units and Loads

Assuming that the frequency response of the thermal unit remains linear and its inertial time constant and regulation parameters remain constant. The speed of traditional thermal power units depends on the real-time state of the unit’s input and output energy, exhibiting inertia. The relationship is shown in Equation (1).

$$P_G(s)={\displaystyle \frac{1+s{F}_s{T}_s}{1+T_{s}s}}$$

(1)

where $T_s$ represents the inertia time constant of the steam turbine, and $F_s$ is the characteristic coefficient of the steam turbine.

The characteristic whereby the load automatically adjusts its active power consumption to counteract frequency changes is represented by the load’s damping constant, $D_s$,

$$D_s=K_L={\displaystyle \frac{\Delta P_L}{\Delta f}}$$

(2)

The frequency regulation mechanism of regional power systems focuses on evaluating the overall efficiency of all generating units within the region, where the equivalent inertia time constant $H_s$ of a single generating unit is defined as the sum of the inertia time constants of all constituent generating units in the area.

According to the Chinese National Standard [16], the primary frequency regulation deadband for thermal power generating units shall not exceed ±2 r/min (±0.033 Hz).

2.2. Frequency Characteristic Model of Wind Turbine Generating Units

Assume that the regulation of the wind turbine is constant, and ignore the large variations in the frequency response of the wind output due to the volatility of wind speeds. The Doubly Fed Induction Generator (DFIG) can be equipped with system inertial support capability by controlling rotor inertia and blade pitch angle. DFIG participates in grid frequency regulation by emulating the characteristics of conventional synchronous generators, with its mathematical transfer function expressed as

$$\Delta P_{\beta }=-{\displaystyle \frac{k_{pf}}{1+T_{\beta }s}}\cdot \Delta f(s)$$

(3)

where $\Delta P_{\beta }$ denotes the frequency support power of the wind turbine; $T_{\beta }$ represents the response time constant; and $k_{pf}$ is the primary frequency regulation coefficient of the wind turbine.

Based on the inertial time constant and output power of the DFIG-based wind turbine, the frequency characteristic equation can be derived and normalized as

$$2H_w{w}_{\ast }{\displaystyle \frac{d{w}_{\ast }}{dt}}=\Delta P_G-\Delta P_L$$

(4)

where ${\omega }_{*}$ is the per-unit value of the wind turbine rotor’s rated rotational speed; $H_w$ is the virtual inertia of the wind turbine.

Based on the above analysis, the DFIG can respond to system frequency variations by adjusting its active power output, with the schematic diagram of its frequency regulation mechanism illustrated in Figure 2.

A properly configured deadband not only satisfies frequency-support requirements but also balances response sensitivity with the equipment’s operational economy. The relationship between the input $\Delta f(t)$ and output $x_w(t)$ of the wind turbine generator’s frequency regulation deadband is given in Equation (5).

$$x_w(t)=\left\{\begin{array}{l}\Delta f(t)-d_1 \Delta f(t)>d_1\\ 0 |\Delta f(t)|\le d_1\\ \Delta f(t)+d_1 \Delta f(t)<-d_1\end{array}\right.$$

(5)

where $d_1$ represents the deadband threshold of the wind turbine generator.

According to Equation (5), the deadband input–output relationship of a wind turbine can be described as

$$\Delta P_{\beta }=\left\{\begin{array}{l}{K}_f\cdot \Delta f \mathrm{if}\left|\Delta f>\Delta f_{DB}\right|\\ 0 \mathrm{if}\left|\Delta f\le \Delta f_{DB}\right|\end{array}\right.$$

(6)

In small signal analysis, linearization can be performed when the system frequency deviation Δf is small and close to the deadband threshold. Assuming a small deadband width Δf_DB, the power response of the system is zero when the frequency deviation Δf is within the deadband. Outside the deadband, the power response is proportional to the frequency deviation. Therefore, the transfer function of the wind turbine can be linearized as

$$\Delta P_{\beta }(s)={\displaystyle \frac{K_f}{s+T_r}}\cdot \Delta f(s)$$

(7)

where K_f is the gain coefficient of the wind turbine and $T_r$ is the inertia time constant of the system.

2.3. Frequency-Response Characteristic Model of Photovoltaic (PV) Generator Units

The solar model is based on an idealized frequency response assumption of the PV system, which is assumed to provide stable virtual inertial support. Photovoltaic (PV) systems, when participating in grid frequency regulation, reserve a portion of their available active power as a spinning reserve, thereby enabling a rapid response to system frequency deviations and the provision of active power support.

Based on the rate of change in grid frequency, the active power increment $\Delta P_{PV}$ of the photovoltaic generation unit can be calculated, as shown in Equation (8):

$$\Delta P_{PV}=2H_{PV}{\displaystyle \frac{df}{dt}}=2H_{PV}{\displaystyle \frac{U_{tq}{k}_4}{2\pi }}$$

(8)

where $H_{PV}$ denotes the virtual inertia time constant of the photovoltaic generation, $U_{tq}$ represents the q-axis component of the voltage vector at the point of common coupling, and $k_4$ indicates the index of the connection point.

