The accelerating integration of renewable energy sources (RESs) into power grids poses a significant challenge to system inertia, primarily due to a reduced dependence on conventional synchronous generators (SGs). This transition profoundly affects frequency stability, rendering grids more susceptible to disturbances. This review offers an in-depth examination of contemporary and emerging strategies to bolster grid inertia, with a focus on virtual synchronous machines (VSMs), advanced energy storage systems, and the transformative potential of artificial intelligence (AI) in optimizing inertia emulation. Unlike prior reviews that primarily catalog existing approaches, this work distinguishes itself by presenting a comparative analysis of various VSM topologies tailored to distinct RES integration contexts, supplemented by real-world case studies and a comprehensive SWOT analysis of AI-driven inertia solutions. The results provide practical insights and guidance for both researchers and industry professionals, underscoring the importance of these adaptive strategies in fostering resilient, sustainable power systems essential for the energy transition.

1. Introduction

Power system stability depends on balancing generation and demand, with grid frequency as an indicator of this balance [1]. The grid frequency is typically maintained at 50 Hz (or 60 Hz in some countries) to ensure stability. A decrease in frequency indicates that demand exceeds generation, and vice versa [2] (see Figure 1). In traditional power grids, frequency stability is maintained by synchronous generators (SGs) and ancillary protection systems [3].

Details are in the caption following the image — **Figure 1**
Open in figure viewer PowerPoint

Fundamental principle of frequency control in power systems.

The net-zero carbon politics drives many countries to the utilization of decarbonized and decentralized systems [4]. However, the high injection of renewable energy sources (RESs) causes a major perturbation in grid frequency and increases the rate of change of frequency (RoCoF) and frequency deviation [5]. The speed of frequency changing after an unexpected imbalance between load and generation is called the RoCoF [6]. The RoCoF is measured in Hz/s and its main job is detecting islanding and disconnection of generation units. After the high penetration of RESs, the majority of countries were obliged to change their RoCoF relay standard [7, 8]. For example, Denmark changed the RoCoF relay standard from 0.75 Hz/s to 2.5 Hz/s [8] (see Table 1).

Table 1. Rate of change of frequency (RoCoF) standards across selected European countries [8].

Country	RoCoF previous standard (Hz/s)	RoCoF updated standard (Hz/s)
Great Britain	0.2	0.5
Ireland	0.5	1
South Africa	0.5	1.5
Spain	0.4	2
Finland	0.75	2
Denmark	0.75	2.5

Some reviews have been made about inertia emulation and enhancement. In [9], the authors discussed some VSM topologies. They also compared two topologies (virtual synchronous machine zero inertia (VSM0H) and universal VSM) and tried to distinguish the performances of each technique. In [10], some inertia emulation techniques were reviewed. The authors in [10] focused more on the methods of enhancement of wind turbine’s (WT’s) inertia. Ratnam, Palanisamy, and Yang [11] have tried to summarize some inertia enhancement techniques and covered some old and new methods for inertia emulation. In [12], the authors examined the integration of renewable energy (RE) in sustainable development, its environmental impact, recent trends, and technical and operational challenges including frequency stability and power quality. Various sources of inertia and their corresponding control strategies have been comprehensively examined in [13]. Additionally, a modified interval-based optimal generation mix formulation has been proposed in [14] to ensure adequate inertial response and power frequency stability while supporting the expansion of RES.

Previous studies have reviewed various inertia emulation techniques and their applications in low-inertia systems. However, while these studies cover essential aspects of grid inertia, they often lack a forward-looking perspective on artificial intelligence (AI) as a potential solution for enhancing inertia emulation. Table 2 presents a comparative overview of similar studies in the field of grid inertia with high-RES integration. It highlights their primary focus, the techniques they emphasize, the specific challenges they address, and the unique contributions of each. This table underscores the unique contributions of our review, particularly its exploration of AI-driven solutions, practical case studies, and a SWOT analysis on AI-based inertia solutions.

Table 2. Comparative overview of similar studies in the field of grid inertia with high-RES integration.

