Inertia and Primary Frequency Response Requirement Assessment for High-Penetration Renewable Power Systems Based on Planning Perspective

Abstract

In order to ensure the sustainable development of energy, the development of new power systems with a high penetration of renewable energy has become a key research direction in the field of power systems. This paper studies the system frequency response process and key indicators from the perspective of high-penetration renewable power systems and proposes an inertia and primary frequency response requirement assessment method for power system planning under high renewable penetration. First, by analyzing the frequency dynamic response process, the key parameters affecting frequency stability are determined, and the evolution trend of system inertia with increasing renewable penetration is analyzed. Second, based on the real-system data, the inertia and primary frequency response parameters for each generator are obtained. With the planning generation mix and load as the goal, whether the synchronous generators in the target system can meet the frequency stability requirements is determined. Finally, with the system inertia demand under the maximum rate of change of frequency (RoCoF) constraint as the starting point, we iteratively increase inertia and the primary frequency response capacity until the minimum matching configuration is found. The simulation results verify the correctness of the proposed assessment method. This method considers various processes in frequency response and multiple influencing factors, providing a practical evaluation tool for the inertia and primary frequency response requirements of high-penetration renewable power systems.

1. Introduction

China proposes to realize carbon peaking by 2030 and carbon neutrality by 2060, and it is expected that the installed capacity of wind power and photovoltaic power will reach 1.2 billion kilowatts by 2030 [1]. With the increasing proportion of renewable power represented by wind and solar power generation, the high penetration of renewable power systems and power electronic devices will become the basic characteristics of future power systems, and the consequent low inertia and insufficient primary frequency response capacity will make the power system frequency instability problem prominent, which will become a key factor limiting the further increase in renewable power penetration [2,3,4].

The reduction of system inertia results in a decrease in frequency resistance to perturbations, and the RoCoF increases when perturbations occur, exacerbating the risk of distributed power off-grid and threatening the safe and stable operation of the power grid.

Aiming at the problem of frequency stability of high renewable penetration power systems, scholars in China and abroad have studied the inertia and primary frequency regulation capacity problem. In terms of inertia monitoring, study [5] indirectly shows the estimation of system-equivalent inertia by identifying system oscillation modes. Combining the correlation between system inertia and frequency fluctuation paper [6] constructs a Markov inertia assessment model based on the historical measurement data, showing real-time estimation of system inertia, and paper [7] introduces the concept of center frequency squared deviation and constructs a renewable power system inertia assessment method. Other studies [8,9] utilize data-driven technology to realize the single-point time series prediction of short-term trends of system inertia, which provides auxiliary decision-making information for the arrangement of the operation mode of the new type of electric power system in low-inertia scenarios. Paper [10] proposed a system inertia estimation method based on the proportion of renewable power output, utilizing the statistical average of the inertia of existing generating units to estimate the planning system inertia, which provides a reference for the planning system inertia assessment but does not take into account the limitation requirements of, and the cooperation between, inertia and primary frequency response. Paper [11] establishes a capacity assessment model for the minimum inertia of the system with primary frequency response by deriving the frequency response expression of the counting and FM dead zones, but the model is complex, with many parameters, and the modeling process requires more assumptions and does not take into account the limitation, and the actual effect of guiding the planning has to be verified. Paper [12] assesses the medium- and long-term inertia level trend of the power system and proposes the estimation method of renewable power penetration, which provides a good direction for the inertia assessment of the planning system and still needs to be improved for guiding the actual planning. The existing research on inertia and FM capacity estimation methods focuses on online or offline assessment under the operation perspective and only focuses on one aspect of the maximum frequency rate of change, the minimum frequency or inertia, and the FM, and there is no practical planning method that takes into account the mutual influence and cooperation. Therefore, there is an urgent need to establish inertia and primary frequency response capacity assessment tools that are considered comprehensively and are easy to practically operate under the planning perspective, which has important theoretical and practical value.

This paper proposes a method for assessing the inertia and primary frequency response demand of a high percentage of renewable penetration power systems for practical application in power system planning with comprehensive consideration and constraints, which provides, for the planners and operators, a quantitative means of assessing the frequency stability of the power system under the scenario of large-scale renewable power access in the future. First, by analyzing the dynamic process of power system frequency response and the supporting role of load, energy storage, and primary frequency response on frequency, the assessment method of the inertia of a high-proportion renewable penetration power system is proposed. Then, based on the actual power system simulation and historical statistical data, the system demand for inertia and primary frequency response capacity is evaluated under the limitation of the maximum frequency rate of change, taking the system planning installed structure and load level as the target. Finally, an arithmetic example is analyzed in the improved WSCC 9-node test system, and the influence factor of inertia is verified in real-grid data.

The method proposed in this study can provide a reference by which the actual power system planning and dispatching operators can determine the start-up mode and ensure the safe and stable operation of the power system.

• For a high percentage of renewable penetration power systems, the process of system frequency response was studied, and the maximum frequency rate of change and maximum frequency deviation during the frequency response process were analyzed;
• From the perspectives of frequency rate of change and maximum frequency deviation, an evaluation method for system inertia and primary frequency response capacity is proposed;
• This provides a practical means for the planning, construction, and operation of a high percentage of renewable penetration power systems, specifically in the assessment of inertia and the design of primary frequency response capacity.