Based on the above analysis, the schematic diagram of the PV unit’s participation in grid frequency regulation control is shown in Figure 3.

The relationship between the deadband’s input $\Delta f(t)$ and output $x_{PV}(t)$ for PV unit frequency regulation is given by Equation (9).

$$x_{PV}(t)=\left\{\begin{array}{l}\Delta f(t)-d_2 \Delta f(t)>d_2\\ 0 |\Delta f(t)|\le d_2\\ \Delta f(t)+d_2 \Delta f(t)<-d_2\end{array}\right.$$

(9)

where $d_2$ denotes the deadband threshold of the photovoltaic generation unit.

According to Equation (9), the deadband input-output relationship of the PV unit can be expressed as

$$\Delta P_{pv}=\left\{\begin{array}{l}{K}_1\cdot \Delta f \mathrm{if}\left|\Delta f>\Delta f_{\mathrm{DB}}\right|\\ 0 \mathrm{if}\left|\Delta f\le \Delta f_{\mathrm{DB}}\right|\end{array}\right.$$

(10)

Similarly, under small-signal analysis, the output power is zero when the frequency deviation is less than the deadband width, and the power response is proportional to the frequency deviation beyond the deadband. Therefore, the small signal transfer function is

$$\Delta P_{pv}(s)={\displaystyle \frac{K_1}{s+T_1}}\cdot \Delta f(s)$$

(11)

where K₁ is the gain coefficient of the photovoltaic generator unit and $T_1$ is the inertia time constant of the photovoltaic unit.

2.4. Frequency-Response Characteristic Model of Energy Storage Units

The energy storage system model assumes that the efficiency of the battery remains constant during charging and discharging and ignores the effects of battery life decay and performance changes on the frequency response. The transfer function of the energy-storage battery, as represented by a first-order inertial model, can be expressed as

$$G_E(s)={\displaystyle \frac{1}{1+s{T}_E}}$$

(12)

where $T_E$ denotes the response time constant, and $G_E(s)$ represents the transfer function of the energy-storage system.

Based on the foregoing analysis, the state-of-charge (SOC)-aware frequency-response characteristic model of the energy-storage system is constructed, as illustrated in Figure 4.

The input–output relationship of the energy-storage system is expressed by Equation (13).

$$x_b(t)=\left\{\begin{array}{l}\Delta f(t) \left|\Delta f(t)\right|>d_3\\ 0 \left|\Delta f(t)\right|\le d_3\end{array}\right.$$

(13)

where $d_3$ denotes the deadband threshold of the energy-storage unit.

3. Analysis of the Impact of the Deadband Parameter on System Frequency Stability

3.1. Deadbband Characteristic Model

Based on the multi-frequency regulation resource participation model in Figure 1 of Section 2, the deadband characteristic model of the system is analyzed from two perspectives: (1) when the frequency deviation lies within the deadband range and (2) when it lies outside the deadband range.

3.1.1. Within the Frequency Regulation Deadband Range

Primary frequency regulation of the wind, photovoltaic, and thermal generating units has not been activated. Based on the frequency response model shown in Figure 1, the system can be described by the following first-order differential equation:

$$2(1-\rho )H_s{\displaystyle \frac{d\Delta f(t)}{dt}}+(1-\rho )D_s\Delta f(t)=-\Delta P_d(t)$$

(14)

Under the initial condition of the system frequency deviation and accounting for the deadband, the expression for the system’s frequency response is given by

$$\Delta f(t)=-{\displaystyle \frac{\Delta P_d}{D_s(1-\rho )}}\left(1-e^{-{\displaystyle \frac{D_s}{2H_s}}t}\right)$$

(15)

Let $t_0$ denote the instant at which the system frequency reaches the boundary of the deadband; then,

$$t_0=-2{\displaystyle \frac{H_s}{D_s}}\ln \left[1-{\displaystyle \frac{\eta D_s(1-\rho )}{\Delta P_d}}\right]$$

(16)

where $\eta$ denotes the width of the deadband.

The rate of change of frequency at the frequency regulation deadband boundary is

$${\displaystyle \frac{\mathrm{d}\Delta f}{\mathrm{d}t}}{|}_{t=t_{0_{-}}}={\displaystyle \frac{\eta D_s(1-\rho )-\Delta P_d}{2H_s(1-\rho )}}$$

(17)

where ${\displaystyle \frac{\mathrm{d}\Delta f}{\mathrm{d}t}}{|}_{t=t_{0_{-}}}$ represents the rate of change of the system frequency at time $t_{0_{-}}$.