Study	Focus areas	Inertia emulation techniques	Challenges addressed	Unique contributions
Ratnam, Palanisamy, and Yang (2020) [11]	Inertia enhancement in low-inertia power systems	VSM topologies, synchronous condensers	Frequency stability with high RES	Comparison of conventional versus advanced VSM topologies
Muftau and Fazeli (2022) [9]	VSM implementation in modern grids	Virtual synchronous machines, energy storage	Grid stability and transition to RES	Analysis of VSM effectiveness across different RES integration levels
This study	Comprehensive review of inertia with high-RES integration	AI-enhanced VSMs, ESSs, wind turbines, condensers	Frequency stability, cost, operational feasibility	Forward-looking AI role, practical applications, SWOT on AI, unique case studies

This review not only synthesizes current inertia enhancement methods but also explores the transformative potential of AI in addressing grid stability. By focusing on practical applications and a SWOT analysis, our study provides a holistic perspective that aims to guide future research and industry efforts in achieving resilient and sustainable power grids.

This article thoroughly examines techniques for enhancing inertia, discussing potential challenges associated with each method and highlighting technical issues related to integrating virtual inertia into the power grid. The article also investigates futuristic solutions that incorporate AI to predict and optimize VSM’s inertia emulation. Figure 2 includes a flowchart detailing the process for conducting this study.

The paper is organized as follows. Section 2 explores inertia in the conventional power grid. Section 3 presents techniques to enhance inertia. Section 4 investigates and discusses various control topologies for VSMs. Section 5 highlights the technical challenges and issues related to enhancing inertia. Section 6 proposes the use of AI as a solution to predict and regulate power system frequency perturbations. In Section 7, a series of case studies are presented, along with their respective applications. Lastly, Section 8 provides a conclusion.

2. Inertia in Conventional Power Grid

SGs are the most utilized in the traditional power system generation for all types of conventional sources such as coal, natural gas, nuclear, and hydroelectric [15, 16]. Frequency stability is achieved through the rotating mass of the SG [17, 18]. In frequency events or power imbalance (load/generation variations), the rotational speed will be adapted by inertia and controller actions [19]. In this way, the synchronism is maintained and the grid is protected from big stability issues and blackouts.

Grid inertia is maintained by the kinetic energy produced or absorbed by the rotor’s mass, as shown in the following equation [10].

()

where E_kin represents the kinetic energy, ω_r the rated velocity of the rotor, and J the moment of inertia.

However, the penetration of RESs reduces the inertia in the power grid. SGs could assure inertia and grid stability only if the penetration of RESs is less than its capacity in the power system [20]. So, more the penetration of RESs increases, more the inertia of the system decreases. In future power systems, the integration of RESs is going to be significantly greater, so the RoCoF and frequency deviation will increase too [21]. Figure 3 presents an example of the drop of the equivalent inertia constant H_eq in some European countries due to the integration of RESs.

The equivalent inertia constant H_eq is the power system’s global inertia. Figure 3 proves that the injection of more RESs in power systems decreases the impact of SGs on maintaining the inertia at its higher levels.

3. Techniques to Enhance the Inertia

To maintain power system stability under high-RES penetration, grid inertia must be increased. In this section, some new and old techniques to enhance and emulate inertia will be presented.

3.1. Synchronous Condensers (SCs)

SCs are free-spinning SGs that are connected to the grid [23]. The main goal of these SCs is to regulate the voltage by absorbing or injecting the reactive power [24]. Generally, all SGs without loads are considered as SC [25]. SC can enhance the inertia of the grid power system due to its rotating mass (the rotor) [26] (see Figure 4).

The following equations describe the principle of this technique:

()

where J denoted the moment of inertia, f_nom the nominal frequency, H_gen the inertia constant of the generator, H_sys the inertia constant of the system (global inertia), S_gen the rated power of the SG, S_sys the rated power of all the system, and E_gen the kinetic energy of the SG.

It can be derived from these equations that the system inertia constant can be increased by increasing the individual inertia of each generator composing the system.