2. Key Indicators of Frequency Stabilization of High Ratio System and Relationship with Inertia [13]

2.1. Frequency Change Process after Power Disturbance

Frequency stability refers to how well the power system after the occurrence of perturbation, can remain stable or recover to the allowable range. Figure 1 is a typical system frequency simulation curve after a power shortage (power excess can also be analyzed analogously) perturbation occurs in the system.

The curve can be divided into several typical phases, during which the methods and capabilities of the generators and the loads affecting system frequency change vary.

At the moment of disturbance occurrence at time t₀, only synchronous machine inertia, voltage source equivalent virtual inertia, and load voltage equivalent inertia come into play. At this point, the system’s inertia is at its minimum, and the rate of frequency change is at its maximum.

From t₀ to the t₁ stage, during this period, primary frequency response does not participate due to action headbands and control system delays. It primarily involves the deceleration of the synchronous generator rotor to release the kinetic energy stored in the rotor and the inertia response brought about by the release of kinetic energy from asynchronous machines on the load side.

From t₁ to t₂ stage, the primary frequency response begins to respond, working in conjunction with inertia to slow down the frequency decline and reach the minimum frequency. If the minimum frequency is above the set threshold for low-frequency load shedding, the power system protection does not participate in the response. At the lowest frequency point $f_{nadir}$, the system primarily balances power disturbances through the generator’s primary frequency response and load frequency response. Inertia mainly affects the rate of frequency change, thereby providing time to utilize the generator’s primary frequency response reserves. During the period from t₂ to t₃, the primary frequency response continues to play a role, and the synchronous generator rotor begins to accelerate, gradually increasing the system frequency. During this time, various types of power sources start to intervene in the secondary frequency response, and primary and secondary frequency responses work together.

After t₃, the primary frequency response no longer operates, and the system uses the secondary frequency response to restore the frequency to its normal operational level.

2.2. Frequency Stability Key Indicators

Key indicators for assessing the frequency stability of an electric power system under disturbances include the maximum rate of frequency change and the lowest frequency drop. During the calculation and evaluation of the maximum rate of frequency change (${RoCof}_{max}$) and the lowest frequency nadir ($f_{nadir}$), several other critical parameters are typically assessed, including system inertia, primary frequency response capacity, and load frequency response coefficient [14].

2.2.1. Frequency Nadir

The lowest frequency drop ($f_{nadir}$) refers to the minimum frequency reached by the system during the frequency drop process following a deficit in active power generation. Once the frequency reaches the set threshold for low-frequency load-shedding protection, it may trigger a widespread power outage. Therefore, considering the constraint for the $f_{nadir}$ is defined as [13] follows:

$$f_{Nadit}>f_{UFLS},$$

(1)

where $f_{UFLS}$ represents the initiation threshold for low-frequency load-shedding action. It indicates the point at which the low-frequency load-shedding protection starts to activate, i.e., when the system frequency drops below this value.

2.2.2. Rate of Change of Frequency

Rate of change of frequency $RoCoF$ refers to the rate at which the system frequency changes and is determined by the magnitude of unbalanced power and the system’s inertia. Typically, $RoCoF$ is at its maximum when a disturbance begins. Significant $RoCoF$ caused by disturbance can lead to operational issues with synchronous generator equipment and constraints on renewable power sources. Therefore, European power grids require the system to withstand a $RoCoF$ of 1 Hz/s during major disturbances, and as the penetration of renewable power sources increases, this tolerance threshold is expected to rise in the future. Additionally, the excessively high $RoCoF$ can indirectly impact the time at which the lowest frequency point occurs. As a result, $RoCoF$ will become a crucial constraint indicator for high-penetration renewable power systems, and its constraint can be expressed as [13] follows:

$${RoCoF}_{max}<{RoCOF}_{limit} ,$$

(2)

where ${RoCoF}_{max}$ represents the maximum rate of frequency change at the moment of disturbance; and ${RoCoF}_{limit}$ represents the limit value for the rate of frequency change.

2.2.3. Inertia

Inertia is a physical quantity that represents an object’s resistance to changes in its state, including changes in velocity and direction. In theory, inertia includes not only the inertia response characteristics of synchronous and asynchronous machines but also load responses. The analysis of electrical power systems primarily refers to the rotational inertia of synchronous generator rotors. Its expression is as follows [11]:

$$J=\int r^{2}dm,$$

(3)

where $r$ is the radius of rotation; $m$ is the mass of the rigid body; and $J$ is the moment of inertia in $\mathrm{kg}·{\mathrm{m}}^2$. For a synchronous generator or synchronous regulator, its moment of inertia is a constant.

For a single synchronous machine, the rotor stored kinetic energy is [11] as follows:

$$E_s=\frac{1}{2}J{\omega }^2,$$

(4)

where $\omega$ is the mechanical angular velocity. From the above formula, for the rated operating condition of the unit, the kinetic energy is determined only by the rotational inertia.