3.1.2. Outside the Frequency Regulation Deadband Range

The frequency response of both new energy units and thermal synchronous units to changes in system frequency provides frequency support to the grid. Using the model shown in Figure 1, the system frequency response outside the deadband can be expressed as

$$p{\displaystyle \frac{{\mathrm{d}}^2\Delta f\left(t\right)}{\mathrm{d}{t}^2}}+q{\displaystyle \frac{\mathrm{d}\Delta f\left(t\right)}{\mathrm{d}t}}+r\Delta f\left(t\right)=-{\displaystyle \frac{\Delta P_d}{1-\rho }}$$

(18)

where $p$, $q$, and $r$ assume the values specified in Equation (19).

$$\left\{\begin{array}{l}p={\displaystyle \frac{2H_s{T}_s(1-\rho )+\rho T_s{\displaystyle \sum _{i=1}^n}{k}_{Hi}}{1-\rho }}\\ q={\displaystyle \frac{(1-\rho )(2H_{s}R+T_s{D}_{s}R+F_s{T}_s)}{(1-\rho )R}}+\\ {\displaystyle \frac{\rho R\left({\displaystyle \sum _{i=1}^n}{k}_{\mathrm{H}i}+T_s{\displaystyle \sum _{i=1}^n}{k}_{\mathrm{D}i}\right)}{(1-\rho )R}}\\ r={\displaystyle \frac{(D_{s}R+1)(1-\rho )+\rho R{\displaystyle \sum _{i=1}^n}{k}_{Di}}{(1-\rho )R}}\end{array}\right.$$

(19)

Considering the initial conditions of the second-order differential equation outside the deadband, the system frequency response expression beyond the deadband can be written as

$$\Delta f\left(t\right)=C_1{\mathrm{e}}^{{\lambda }_1\left(t-t_0\right)}+C_2{\mathrm{e}}^{{\lambda }_2\left(t-t_0\right)}+\Delta f^{\ast }$$

(20)

By differentiating Equation (20) and applying the initial condition of zero frequency-change rate, the time $t_{\max }$ at which the frequency reaches its nadir is given by

$$\begin{array}{l}{t}_{\max }={\displaystyle \frac{1}{{\lambda }_1-{\lambda }_2}}\ln \left(-{\displaystyle \frac{C_2{\lambda }_2}{C_1{\lambda }_1}}\right)+t_0={\displaystyle \frac{1}{{\lambda }_1-{\lambda }_2}}\\ \ln \left(-{\displaystyle \frac{C_2{\lambda }_2}{C_1{\lambda }_1}}\right)-2{\displaystyle \frac{H_s}{D_s}}\ln \left[1-{\displaystyle \frac{\eta D_s(1-\rho )}{\Delta P_d}}\right]\end{array}$$

(21)

Maximum frequency deviation after disturbance:

$$\Delta f_{\max }=C_1{\mathrm{e}}^{{\lambda }_1(t_{\max }-t_0)}+C_2{\mathrm{e}}^{{\lambda }_2(t_{\max }-t_0)}+\Delta f^{\ast }$$

(22)

By combining Equations (21) and (22) to examine the relationship between the deadband setting and the system’s maximum frequency deviation, Ref. [17] shows that the width of the frequency regulation deadband and the system’s maximum frequency deviation can, in general, be approximated by a linear relationship, expressed as

$$\Delta f_{\max }=k\cdot \Delta f_{DB}$$

(23)

where $\Delta f_{DB}$ denotes the width of the frequency regulation deadband and k is the proportional coefficient.

With the parameters of both renewable generating units and conventional thermal units held constant, an excessively large frequency regulation deadband following a load disturbance $\Delta P_d$ increases $\Delta f_{\max }$. According to Equation (22), a larger $\Delta f_{\max }$ lengthens $t_{\max }$, delaying the frequency response of the renewable units and preventing full exploitation of their fast-response capability. In addition, the deadband affects the units’ output power, as shown in Figure 5. Where −d₁ represents the lower limit of the frequency deviation of the system, while d₁ represents the upper limit, and they constitute the width of the frequency deadband (Δf_DB).

Figure 6 presents the system’s primary frequency control dynamic response curves under two distinct deadband configurations. Deadband Scheme 1 adopts relatively wide bands—±0.10 Hz for wind power units, ±0.05 Hz for photovoltaic units, and ±0.05 Hz for the battery energy-storage station—whereas Scheme 2 employs narrower settings of ±0.04 Hz, ±0.03 Hz, and ±0.04 Hz for the respective units. Comparing the resulting frequency regulation trajectories enables a detailed investigation of how deadband width affects frequency-control performance.

• Differences in the sequencing of frequency regulation actions

According to Equation (16), the time $t_0$ at which the system frequency deviation reaches the deadband threshold is inversely logarithmically related to the deadband width $\eta$. Because Scheme 1 employs a wider deadband ($d_1>d_2$), the calculated result $t_{01}>t_{02}$ indicates that frequency regulation actions are delayed under the wide-deadband configuration. As shown in Figure 6, the activation times of the wind turbine generators ($t_3$), photovoltaic units ($t_1$), and the energy-storage system ($t_3$) in Scheme 2 all precede those in Scheme 1 ($t_2$ and $t_4$). This finding confirms that a narrow deadband triggers the response of frequency regulation resources earlier, thereby shortening the initial phase of frequency instability.

2.

Maximum frequency deviation;

Equation (22) shows that the post-disturbance maximum frequency deviation $\Delta f_{\max }$ is approximately linearly related to the deadband width, as expressed in the empirical relation (23). The wider deadband adopted in Scheme 1 postpones the release of regulating power, so the system must rely solely on the inertia of the synchronous units to counter the disturbance, leading to $\Delta f_{\max 1}>\Delta f_{\max 2}$. Moreover, Equation (22) indicates a positive correlation between the time $\Delta t_{\max }$ at which the frequency reaches its minimum and $\Delta f_{\max }$. Consistently, Figure 6 shows that the $t_{\max }$ for Scheme 1 exceeds the time at which the frequency achieves its minimum in Scheme 2, thereby further increasing the risk of frequency instability.