This method is among the simplest and most efficient ways to enhance inertia, improving RoCoF and frequency nadir [28]. However, there are some major drawbacks:

•
High operational cost: Generally, SG uses gas, coal, oil, or even nuclear reactions. So, the cost of these resources is high, and the majority of the time these SGs run without loads, which does not make this method cost-effective [19].
•
The installation cost: Installing an SG power station only to regulate the inertia is not a powerful solution [19] (economical point of view).
•
The utilization of fossil fuels: The first objective of using RESs is to reduce CO₂ emissions [29]. So, using this technique will not help the case.

SCs contribute to grid stability through natural inertia, making them reliable for sustained support. Yet, their dependence on traditional energy sources and high operational costs poses challenges for high-RES grids aiming for sustainability. Despite these limitations, SCs remain effective in stabilizing grids with high renewable penetration.

3.2. WTs

As a RES, wind is the most promising power. It is available day and night throughout the year. WTs are one of the most powerful RESs. Wind generation systems are spreading rapidly (through the different levels of the power grid), especially double-fed induction generators (DFIGs). For the inertia emulation, WTs make a huge contribution which makes wind energy more attractive [30, 31]. WTs could increase the inertia of power systems with their dominating topologies such as DFIG, fixed speed induction generator (FSIG), and permanent magnetic synchronous generator (PMSG) [32, 33].

DFIG is connected directly to the grid by the stator which gives it a powerful inertia. The rotor is connected to the power network through a back-to-back converter (grid side and generation side) to regulate the DC-link voltage and the reactive power (grid side) and to control the active power, rotor speed, and also sometimes the reactive power (generation side) [34, 35]. PMSG is connected by its stator through a back-to-back converter. PMSG is characterized by its simplified gearbox, speed, and power controllability [36]. FSIG is directly connected to the grid by its stator which gives it a strong inertia [37]. Different control systems are added to enhance the inertia of WTs, i.e., blade pitch angle control and power electronics control systems [38, 39]. Further details will be discussed in Section 4.1.2. This technique is powerful and green but the high cost of wind energy technology and the irregularity of wind power (the speed of wind and limited windy regions) are the biggest obstacles to the utilization of this technique [40].

Figure 5 shows the WT schema for inertia enhancement.

3.3. Storage Energy Systems

These techniques consist of the use of energy storage systems (ESSs) such as capacitors, ultracapacitors, batteries, and flywheels for the reinforcements of highly penetrated RES grid inertia. This technique is based on charging and discharging the ESS to provide active power to the electrical grid. This means that the ESSs must be 50%–80% charged to make up for the missing power to the power grid or to store the excess energy produced by renewable generators in the moment of power/frequency disturbance [41]. Many techniques and topologies are proposed.

3.3.1. DC-Link Capacitor

The DC-link capacitor is a capacitor used in a DC-link to separate two electrical circuits (RESs and the inverter) [42]. This technique is used for DC-link voltage support, harmonic filtering, and reactive power compensation [43]. In addition, these capacitors have shown a big potential in reducing the frequency nadir and RoCoF in power imbalance through inertia emulation [44]. Equations (3) and (4) show the similarities between SGs and capacitors [45]. We see that the DC-link voltage V_cdc and capacitance C_cdc play similar roles as the frequency f_r derived from ω_r as mentioned in equation (5) and moment of inertia J, respectively.

()

As a result, DC-link is utilized to emulate the inertia (virtual inertia) in the power grid by the use of different control algorithms. A typical scheme of a DC-link capacitor is shown in Figure 6.

3.3.2. Ultracapacitor

The high performance, the high discharge current, and the charge-discharge cycle life make supercapacitors suitable for providing pulse power for primary frequency response [46]. The supercapacitor is utilized when a DC-link capacitor is insufficient or some frequency support functions are required. Many topologies have been described in [41]. A typical scheme of an ultracapacitor is shown in Figure 7. Its high efficiency, fast load response, modularity, long lifetime, no maintenance requirements, and environmentally friendly characteristics make it a good alternative to batteries in many applications [47]. It delays frequency nadir and RoCoF decreases significantly and gives sufficient time for other sources to respond to the frequency deviation. However, it does not have a long discharge time. In consequence, it has a short operation time.