Without considering the spatial distribution of inertia, it can be approximated that the system inertia is the superposition of each source of inertia, which can be expressed by the superposition of rotational inertia or by the superposition of kinetic energy, which are basically equivalent.

The system inertia with kinetic energy can be expressed as [11] follows:

$$E_{sys}={\sum }_{i=1}^n{(E}_{Gi}{x}_{Gi})+{\sum }_{j=1}^m\left(E_{Mk}{x}_{Mk}\right)+{\sum }_{l=1}^p\left(E_{Qi}{x}_{Qi}\right),$$

(5)

where $E_{Gi}$ represents the kinetic energy of synchronous generator i; $E_{Nj}$ represents the equivalent kinetic energy of the renewable power unit; $E_{Mk}$ represents the asynchronous kinetic energy; and $E_{Qi}$ represents the kinetic energy of other facilities that can provide virtual inertia.

2.2.4. Primary Frequency Response

Once the primary frequency response initiates, the output power of the prime mover increases, reducing the imbalance power in the system. When the frequency reaches its lowest point, primary frequency response power is at its maximum. Therefore, the power of the primary frequency response varies with frequency, and its expression is as follows [12]:

$${∆P}_{PFR}={∆P}_{initial disturbance}-{∆P}_{load response}-{∆P}_{enegry storage response}-\frac{2E}{f_0}\frac{df}{dt},$$

(6)

where $\Delta P_{pfr}$ represents the primary frequency modulation power; $\Delta P_i$ represents the initial disturbance power; $\Delta P_{lr}$ indicates load response power; $\Delta P_{esr}$ represents energy storage response power; $E$ represents system inertia; $f_0$ indicates that the system frequency is generally 50 Hz; and $\frac{df}{dt}$ represents the rate of frequency change.

Therefore, it is possible to calculate the primary frequency response power based on the inertia support power provided by loads and energy storage.

2.2.5. Load Frequency Response

When an electrical power system experiences an imbalance disturbance, the frequency changes, and the energy stored in the electromagnetic field and rotor of the system’s loads (such as electric motor loads) can help suppress the frequency variations. This is known as the load frequency response effect. Neglecting the influence of voltage factors, the active power response power ${\mathrm{P}}_{\mathrm{P}\mathrm{R}}$ of the load is given by the following [7]:

$$\begin{array}{c}∆P_{PR}=P_0\left[P_1{\left(\frac{V}{V_0}\right)}^{2 }+P_2\left(\frac{V}{V_0}\right)+P_3\right]\times \left(1+△f·L_{DP}\right)\\ P_1+P_2+P_3=1\end{array}$$

(7)

In the equation, $P_0$ signifies the initial active power of the load; $P_1$ represents the proportion of constant impedance load; $P_2$ denotes the proportion of constant current load; $P_3$ stands for the proportion of constant power load; $V$ signifies the voltage at the load node; $V_0$ indicates the initial voltage; $∆f$ represents the percentage of frequency deviation; and $∆P$ signifies the percentage change in active power due to a 1% frequency variation.

2.3. Impact of Renewable Power Penetration on Inertia

Currently, grid-connected renewable power sources operate under conventional control and do not provide inertia support to the system. According to the rotor motion equation, after a disturbance, the rate of frequency change in the system is given by the following [12]:

$$\frac{df}{dt}=\frac{f_0∆P}{2E_s}=\frac{f_0∆P}{2H_s{S}_s},$$

(8)

where $H_S$ represents the inertia time constant of the system; and $S_S$ indicates the power supply installed.

During the inertia response phase, the system’s frequency is determined by both the disturbance power and the system’s inertia. With the same disturbance power, a larger system inertia results in a smaller rate of frequency change.

Under constant system-load conditions, the large-scale integration of renewable power sources can have two impacts on the system’s frequency:

In the case of significant renewable power integration, which reduces the number of conventional synchronous generators in operation, the system’s inertia decreases. As a result, under the same disturbance power, the rate of frequency change increases. The increased rate of frequency change may cause primary frequency response mechanisms to be insufficiently fast to act, leading to a lower frequency nadir and a higher risk of triggering low-frequency load shedding, thereby threatening the safety and stability of the system.

In the case of significant renewable power integration without changing the operating capacity of conventional generators, the integration is achieved by reducing the output of conventional generators.

If renewable power contributions to inertia and other sources of inertia are not considered, the system’s inertia constant can be expressed as follows [11]:

$$H_{sys}=\frac{E_s}{S_G+S_R}.$$

(9)

In the equation, $S_G$ represents the installed capacity of synchronous power sources; and ${\mathrm{S}}_{\mathrm{R}}$ represents the installed capacity of renewable power sources.

As per the above equations, it is evident that the large-scale integration of renewable power sources reduces the system’s inertia constant. However, the operating capacity of synchronous generators remains unchanged, keeping the system’s kinetic energy constant. Therefore, under the same disturbance magnitude, the rate of frequency change remains the same [15].

2.4. Voltage Characteristics of Load

In power systems, when the frequency changes, the energy stored in the electromagnetic field and rotors of system loads (such as electric motor loads) can dampen the frequency variations. This phenomenon is known as the voltage characteristics of loads [16]. During the inertia response phase, the static frequency characteristics of loads are primarily provided by electric motor loads. However, during the disturbance moment, the support power provided by asynchronous motors is minimal and has little effect on the maximum rate of frequency change. Still, it can increase the lowest frequency value and steady-state value.