3.

Rate of change of frequency and associated dynamic characteristics;

Equation (17) indicates that the rate of change of frequency (ROCOF) at the deadband threshold is directly proportional to the deadband width. Because Scheme 1 adopts a wider deadband (${\eta }_1>{\eta }_2$), the magnitude of $df/dt$ in the initial stage is larger—the initial slope of the curve in Figure 6 is noticeably steeper—signifying a faster frequency decline. By contrast, Scheme 2 employs a narrow deadband that prompts an earlier release of renewable-frequency regulation power, effectively curbing the ROCOF and markedly improving dynamic stability.

4.

Synergistic effects arising from the coordination of multiple resources.

With the narrow-deadband configuration of Scheme 2, differentiated deadband widths are assigned to the individual resources (wind > storage > PV). This design exploits the rapid response capability of the PV units (±0.03 Hz) and the high-precision control of the battery-storage system (±0.04 Hz), thereby establishing a staged sequence of frequency regulation support. As shown in Figure 6, the PV units respond first at $t_1$, followed successively by the storage system and the wind turbine generators, delivering power supplements on multiple time scales. In contrast, under Scheme 1 all wind turbine generators respond concurrently at $t_4$, a pattern that readily produces power overshoot and oscillatory behavior.

In summary, the frequency regulation scheme with a narrow deadband outperforms its wide-deadband counterpart in every key metric: the initiation timing of regulating resources, the post-disturbance maximum frequency deviation, and the rate of change of frequency. These results are consistent with the theoretical derivations in Equations (16)–(22), confirming that reducing the deadband width is an effective way to enhance the frequency regulation performance of renewable resources. On this basis, and within the framework of the Chinese national standard, we propose the following deadband settings: ±0.03 Hz for wind turbine generators, ±0.02 Hz for photovoltaic units, and ±0.03 Hz for battery energy storage plants. Multi-scenario simulations will be conducted to further verify the applicability of this scheme to the East China power grid under conditions of high renewable penetration.

3.2. Performance Metrics for Assessing the Frequency Regulation Effectiveness of Deadband Configurations

The system’s primary frequency regulation characteristic curve is shown in Figure 7. To quantify the frequency regulation performance of renewable units under the deadband configuration, the following primary regulation metrics are defined:

• The absolute difference between the post-disturbance minimum system frequency and the nominal (rated) frequency is defined as the maximum frequency deviation, SSFD; that is,

$$\mathrm{SSFD}=\left|f_0-f_{nadir}\right|$$

(24)

SSFD characterizes the magnitude of the system’s frequency excursion following the initial adjustment.

2.

The time at which the system frequency reaches its post-disturbance minimum is denoted as $t_{\max }$ . A shorter $t_{\max }$ implies a greater risk of rapid frequency destabilization;

3.

The ROCOF denotes the time derivative of the system frequency in a power network and is commonly used to quantify how rapidly the frequency varies over short intervals. Its mathematical definition is:

$$\mathrm{ROCOF}={\displaystyle \frac{\mathrm{d}f}{\mathrm{d}t}}$$

(25)

The ROCOF measures how rapidly the system frequency declines or rises after a disturbance. In this section, because the deadband causes renewable units to supply frequency support at different moments, the average ROCOF is typically used for evaluation, namely,

$${\mathrm{ROCOF}}_{avg}=\mathrm{SSFD}/(t_{\max }-t_0)$$

(26)

4.

The time required for the system frequency to rise from its initial post-disturbance condition and attain a new steady-state value is defined as the settling time, $t_{ss}$. This metric captures the interval during which the power system transitions from the dynamic response stage—comprising the frequency dip and subsequent recovery—to steady-state operation;

5.

The final steady-state frequency reached after a power disturbance is denoted as $f_{ss}$. Upon completion of primary frequency regulation, the steady-state frequency generally exhibits a residual offset, but this deviation should remain within the permissible band (e.g., ±0.2 Hz).

6.

The SSFD improvement metric is defined as $\sigma$,

$$\sigma ={\displaystyle \frac{\Delta f_{SSFD}}{\Delta f_d}}$$

(27)

where $\Delta f_{SSFD}$ denotes the difference between the minimum frequencies obtained under the two deadband configurations, while $\Delta f_d$ represents the deviation between the minimum frequency under the original deadband configuration and the rated frequency.

7.

The frequency regulation contribution is defined as $\mu$,

$$\mu ={\displaystyle \frac{P_i}{P_{sum}}}$$

(28)

where $i$ denotes the type of frequency regulation resource, $P_i$ is the output power of the $i$ renewable generating unit, and $P_{sum}$ is the sum of the output powers of all renewable generating units.