3.3.3. Batteries

The battery is an electrical storage element. It is characterized by its high density of energy, fast response, moderate cost, and long discharge time which puts it above all ESSs for frequency control and regulation [32]. The battery operates at a direct current. It needs a stable and fixed voltage in normal charging mode. The use of power electronic converters and a proper control algorithm is necessary to regulate the output power and emulate the inertia [48]. Different topologies are represented in [49]. Batteries could be connected to the grid through DC-link as mentioned in Figure 8.

The response time of batteries is longer than supercapacitors. In addition, the discharging time of batteries is much longer than the discharging time of supercapacitors. To benefit from the advantages of both ESSs, a proposed technique is given in [50]. The authors proposed a hybrid system with both batteries and ultracapacitors. The topology scheme is shown in Figure 9. As a result, the system will respond faster and operate longer.

3.3.4. Flywheels

Figure 10 represents the schema of the flywheel for inertia support. Flywheel is considered a powerful ESS due to its fast response and long cycle life [52, 53]. This ESS has an important inertia and good flexibility providing ancillary services in the power grid such as frequency regulation and voltage support [54, 55]. In [56], a frequency control method for a microgrid-connected flywheel ESS has been proposed. This control method has led to a fast power injection and less DC-link voltage variation. A comparison between different control schemes of the flywheel ESS has been made in [57]. A flywheel and lithium battery hybrid energy storage control strategy for smoothing PV systems has been proposed in [58].

ESSs such as batteries and flywheels provide valuable support for frequency stability, with flywheels excelling in short-term frequency response and batteries offering extended support during prolonged deviations. However, the high initial cost of ESSs and their sensitivity to discharge rates limit their universal application. Hybrid ESS configurations can mitigate some of these challenges by combining rapid response with sustained support.

3.3.5. Hydropower

Hydropower accounts for 99% of global electricity storage, playing a crucial role in ensuring a reliable power supply [59]. Pumped storage micro-hydroelectricity plants (PS-MHPPs) have two modes of operation: generation and pumping. During grid power shortages, water from the reservoir generates electricity in the generation mode, while surplus power in the grid pumps water back to the reservoir in the pumping mode. To ensure consistent power generation, PS-MHPPs require a modern control scheme that can adapt to rapid variations and fluctuations in power production. To address this issue, power electronic converters are utilized to separate the machine from the traditional power grid. Adjustable speed units are used to improve efficiency. The precise control of power production in PS-MHPPs with power converters contributes to the frequency stability of the power grid [60]. However, the introduction of power converters reduces the inertia contribution of PS-MHPPs. Table 3 gives a qualitative comparison between the methods cited above.

Table 3. Summary of inertia enhancement techniques [17].

Technology	Inertia compensation	Cost	Functions	Problems	Proven	References
Synchronous condensers	High	High	Reactive power compensation and voltage control	Nonrenewable sources	Yes	[22, 61–63]
Wind turbines	High	Medium	Frequency control and renewable source	Nonlinear inertia emulation	Yes	[64–66]
DC-link capacitor	Low	Low	DC-link voltage support and harmonic filtering	Sizing of DC-link capacitors	No	[44, 67, 68]
Ultracapacitor	High	High	Frequency control	Sizing and placement of ultracapacitors	No	[41, 50]
Batteries	High	High	Frequency control	RoCoF measurement, sizing, and placement of batteries	No	[69, 70]
Flywheels	High	High	Reactive power compensation and voltage control	—	No	[53, 71]
Hydropower	High	High	Frequency control and renewable source	Dependency on water availability and land use	Yes	[59, 60]

Table 3 presents a summary of the above inertia enhancement techniques, and Table 4 presents a qualitative comparison of the costs associated with various inertia enhancement techniques. As illustrated, SCs and flywheels have high costs due to their reliance on mechanical components and energy sources. On the other hand, battery systems and ultracapacitors are promising but also come with high initial investments. WTs offer a medium-cost solution but are contingent on environmental conditions.

Table 4. Qualitative comparison of the costs associated with various inertia enhancement techniques.