The voltage characteristics of loads play a role in suppressing frequency variations by responding to changes in power, which ultimately reduces system imbalances. This responsive power is known as the load frequency control quantity [17].

2.5. Analysis of Energy Storage Equivalent Inertia Response

Energy storage, with its rapid response capabilities, can control active power charge and discharge through inverters during system imbalances. This enables the quick release or absorption of active power, reducing system imbalance power, frequency rate of change, and maximum frequency deviation. Energy storage devices can also provide inertia support for different scenarios by adjusting various parameters [18].

Common methods for energy storage participation in frequency regulation include droop control and virtual inertia control. Droop control simulates the droop characteristics of conventional synchronous machines during frequency response and is expressed as follows [12]:

$${∆P}_{Energy Storage}=-K_c∆f,$$

(10)

where ${∆P}_{Energy Storage}$ represents the active power charge and discharge of energy storage; and $K_c$ is the energy storage droop coefficient.

“Virtual Inertia Control of Energy Storage” is similar to inertia control of renewable power current sources and participates in frequency regulation by simulating the inertia response of synchronous machines. Its expression is as follows [12]:

$$∆P_{Energy Storage}={-K}_E\frac{df}{dt},$$

(11)

where $K_E$ represents the coefficient of virtual inertia for energy storage.

3. Evaluation Method Based on Planning System for Inertia and Primary Frequency Response

3.1. Evaluation Approach

Inertia and primary frequency response are the key determinants of system frequency stability. Frequency, as a vital global metric in the power system, significantly impacts the safe and stable operation of the entire system [19]. This importance becomes even more pronounced during the rapid expansion of renewable power sources. There is a critical need for a baseline approach to frequency stability, requiring precise evaluation of the inertia and primary frequency response requirements in a specific planning scenario, along with their potential ranges. This assessment provides planning and operational decision-makers with the necessary tools and methods with which to comprehensively understand the frequency stability characteristics of the system in future planning scenarios.

In a planning perspective, where actual operational data and equipment parameters are unavailable, it is impossible to measure the system’s inertia and primary frequency response through real-world measurements or frequency event calculations. Instead, the study relies on existing unit data to estimate the inertia of the target system. It is important to note that the stability characteristics after a disturbance result from the collaborative effects of both inertia and primary frequency response. Thus, independently calculating the minimum inertia or primary frequency response is not sufficiently accurate. Consequently, the estimation of inertia and primary frequency response must be interrelated and mutually coordinated [20].

This paper starts with the minimum required inertia as dictated by $RoCo{f}_{max}$ constraints, along with the corresponding primary frequency response of synchronous units. Using existing unit data, it estimates the inertia of the target system and determines the primary frequency response parameters in accordance with relevant standards. The primary frequency response scale of the target system is then estimated. Simulation results are combined to alliteratively adjust the inertia and primary frequency response capacities until a mutually suitable minimum configuration capacity is identified.

3.2. Evaluation Method

First, at different stages of power disturbance, inertia and primary frequency response play different roles. At the initial moment of disturbance, when the frequency deviation is at its maximum, only inertia participates in primary frequency response. In the same system and under the same disturbance conditions, the required system inertia is a constant value. This value can be accurately calculated under this constraint condition [13]:

$$H_{min}\ge H_{min}^{{RoCoF}_{max}} ,$$

(12)

where $H_{\min }$ is the minimum inertia requirement of the system; and $H_{\min }^{RoCoF}$ is the minimum inertia of the system constrained by the rate of frequency change.

Hence, it is appropriate to start by estimating the minimum system inertia upwards from the point defined as $H_{min}^{RoCo{F}_{max}}$. Second, after primary frequency response, inertia and primary frequency response jointly maintain system frequency stability until it reaches the minimum frequency $f_{nadir}$. During this process, rotor kinetic energy and primary frequency response both undergo nonlinear changes and mutually influence each other. The relevant parameters and variables are complex, making it challenging to directly solve for inertia and primary frequency response capacity at this stage [21]. It is worth noting that the theoretical methods and standards for virtual inertia provided by wind and solar power sources are still being researched and perfected [13], with limited practical applications. Although China’s “Guidelines for Power System Safety and Stability” outline principles for inertia provision by renewable power sources, it remains to be verified through engineering practices whether virtual inertia provided by wind and solar sources can support frequency stability under significant power shortages. On the other hand, primary frequency response, as a mature frequency control method, already has well-defined standards. «Technical Specification for Coordination of Power Systems and Sources of DL_T_1870-2018» specifies clear requirements for the primary frequency response capability of wind and solar power plants, and the ability to provide primary frequency response has become a prerequisite for grid connection [22]. Therefore, in the process of estimating system inertia and primary frequency response capacity, priority should be given to satisfying the minimum frequency limit requirement by increasing primary frequency response capacity while meeting $f_{nadir}$.