4. Simulation Verification

This chapter constructs a frequency-domain simulation system in MATLAB/Simulink, which includes traditional synchronous generators, wind power generators, photovoltaic generators, and independent energy storage. The system is used to analyze the impact of renewable energy penetration on the frequency regulation stability of the system. Additionally, it compares the frequency regulation schemes under the original East China deadband configuration with those under the deadband configuration proposed in this study.

4.1. Simulation Analysis of the Impact of Renewable Energy Penetration on System Frequency Regulation Stability

As seen from the generator-load transfer function in Figure 1, an increase in the penetration rate of renewable energy generation $\rho$ will reduce the system’s equivalent inertia time constant, thereby lowering the system’s resistance to disturbances. This results in a significant increase in the rate of frequency change and exacerbates the system’s frequency instability.

In the MATLAB/Simulink environment, the renewable energy penetration rate $\rho$ is gradually increased for the system, and Bode plots under different renewable energy penetration conditions are obtained, as shown in Figure 8.

From the perspective of the system’s frequency dynamic characteristics, as the renewable energy penetration rate increases, the gain peak in the mid-frequency range of the system significantly increases, while the phase rapidly decreases. This reflects a reduction in the system’s damping characteristics and a decrease in stability margin. From the viewpoint of the system’s stability margin, both the gain margin and phase margin under high penetration conditions decrease, especially in the mid-frequency range. The reduction in phase margin indicates that the system is closer to the instability threshold, manifested by a slower frequency dynamic response and an increased likelihood of oscillations.

Under the same gradient condition for the value of $\rho$, the system’s zero-pole distribution plots are drawn for different renewable energy penetration rates. This allows observation of the pattern of system stability changes with varying penetration rates, as shown in Figure 9.

From the zero-pole distribution plot, it can be observed that as the renewable energy penetration rate increases, the system’s poles move toward the right side of the complex plane, closer to the imaginary axis, indicating a reduction in the system’s stability margin. When the penetration rate reaches 80%, the poles cross the imaginary axis and enter the right half-plane, causing the system to lose stability.

As the renewable energy penetration rate increases, the system’s inertia and damping characteristics decrease, leading to slower frequency response and intensified oscillations. To improve the frequency stability of the system under high penetration conditions, it is essential to optimize the frequency regulation control strategy for renewable energy. In addition to the control methods for the renewable energy units themselves, a reasonable setting of the frequency regulation deadband and harnessing of the frequency regulation potential of renewable energy units to provide additional inertia support for the system is a feasible strategy to enhance the system’s frequency stability.

4.2. Simulation Analysis of the Deadband Configuration Scheme

As demonstrated in Section 3, the deadband configuration materially influences frequency regulation performance. This subsection therefore conducts simulation tests on the existing East China deadband settings and on the configuration proposed in this study. The incumbent scheme—drawn from the Implementation Rules for Grid Operation in the East China Power System—specifies deadbands of ±0.10 Hz for wind power, ±0.05 Hz for photovoltaics, and ±0.05 Hz for battery storage. By contrast, the present study proposes deadbands of ±0.03 Hz for wind, ±0.02 Hz for photovoltaics, and ±0.05 Hz for storage. All other simulation parameters are given in

Table 1. Simulation parameters.

Parameter	Numerical Value	Parameter	Numerical Value
Ds	1	Kw	1.5
Hs/s	5	Ks	6.84 × 10−4
Ms/s	6.46	Ke	5 × 10−3
KG	0.05	ρ	0.3537

.

By analyzing the power generation of various types of renewable energy units in the East China Grid throughout the year across different seasons, this study compares the frequency regulation performance of two deadband configuration schemes under three typical renewable energy output scenarios: (1) In summer, wind power generation is insufficient, while other energy sources generate normally (wind power output is 40% of the full capacity, and photovoltaic generation is 75% of the full capacity). (2) In spring and autumn, photovoltaic generation is abundant, and other energy sources generate normally (wind power output is 70% of the full capacity, and photovoltaic generation is 95% of the full capacity). (3) In winter, both wind and photovoltaic generation are insufficient (both wind and photovoltaic generation are 40% of the full capacity).

4.2.1. Typical Output Scenarios for Different Types of Renewable Energy Units

Based on the generation data of renewable energy units in different seasons of the year in the East China Power Grid and after collation, the three output scenarios described in the previous section are shown in Figure 10.

Through the analysis of the renewable energy output characteristics in three typical seasons, it can be observed that the output levels of wind power and photovoltaic generation significantly affect the system’s frequency regulation requirements and the distribution strategy of frequency regulation resources. In the summer, spring/autumn, and winter scenarios, the characteristics of high photovoltaic output, balanced wind and solar output, and insufficient renewable energy output are, respectively, reflected. Subsequent simulation analyses will be based on these typical scenarios to further compare the effectiveness of the two deadband configuration schemes in improving the system’s frequency stability, thereby validating their adaptability under different seasonal renewable energy output conditions.

4.2.2. Frequency Regulation Waveforms of the System Under Two Deadband Configurations

Based on the frequency-domain response mathematical models of the four frequency regulation resources proposed in Section 2, the deadband configuration is set into two groups. The original East China deadband configuration used in the simulation runs is set as follows: wind power ±0.1 Hz, photovoltaic ±0.05 Hz, and energy storage ±0.05 Hz. In contrast, the deadband configuration proposed in this study is set as follows: wind power ±0.03 Hz, photovoltaic ±0.02 Hz, and energy storage ±0.03 Hz. The coordinated control effects of the two deadband configurations are compared under the three typical output scenarios presented in Section 4.2.1.