Technology	Initial investment	Operational costs	Maintenance costs	Comments
Synchronous condensers	High	High	High	Effective, but costly due to reliance on conventional energy and complexity
Wind turbines (with VSMs)	Medium	Medium	Medium	Renewable source, reliable but subject to wind availability
DC-link capacitors	Low	Low	Low	Limited inertia compensation, primarily supports DC voltage regulation
Ultracapacitors	High	High	Medium	Quick response, but expensive and short operational times
Batteries	High	Medium	Medium	Excellent for long-term support, but high initial costs and resource concerns
Flywheels	High	Medium	Medium	Effective, with fast response and long cycle life

4. Virtual Synchronous Machines (VSMs)

The fundamental concept behind VSMs is to replicate the operational characteristics of an SG [72]. Inertia emulation techniques differ based on factors such as the type of RES, its geographic location, the integration of ESSs, and the specific ESS types employed. To address inertia challenges in high-RES power grids, it is crucial to understand the impact of these key parameters. The following section explores how these parameters affect grid stability and establishes a framework for assessing the effectiveness of various inertia enhancement methods. Techniques like VSMs, ESSs, SCs, and WTs depend on optimized parameters settings to emulate inertia successfully and support frequency stability.

In power grids with high-RES integration, the success of inertia emulation relies on several critical parameters:

•
RoCoF: As a key indicator of how quickly frequency shifts following a disturbance, RoCoF directly influences the stability of low-inertia systems. Higher RoCoF values require more rapid responses from inertia emulation systems to maintain grid stability.
•
Inertia constant (H): This parameter reflects the kinetic energy stored in the grid. RES-dominant grids typically exhibit lower inertia constants, resulting in faster frequency deviations and greater instability.
•
ESS capacity and discharge rates: These factors determine the extent and duration of support during frequency events, directly impacting the effectiveness of inertia emulation.
•
VSM settings (damping and droop control): These parameters must be fine-tuned to effectively replicate traditional SG behavior and contribute to frequency stability.
•
Control delays: Delays in the response of inertia emulation systems to frequency fluctuations can significantly undermine stability, as timely responses are crucial to maintaining grid balance.

4.1. Deloading Technique

It is a technique that gives the RESs some power reserve to face the frequency perturbations.

4.1.1. For PV Power Plant

Generally, PV systems work on the maximum power point tracking (MPPT) mode according to temperature T and irradiance G [73]. However, in a frequency event, the system is not able to respond, due to the absence of a reserved power [74]. Many techniques are presented in the literature to give inertia to the PV plant [73, 75–80]. The deloading mode is one of these methods [77, 81]. The deloading technique is a mode of function of the PV system that helps it to have some reserved power [80], which gives the system the ability to respond to frequency deviations. In addition, this technique does not require ESSs [76]. The authors in [82] proposed a technique utilizing active power control to maintain frequency stability. This involves reducing the active power output fed into the grid as the frequency increases. In the deloading mode, the PV system’s power will decrease below the power at maximum power point (P_MPP). The difference between power deloaded (P_del) and (P_MPP) is the amount of power reserved to face the power/frequency perturbations. To realize this technique, it is necessary to regulate the DC bus voltage as represented in Figure 11 and in equations (6) and (7):

()

During a lack of power at the production level, the PV system operates in the MPPT mode. In contrast, if the power generated by the PV system is more than the demand, the PV plant or a partial PV plant will operate in deloading mode. Figure 12 illustrates the deloading method diagram.

The droop controller detects frequency errors. Δf and calculates the power error ΔP. The power error ΔP will be added to P_del. Then, the P-U curve block regulates the DC voltage corresponding to the new power deloaded P_del. Finally, the PI regulation generates the direct current i_d to command the DC bus. The P-U curve must be precisely set to make the system work perfectly.

4.1.2. For Wind Power Plants

As in PV systems, WTs also operate, generally, in the MPPT mode. To give the system a power reserve and the ability to respond to frequency variations, the deloading method could be utilized [84]. Two operation possibilities for the deloading method with wind power generator technologies are presented [85]. Pitch angle control: It is based on the variation of the pitch angle β (rotor blade angle) between two angles β₀ and β₁ to adjust the active power output P_del with a constant rotor speed Ω_MPP to finally give the system power reserve (see Figure 13) [86].