To address the issue of uncertain planning parameters, the rotational inertia of target network synchronous units can be calculated using the existing unit rotor kinetic energy. The inertia of synchronous units in the planning system can be represented as follows [12]:

$$\left\{\begin{array}{c}{E}_{sys-av}=E_{sys}/S_{sys-G}\\ E_{sys-p}=E_{sys-av}/S_{sys-p}\end{array}\right.,$$

(13)

where $E_{sys}$ represents the total kinetic energy of synchronous units in the current system; $S_{G-sys}$ represents the installed capacity of synchronous units in the current system; and $E_{sys-av}$ represents the average kinetic energy of synchronous units per unit installed capacity, considering statistical significance.

For the total kinetic energy of synchronous units in the target system, it is represented as $E_{sys-p}$, and $S_{sys-p}$ represents the installed capacity of synchronous units in the target system.

The primary frequency response capabilities of various power sources are calculated according to the standards specified in [22], which include parameters such as speed deviation, frequency control bandeau, response time, stability time, compensation amplitude, etc. The regulation capacity is as follows [11]:

$$\left\{\begin{array}{c}∆P_{f-p}=K∆f{S}_p\\ ∆P_{max}=S_{p}L\%\\ K=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left(\delta n_0\right)$}\right.100\%\end{array}\right.,$$

(14)

where $∆P_{f-p}$ represents the one-time frequency regulation capability per unit installed capacity of synchronous generators or wind and solar power sources. It is measured in $\mathrm{M}\mathrm{W}/\mathrm{r}/\mathrm{m}\mathrm{i}\mathrm{n}$ units. $\mathrm{K}$ stands for the frequency regulation coefficient; $\delta$ is the speed deviation rate; ${\mathrm{n}}_0$ represents the rated rotor speed; $S_p$ denotes the capacity of a specific type of power source in the target planning system, measured in $\mathrm{M}\mathrm{W}$ units; $∆P_{max}$ represents the depth of adjustment in $\mathrm{M}\mathrm{W}$ units; and $\mathrm{L}\mathrm{\%}$ represents the compensation amplitude [23].

It is important to note that during the estimation process, system inertia is based on the inertia provided by synchronous generators, without considering load-side responses. Therefore, the calculation results have some margin. The one-time frequency regulation capacity starts with inertia corresponding to synchronous generators, and if it is insufficient, it can be supplemented using the one-time frequency regulation capability of wind and solar power sources. Similarly, in the actual estimation process, if synchronous generators in the target system cannot meet the inertia requirements, the use of virtual inertia may be considered as a supplement [24]. The evaluation framework is illustrated in the diagram below.

In Figure 2, SPS represents synchronous power system, Pmax represents the maximum power disturbance, and PFR represents the primary frequency response.

3.3. System Minimum Inertia Requirement and Measures for Inadequate Inertia

The minimum inertia requirement of a system is constrained by the stability of the system’s frequency following a disturbance. When the governor control is not involved in frequency regulation, the minimum inertia assessment can be based on the constraint of the maximum rate of frequency change rather than the maximum frequency deviation [25].

3.3.1. System Minimum Inertia Requirement

The system’s minimum inertia requirement should satisfy constraints imposed by both the maximum rate of frequency change and the maximum frequency deviation. First, we calculate the minimum inertia requirement separately under these two constraints. Then, we take the larger of the two minimum inertia values obtained under these constraint conditions as the system’s minimum inertia requirement [26].

3.3.2. Measures for Inadequate Inertia

If the system lacks adequate inertia, certain measures can be taken in planning and operation to meet the inertia requirement. Primarily, increasing the system’s inertia is crucial and can be achieved through the following methods:

• For synchronous machine inertia, consider the commissioning of synchronous condensers, reducing the output of conventional generators, or retrofitting retired thermal power plants into synchronous condensers to maintain the system’s synchronous inertia. Additionally, increasing virtual inertia is an option, which involves improving control strategies for renewable power sources such as wind and solar, introducing energy storage systems to provide virtual inertia support, or employing grid-forming control strategies [27].
• Enhancing primary frequency response capacity can be achieved by reducing the droop coefficient and shortening the response time. For conventional generators, improvements in primary frequency response can be made. For renewable power sources, enhancing primary frequency response can be accomplished through outer-loop control strategies, adjusting operating points, or incorporating energy storage systems. In terms of the virtual inertia provided by new energy sources, there are mainly voltage source type and current source type. Current-source-type virtual inertia design is simple, but there is a short delay (about 100 ms); while voltage-source-type virtual inertia can provide no inertia support delay, but the design is complex, and the investment cost is high. In terms of the virtual inertia energy source, it can come from the rotating kinetic energy of the fan or various forms of stationary energy storage. Due to the uncertainty of fan operation, the rotational kinetic energy alone cannot provide stable inertia support, but the virtual inertia achieved by energy storage can significantly increase the equivalent inertia level of the system [28].
• Reducing disturbance power can lower the maximum frequency deviation, thereby reducing the system’s minimum inertia requirement. As mentioned earlier, both load frequency response characteristics and energy storage response can offset some of the imbalance power following a disturbance [29].