• Scenario 1: In summer, wind power generation is insufficient, while other energy sources generate normally.

The system is disturbed at 2 s. The frequency regulation simulation results under Scenario 1 for the two deadband configuration schemes are shown in Figure 11.

Based on the system frequency disturbance data during the frequency regulation process in the waveform, the first five indicators from Section 2.2 are selected to compare the frequency support capability during primary frequency regulation in a high-penetration renewable energy system for both the East China deadband configuration and the experimental deadband configuration. The relevant indicator data for the two deadband configuration schemes are shown in

Table 2. Metrics data under Scenario 1 for both deadband configuration options.

	SSFD	$t_{\max }$	ROCOFavg	$t_{ss}$	$f_{ss}$
Primary Frequency Regulation with Only Thermal Power Units	0.20 Hz	2.818 s	0.250 Hz/s	10.669 s	49.96 Hz
Original Scheme	0.14 Hz	2.737 s	0.187 Hz/s	6.300 s	49.97 Hz
Proposed Scheme	0.13 Hz	2.786 s	0.166 Hz/s	6.352 s	49.97 Hz

.

Based on the improvement and contribution indicators from Section 3.2, along with the output data of each frequency regulation resource from the simulation, the contribution comparison between the East China deadband configuration and the experimental deadband configuration is shown in

Table 3. Contribution of each frequency regulation resource under Scenario 1 for both deadband configurations.

Type of Energy	Original Program Contribution	Program Contribution of Proposed Method	Degree of Improvement
Thermal Power	67.70%	67.21%	5.75%
Wind Power	10.40%	10.18%
Photovoltaic	17.47%	18.02%
Energy Storage	4.44%	4.58%

.

As shown in Figure 11, Table 2 and Table 3, under the typical scenario in the East China region where wind power generation is insufficient in summer and other energy sources generate normally, the proposed scheme outperforms the original East China deadband configuration in terms of maximum frequency deviation and frequency rate of change after the system disturbance. At the same time, the proposed scheme slightly increases the frequency regulation contribution of renewable energy, enhancing the system’s ability to absorb renewable energy.

2.

Scenario 2: In spring and autumn, photovoltaic generation is abundant, while other energy sources generate normally.

The system is disturbed at 2 s. The primary frequency regulation simulation results under Scenario 2 for the two deadband configuration schemes are shown in Figure 12. The relevant indicator data for the two deadband configuration schemes are shown in

Table 4. Metrics data under Scenario 2 for both deadband configuration options.

	SSFD	$t_{\max }$	ROCOFavg	$t_{ss}$	$f_{ss}$
Primary Frequency Regulation with Only Thermal Power Units	0.20 Hz	2.818 s	0.250 Hz/s	10.669 s	49.96 Hz
Original Scheme	0.13 Hz	2.735 s	0.175 Hz/s	6.372 s	49.97 Hz
Proposed Scheme	0.12 Hz	2.805 s	0.150 Hz/s	6.432 s	49.97 Hz

. The contribution comparison between the original scheme and the proposed scheme is presented in

Table 5. Contribution of each frequency regulation resource under Scenario 2 for both deadband configurations.

Type of Energy	Original Program Contribution	Program Contribution of Proposed Method	Degree of Improvement
Thermal Power	62.12%	62.57%	6.16%
Wind Power	15.90%	14.31%
Photovoltaic	17.70%	18.62%
Energy Storage	4.28%	4.50%

.

As shown in Figure 12, Table 4 and Table 5, under the typical scenario in the East China region where photovoltaic generation is abundant in spring and autumn and other energy sources generate normally, the proposed scheme outperforms the original East China deadband configuration in terms of maximum frequency deviation and frequency rate of change after the system disturbance. At the same time, the proposed scheme also slightly increases the contribution of photovoltaic and energy storage units, enhancing the system’s ability to absorb renewable energy.

3.

Scenario 3: In winter, both photovoltaic and wind power generation are insufficient.

The system is disturbed at 2 s. The primary frequency regulation simulation results under Scenario 3 for the two deadband configuration schemes are shown in Figure 13. The contribution comparison between the original scheme and the proposed scheme is presented in

Table 6. Metrics data under Scenario 3 for both deadband configuration options.

	SSFD	$t_{\max }$	ROCOFavg	$t_{ss}$	$f_{ss}$
Primary Frequency Regulation with Only Thermal Power Units	0.20 Hz	2.818 s	0.250 Hz/s	10.669 s	49.96 Hz
Original Scheme	0.15 Hz	2.744 s	0.197 Hz/s	6.481 s	49.97 Hz
Proposed Scheme	0.14 Hz	2.796 s	0.176 Hz/s	6.538 s	49.97 Hz

.

The relevant indicator data for the two deadband configuration schemes are shown in Table 6.

As shown in Figure 13, Table 6 and

Table 7. Contribution of each frequency regulation resource under Scenario 3 for both deadband configurations.

Type of Energy	Original Program Contribution	Program Contribution of Proposed Method	Degree of Improvement
Thermal Power	70.99%	70.99%	5.16%
Wind Power	11.06%	10.50%
Photovoltaic	13.59%	14.02%
Energy Storage	4.36%	4.50%

, under the typical scenario in the East China region where both photovoltaic and wind power generation are insufficient in winter, the proposed scheme outperforms the existing East China deadband configuration in terms of maximum frequency deviation and frequency rate of change after the system disturbance. Additionally, the proposed scheme also slightly increases the contribution of photovoltaic and energy storage units, thereby enhancing the system’s ability to absorb renewable energy.

In summary, the proposed deadband configuration scheme, with wind power at ±0.03 Hz, photovoltaic units at ±0.02 Hz, and energy storage at ±0.03 Hz, performs better than the existing East China deadband configuration (with wind power at ±0.033 Hz, photovoltaic at ±0.033 Hz, and energy storage at ±0.05 Hz) in three distinct real-world scenarios: summer with insufficient wind power and normal generation from other energy sources, spring/autumn with abundant photovoltaic generation and normal generation from other energy sources, and winter with insufficient photovoltaic and wind power generation. In terms of both maximum frequency deviation (SSFD) and maximum frequency rate of change (ROCOF), the proposed scheme outperforms the existing configuration. Furthermore, under the three typical scenarios, the proposed scheme also slightly improves the contribution of renewable energy frequency regulation, enhancing the system’s ability to absorb renewable energy.

Although the numerical improvement of the simulation metrics is limited, considering the nonlinear characteristics of frequency control, the magnitude is sufficient to significantly reduce the risk of misoperation and improve the system safety margin. Meanwhile, the simultaneous improvement of the frequency recovery time and the ROCOF index indicates that the proposed scheme can suppress the frequency drop trend more quickly at the beginning of the system disturbance, which improves the initial stability of the system. In addition, the configuration enables more renewable resources to play an effective role in the disturbance, which helps to improve the diversity of regulation resources and enhance the system frequency regulation redundancy. This is also of positive significance for the construction of the frequency regulation auxiliary service market and the reduction in the regulation burden of traditional units.

4.3. BPA Simulation Analysis Based on Actual Data from the East China Grid

In this section, the proposed frequency regulation deadband configuration scheme is validated under actual system parameters by using BPA 2024 Version 4.1 simulation software. The actual technical parameters, load distribution, and frequency response requirements of wind, PV, and storage systems of the East China Power Grid are used in the simulation process to ensure the authenticity and representativeness of the simulation results. To validate the applicability of the proposed frequency regulation deadband configuration scheme in actual power grids, a regional grid model with high renewable energy penetration was constructed in the Bonneville Power Administration (BPA) power system simulation software, based on the 2024 operational data of typical regions in Zhejiang and Fujian within the East China Grid. The model includes the distribution of power generation resources, load characteristics, and historical frequency data, and uses the actual grid’s topology and load distribution characteristics. By comparing the frequency response characteristics under the two deadband configurations, the effectiveness of the proposed deadband scheme in enhancing the grid’s frequency stability is further validated.

4.3.1. BPA Simulation Model Parameter Settings

In both the ZheShan wind turbine units and MinyuYang units, the proposed deadband configuration scheme A is set as follows: wind power unit $\pm 0.03 \mathrm{Hz}$, photovoltaic unit $\pm 0.02 \mathrm{Hz}$, and energy storage station $\pm 0.03 \mathrm{Hz}$. The original deadband configuration scheme B is set as wind power unit $\pm 0.1\mathrm{Hz}$, photovoltaic unit $\pm 0.05\mathrm{Hz}$, and energy storage station $\pm 0.05 \mathrm{Hz}$.

4.3.2. Simulation Results and Analysis

In the BPA simulation, a load disturbance is applied to the system with a sudden increase over 10 s, and the system’s frequency dynamic response curves are recorded under both deadband configurations. Figure 14 and Figure 15 show the frequency waveforms for the original scheme and the proposed scheme, respectively. The relevant indicator data for the two deadband configuration schemes are presented in

Table 8. BPA simulation parameters.

ZheShan Wind Turbine Unit	Numerical Value	MinyuYang Unit	Numerical Value
Rated Voltage	0.69 kV	Rated voltage	0.4 kV
Rated Power	11.5 MW	Rated Power	0.5 MW
Number of Units	96	Number of Units	10
Time Constant	0.02 s	Time Constant	0.05 s
Active Power Proportional Coefficient	0.1	Active Power Proportional Coefficient	18
Active Power Integral Coefficient	2	Active Power Integral Coefficient	5
Inertia Proportional Coefficient	10	Inertia Proportional Coefficient	9.2

.

As shown in Figure 14 and Figure 15 and Table 8 and

Table 9. Performance indices for the ZheShan wind and MinyuYang generating units under two configuration schemes.