4. Validation of Inertia Assessment with Case Study

The improved WSCC3 9-node small system was used to simulate and verify a planning system. The system topology diagram, as shown in Figure 3, shows that the installed capacity of synchronous generator G1 is 600 MW; the installed capacity of wind farm station G2 and G3 is 200 MW, with a total load of 480 MW; and the installed capacity of photovoltaic station G4 is 200 MW. The disturbance is the active power output loss of 50 MW or 80 WM due to synchronous machine tripping or partial off-grid loss of the new energy station.

Considering the WSCC9 bus system is suitable for theoretical analysis and simulation verification of small systems, it can more accurately simulate the change of system frequency after the power gap occurs when fans with different new energy permeability and different capacity participate in frequency modulation.

The installed machines and loads are shown in

Table 1. Installed capacity and load. Unit: MW.

Synchronous Generator	Wind Power	Wind Turbine Capacity	Photovoltaic	Load	Fault Loss Power
600	400	1.5	200	480	50/80

.

Among them, the synchronous generators have a minimum technical output of 30%, and the load is modeled as constant impedance.

4.1. The Required Minimum Inertia for $RoCo{f}_{max}$

For the $RoCo{f}_{max}$ system limited to 0.5 Hz/s with a maximum power deficit of 50 MW, the minimum inertia required is 2400 MW·s. Based on the average inertia constant of synchronous generators in the reference system, which is 6 s, the minimum online capacity for synchronous generators is 400 MW. Assuming a rotor speed deviation rate $\mathsf{\delta }$ of 4.5%, the corresponding primary frequency response capacity for synchronous generators at their minimum online capacity is 2.963 MW/r/min.

Similarly, for a maximum power deficit of 80 MW, the required minimum inertia for a system constrained by $RoCo{f}_{max}$ is 3600 MW·s. In this case, the minimum online capacity for synchronous generators is 600 MW, and the corresponding primary frequency response capacity for synchronous generators at their minimum online capacity is 4.444 MW/r/min.

4.2. Primary Frequency Response Parameter Settings

In accordance with the requirements outlined in reference [22], the primary frequency response parameters for synchronous generators and renewable power sources are in

Table 2. Generator primary frequency response parameter settings.

Generator Type	Deadband	Speed Deviation Rate	Lag Time	Amplitude Limiting
Synchronous Generator	±0.033 Hz	4.5%	3 s	8%
Renewable Power	±0.05 Hz	3%	3 s	10%

as follows.

4.3. Minimum Inertia and Primary Frequency Response Requirements

In the case of a maximum power deficit of 50 MW and with constraint $RoCo{f}_{max}$, the inertia and corresponding primary frequency response of synchronous units are used as a starting point. Synchronous units are initially started at 400 MW with a minimum technical output of 30%. Simulations are conducted for different levels of renewable power penetration, and the system’s minimum frequency requirement is 49.5 Hz. The relationship between synchronous units and renewable power penetration is shown in

Table 3. The penetration rate of synchronous generator and the renewable power (synchronous generators start at 400 MW). Unit: MW.

Synchronous Generator Output	Output Ratio	Renewable Power Output	Output Ratio
384	80%	96	20%
336	70%	144	30%
288	60%	192	40%
240	50%	240	50%
192	40%	288	60%
144	30%	336	70%
120	25%	360	75%

. The simulation results are shown in Figure 4.

In the case of a system power loss of 50 MW, where the lost active power accounts for 10.4% of the system load, the lowest frequency does not show significant changes and remains around 49.79 Hz as the penetration rate of renewable power increases. Due to the relatively small power loss, the rotational inertia and primary frequency response capability provided by synchronous generators are sufficient to meet the requirements for system frequency stability. The system’s frequency stability is determined by the inertia required, which corresponds to a minimum rotor kinetic energy of 2400 MW·s and a one-time frequency control capability of 2.963 MW/r/min. Additionally, the simulation results indicate that with the continuous increase in the penetration rate of renewable power, the ability to respond to power disturbances does not decrease.

In the case of a system power loss of 80 MW, where the lost active power accounts for 16.7% of the system load, and the system is constrained, and the minimum required inertia is 3600 MW·s. With the synchronous generator operating at a minimum output of 180 MW and simulating under the conditions of a maximum wind power penetration rate of 62%, the frequency drops to a minimum of 45.48 Hz, which is lower than the limit. To mitigate this, wind power one-time frequency control capability is incrementally increased with a step size of 1.5 MW of wind power capacity, as shown in Figure 5.

From the simulation results, it can be observed that in the scenario with a power loss of 80 MW, system frequency stability is determined by both the inertia and primary frequency response capability required. This corresponds to a minimum rotor kinetic energy of 3600 MW·s, a minimum primary frequency response capability of 4.44 MW/r/min for synchronous generators, and a minimum primary frequency response capability of 0.083 MW/r/min for wind turbine units.

5. Verification of Measures for Insufficient Inertia

Taking a provincial power grid in China as an example, the system inertia under different working conditions is calculated by adjusting the output of new energy, shutting down the conventional unit, or reducing the operating power point of the conventional unit when the overall load is unchanged.