	ZheShan Wind SSFD	ZheShan Wind ROCOFavg	MinyuYang SSFD	MinyuYang ROCOFavg
Original Scheme	0.3430 Hz	0.0172 Hz/s	0.3689 s	0.0181 Hz
Proposed Scheme	0.3243 Hz	0.0162 Hz/s	0.3481 s	0.0171 Hz

, the proposed scheme improves SSFD by 5.76% and 5.97%, and enhances ROCOF_avg by 6.17% and 5.85%, compared to the original scheme. This is consistent with the trends observed in the MATLAB/Simulink simulation. The BPA simulation, based on data from typical regions in Zhejiang and Fujian within the East China Grid, demonstrates that the proposed deadband configuration enhances the frequency regulation potential of renewable energy units, reduces frequency deviation, and accelerates system recovery. This result complements the theoretical analysis and MATLAB/Simulink simulations, providing strong support for the practical application of the proposed scheme.

In practical engineering, although narrowing the width of the deadband of primary frequency regulation helps to improve the frequency response performance of the system, it is usually accompanied by an increase in regulation sensitivity, which leads to an increase in the regulation frequency, increased wear and tear of the equipment and energy loss, thus triggering an increase in operating costs. Under certain operating conditions, frequent regulation actions will significantly increase the marginal cost per unit of regulation energy.

In order to alleviate the economic pressure brought about by the narrowing of the deadband width and to promote a smaller deadband width in the actual system, a comprehensive evaluation and optimization of the configuration should be carried out in conjunction with the regional frequency regulation capacity, the structure of the regulating resources and the cost constraints.

5. Discussion

The simulation results show that appropriately adjusting the width of the frequency regulation deadband for renewable energy stations can effectively enhance the system’s dynamic frequency response capability and reduce the maximum amplitude of frequency deviation. Meanwhile, the proposed frequency regulation strategy significantly reduces the frequency recovery time and improves the reliability of frequency stability, thereby ensuring the efficient operation of the power grid.

Under different typical renewable energy output scenarios, the deadband configuration of the proposed scheme ensures good frequency regulation performance across varying renewable energy generation characteristics, seasonal variations, and load disturbances. The simulation results show that the proposed deadband scheme effectively allocates frequency regulation tasks among wind power, photovoltaic, and energy storage resources, successfully avoiding interference between these resources. This approach enhances the coordination of each frequency regulation resource and reduces the risk of secondary frequency drops.

Through BPA simulation of the actual power grid, the frequency regulation performance of the proposed deadband configuration scheme under high renewable energy penetration scenarios is consistent with the results from the ideal model simulations. This indicates that the scheme has practical engineering value and can provide direct reference for optimizing frequency regulation strategies in the East China Grid.

However, although reducing the deadband width can improve the sensitivity of frequency response, it may bring the following negative impacts: narrow deadband may lead to frequent response to small frequency deviations, which increases the burden of controllers and converters; long-term high-frequency operation may accelerate the wear and tear of the equipment, which increases the cost of operation and maintenance; and frequent adjustments may reduce the energy efficiency of the system, which affects the efficiency of the energy storage and wind power operation. To address these issues, we can increase the response threshold delay or set the upper limit of the response rate to avoid frequent response to small fluctuations; set the upper limit of the number of regulation times or dynamically adjust the deadband parameters at the equipment level, combining the equipment status and frequency fluctuations; and combine the auxiliary services market with the design of the regulation of the fatigue cost compensation mechanism to ensure the balance between economy and technology.

In addition, considering that the operating characteristics of the system may change significantly in different seasons or under higher permeability conditions in the future, the deadband parameter configurations proposed in this paper are still static settings, although they show good adaptability under three typical output scenarios. Moreover, in this paper, PV, wind power, and energy storage are all regarded as regulating resources that can participate in primary frequency regulation, and their response behaviors are coordinated by setting up differentiated frequency deadbands so as to bring into play the frequency regulation potentials of each type of resources. However, in the actual power system, the wind and PV outputs are strongly stochastic and are often regarded as external disturbance sources. In order to further improve the adaptability and robustness of the control strategy, an adaptive control method that dynamically adjusts the deadband parameters based on the real-time state of the system (e.g., renewable permeability, system inertia, ROCOF, etc.) can be investigated in the future to cope with the challenge of continuous changes in the participation conditions of the frequency regulation resources. This will provide new ideas for building a more flexible and efficient frequency regulation system for new energy grids.

6. Conclusions

This paper, based on the actual needs of regional power grids with high renewable energy penetration, proposes an optimized frequency regulation deadband parameter strategy for renewable energy stations and validates its advantages in unlocking the frequency regulation potential of renewable energy units through simulations. The main conclusions are as follows:

By analyzing the frequency expression of the frequency regulation deadband, the impact of deadband configuration on the system’s primary frequency regulation characteristics is quantitatively assessed. Combined with a simulation analysis of system stability considering renewable energy penetration, the importance of properly setting the frequency regulation deadband is highlighted.

It is important to note that this paper focuses on the study of primary frequency regulation response effects based on deadband configuration settings and analyzes these effects under typical renewable energy output scenarios. However, frequency regulation by wind and photovoltaic power is highly influenced by environmental conditions, and extreme scenarios of insufficient wind and photovoltaic output have not been considered in this study. This represents a direction for future research.