In the case verification, the simulation analysis was carried out using the 2.8 version PSD-BPA electromagnetic transient software of the China Institute of Electrical Science and Technology to verify the frequency change of the system subjected to the same disturbance after new energy access, and the influence of energy storage access on the frequency.

The simulation method is to change the proportion of new energy output to the total output and adopt different modes of new energy acceptance under the same proportion of new energy output. The simulation is subjected to the change of system frequency under the same power disturbance.

5.1. Construction of Different Scenario Models

The initial parameters are sourced from summer data related to renewable power generation within a provincial-level power grid in China, as obtained from BPA. We maintain system load and total active power output as constants while increasing the proportion of renewable power generation. This is achieved through strategic actions such as the shutdown of conventional power generation units or the reduction of their operating power points to accommodate a higher penetration of renewable power sources. The original data featured a 35% share of renewable power, which was subsequently increased to 45%. The total generating capacity of the units remains at approximately 34,400 MW, while the local load is kept at around 28,200 MW. The system’s total kinetic energy is calculated based on the provided BPA data.

Given that renewable power units currently operate under conventional control and that the concept of virtual inertia is still under research, the simulations do not consider virtual inertia from renewable power sources. Instead, actual system inertia is calculated based solely on the inertia of synchronous units. The following

Table 4. Grid operation modes.

Number	Renewable Power System (RPS) Ratio (%)	Adaptation of RPS	RPS Output (MW)	General Generator Output (MW)	Total Kinetic Energy (MW·s)
1	35	/	12,100	22,300	185,000
2	45	Reduce the output of general generator	15,400	19,000	185,000
3	45	Shut down general generator	18,900	15,500	153,000
4	55	Shut down general generations; smaller inertia time constants	22,200	12,200	141,000
5	55	Shut down general generations; bigger inertia time constants	22,200	12,200	130,000

provides an objective presentation of the results for power output and system inertia under different scenarios.

5.2. Simulation Validation

In the five operating scenarios mentioned above, this study conducted simulation analyses to investigate the effects of massive disconnection or output fluctuations in renewable penetration power systems. It disregarded differences in primary frequency response (one-time frequency regulation) resulting from variations in renewable energy proportions. Instead, it aimed to analyze the impact of different approaches to renewable power system integration and the percentage of renewable power on system inertia.

5.2.1. Impact of Renewable Power System Integration Approach on System Inertia

Taking methods 1, 2, and 3 as examples, the case imposed a 5000 MW disturbance on the system, and the resulting system frequencies are shown in Figure 6. By comparing the frequency responses under different integration approaches, it is observed that when the penetration of renewable penetration power systems increased from 35% to 45%, Method 2, which involved reducing the operating power of conventional units to accommodate renewable power, exhibited consistent frequency change rates and maximum frequency deviations. In contrast, Method 3, where conventional units were shut down to incorporate renewable power, showed increased frequency change rates and maximum frequency deviations when subjected to the same disturbance.

This analysis indicates that as the penetration of renewable penetration power systems increases, if this integration is achieved by reducing the operating points of conventional units while keeping their startup scale unaffected, the system’s inertia remains unchanged. When subjected to disturbances of the same magnitude, the system’s maximum frequency change rate and maximum frequency deviation remain unchanged. However, if the integration involves reducing the startup capacity of synchronous units, the system’s inertia decreases. Consequently, when exposed to disturbances of the same magnitude, the system’s maximum frequency change rate and maximum frequency deviation increase.

5.2.2. Impact of Inertia Time Constants on System Inertia

Building upon the foundation of Method 1, which increased the share of renewable power, we conducted two additional scenarios: Method 4, where the renewable power proportion was raised to 55%, prioritizing the shutdown of general generators with smaller inertia time constants; and Method 5, where the renewable power proportion was again increased to 55%, but general generators with larger inertia time constants were shut down first. In these scenarios, a 5000 MW disturbance was applied to the system, and the system frequencies are illustrated in Figure 7.

Comparing methods 4 and 5 under the same renewable power penetration rate, it observed that Method 5 exhibited greater frequency change rates and maximum frequency deviations when subjected to disturbances of the same magnitude; in fact, the lowest frequency dropped below 49.5 Hz.

This analysis suggests that when renewable power penetration rates are equal, generators with larger inertia time constants provide greater system inertia and better support for frequency stability during disturbances.

5.2.3. The Impact of Energy Storage on Disturbance Power

Building upon Method 5, a 500 MW energy storage system was added to the system. When a disturbance of 5000 MW was applied to the system, the system frequency response is as shown in Figure 8. Comparing the frequency changes with and without energy storage, it is evident that without energy storage, there is a greater frequency change rate and a larger maximum frequency deviation when the same disturbance occurs. The steady-state frequency is also lower without energy storage.

Therefore, energy storage, with its rapid response capability, provides active power to the system in the initial stages of a disturbance. It reduces the system’s imbalance power, decreases the maximum frequency change rate, and minimizes the maximum frequency deviation, thereby supporting the safe and stable operation of the system [30].

6. Verification of Actual Power Grid Application

The inertia evaluation method proposed in this article has been applied in the planning analysis of a provincial power grid in China, evaluating the trend of inertia level changes in the future planning system of the power grid. The data sources are the planning thematic data of the provincial power grid and the typical operation mode data of BPA.

6.1. Introduction of Example System

The provincial power grid is asynchronously connected to the main grid through multiple DC circuits, with a DC transmission capacity of 41.6 million kilowatts. The main power source of the grid is hydropower. The installed capacity and grid load level of various types of power sources in the planning year are shown in

Table 5. Grid planning data.

Time	Installed Scale of Hydropower and Thermal Power/MW	Renewable Energy Installation Scale/MW	Minimum Load/MW	Maximum Load/MW
2023	90,800	38,600	22,000	44,000
2024	95,400	61,000	25,000	51,000
2025	96,500	78,100	27,000	54,000

. The installed capacity of conventional units participating in primary frequency regulation is 16,000 MW, and the equivalent capacity and inertia of conventional units after aggregation are shown in

Table 6. Equivalent parameters.

Power Source	Number	Equivalent Capacity/MW	Equivalent Inertia Constant/s
Thermal power	1	230	3.9
	2	358	4.2
	3	666	4.3
Hydropower	4	15	3.0
	5	65	3.9
	6	90	4.2
	7	127	3.0
	8	200	4.3
	9	278	2.6
	10	395	4.4
	11	444	4.8
	12	527	4.8
	13	667	4.1
	14	722	5.1
	15	778	4.4
	16	855	4.7
	17	944	5.3

.

6.2. Inertia Evaluation

There is a seasonal complementary characteristic between various types of power sources in the provincial power grid, which means that the output of hydroelectric units is relatively high during high water periods and relatively low during low water periods. New energy accounts for a relatively low proportion of output during high water periods and a relatively high proportion during low water periods. So, the inertia level of the system in the high water period of the power grid is relatively high, while the inertia level in the low water period is relatively low [31].

According to the inertia evaluation method described in Section 2, the system inertia levels of the power grid under different operating modes from 2023 to 2025 are obtained. Under the high-load operation mode, the inertia of the system is greater than that of low-load level scenarios because under a certain output of new energy, the higher the system load, the larger the startup scale of conventional units and the higher the inertia level of the system. For example, the maximum difference in the minimum inertia level of the system during the high/low-load level during the 2025 flood season can reach 136,000 MW·s. In the low-load mode during the dry season, the system inertia level is the lowest. In 2025, the minimum inertia demand of the system in the low-load mode during the dry season is as low as 86,000 MW·s, which is about 116,000 MW·s lower than that in the high-load mode during the wet season. Due to the low external power transmission during the dry season, the scale of synchronous power supply in the system is reduced, and the proportion of new energy output is relatively high. At the same time, the low internal load in the system significantly reduces the system inertia level. Between 2023 and 2025, the installed capacity of new energy in the planning system will significantly increase, and the level of inertia in the system will show a downward trend. For example, the minimum inertia of the system has decreased from 236,000 MW·s to 200,000 MW·s in the low-load mode during the high water period (84.7% of the corresponding mode in 2023) and from 124,900 MW·s to 86,000 MW·s in the low-load mode during the low water period (68.8% of the corresponding mode in 2023). Therefore, the power grid planning and scheduling department should focus on the system inertia level under the low-load operation mode during the dry season and take measures in advance to prevent the system from threatening frequency stability characteristics due to an insufficient inertia level under the low-load operation mode with a high proportion of new energy [32].

7. Conclusions

This study focused on high-penetration renewable power systems and investigated the process and key indicators of system frequency response. It explored the relationship between system inertia and primary frequency response capacity within characteristic planned power systems. Additionally, it examined the evolution of system inertia as renewable power penetration increased and analyzed the load and energy storage response characteristics. The study proposed methods for estimating minimum inertia and primary frequency response capacity.

The main conclusions are as follows:

• By analyzing the frequency response curve of power systems under dynamic conditions, key indicators and requirements for frequency stability in high-penetration renewable power systems were identified.
• As renewable power penetration increased in the system, it was found that with the same synchronous generator capacity, the equivalent inertia constant of the system decreased gradually. However, this decrease had a limited impact on system frequency stability because the rotational kinetic energy of synchronous generators did not change significantly. As renewable power penetration continued to increase and synchronous generators were gradually retired, the system’s frequency stability deteriorated rapidly.
• In the context of high-penetration renewable power systems, both system inertia and primary frequency response capacity play crucial roles in determining frequency stability. The inertia response of loads and energy storage systems could compensate for some of the imbalances in power, supporting frequency stability.
• Under a given power disturbance, the minimum inertia required to meet the maximum rate-of-change of frequency limit can be directly calculated.

The virtual inertia provided by new energy can significantly increase the level of system inertia, and its rapid frequency modulation can reduce the need for minimum inertia of the system. However, the frequency control of new energy, considering the inertia demand of large systems and its coordination with conventional units, need further research. Therefore, there are corresponding limitations in the inertia evaluation of power systems with a high proportion of new energy.

The conclusion of this study should help planning and operation personnel to gain a deeper understanding of the characteristics of high-penetration renewable energy power systems. This promotes the safe and stable operation of high-penetration renewable energy and contributes to the healthy development of renewable energy, promoting green and sustainable development.