Speed control: It consists of varying the rotor speed to change the active power position from P_MPP to P_del with a fixed pitch angle β₀. As illustrated in Figure 14, two distinct strategies are employed in the speed control technique. The first strategy, designated as “under speed control” (Figure 14(b)), is not recommended due to its potential adverse impact on stability. The second strategy, referred to as “over speed control” (Figure 14(a)), is considered more optimal [87, 88].

In addition to the deloading technique, for WTs, there are other techniques for emulating inertia as hidden inertia emulation and the fast power reserve techniques [89]. Hidden inertia emulation control for WTs is an emulation of an inertial control of an SG [90], which makes the WT emulate inertia based on the RoCoF and frequency deviation Δf. There are two types of hidden inertia emulation control:

•
One-loop control: It is based only on the RoCoF. Equation (8) represents the inertial power generated with this technique. P_inertia, ω_g, and H are the inertial power, grid angular frequency, and inertia constant, respectively. Figure 15(a) illustrates its diagram scheme. This control strategy does not have the ability to make the frequency return to its initial value f₀ and this is its major drawback.
()
•
Two-loop control: It is based on both RoCoF and frequency deviation Δf. This control strategy is faster and gives the system the ability to make the frequency return to its initial value f₀. Equation (9) and Figure 15(b) represent the inertial power of the two-loop control strategy and its diagram, respectively.
()
where K_I is the inertia gain and K_droop is the drooping gain.

For the sake of comparison, the variable speed WT absorbs and releases a significantly higher amount of kinetic energy stored in the rotor than fixed WTs, and it does so at an accelerated rate.

The fast power reserve technique is based on making the WT generate active power under the maximum power point by adjusting the rotor speed [92]. This point is called suboptimal power. This control method is activated in a power imbalance. To compensate for power in the grid, WTs will operate in overproduction mode by increasing the speed of the rotor and releasing the kinetic energy stored on it. This energy will be recovered by switching to the underproduction mode. The transition between overproduction and underproduction mode must be smoothly done to avoid a sudden power drop. Equation (10) indicates the power reserve, and Figure 16 illustrates the diagram of the fast power reserve technique.

()

4.2. Inducverters

Inducverter is a technique to emulate grid inertia. The inducverter imitates the induction machine, especially its inertia characteristics [94]. It is known that the induction machine has self and soft start capability and also its automatic synchronization with the grid without the need of PLL. The inducverter utilizes these characteristics to regulate active power and frequency by the exploitation of the virtual rotor inertia of a power electronic inverter.

An inducverter is a combination of an inverter with a filter and control command that makes the inverter behave as an induction machine. Figure 17 shows the control diagram of the inducverter. As it is observed, the control section is composed of two major parts: (i) the current/power damping/synchronizing unit and (ii) the control core. The current/power damping and synchronizing unit enables the inducverter to achieve self-start and soft-start by generating the reference frequency, ensuring smooth, and automatic synchronization with the grid.

The controller core is the part that adjusts the three-phase voltage references to generate the preset real and reactive powers, as shown in Figure 17 and the following equations:

()

where T_m, T_e, D_p, ω_v, ω_slip, and θ are the mechanical torque, electrical torque, damping coefficient, virtual angular frequency, slip frequency, and phase angle, respectively. P, P_ref, Q, and Q_ref are the active power, active power reference, reactive power, and reactive power reference, respectively. I_dref and I_qref represent the dq-axis reference current. K_i and K_p are the PI gains.

The active and reactive power references are regulated by a PI regulation, and the voltage reference applied to the pulse-width modulation (PWM) is generated by the adaptive virtual lead or leg impedance/compensator block. This topology is simple and no PLL is needed. However, the open loop of voltage and current control makes the inducverter generate an undesirable transient during large disturbance. In addition, the inducverter is unable to provide fast-fault current because its power is kept constant regardless of grid variations. The inducverter was not investigated in an islanded operation yet. But overall, in a high penetration of the RESs, this technique of inertia control could give a big help to the grid [94].

4.3. Synchronverters

This topology is based on making the inverter behave as an SG from a grid perspective, which is why the name synchronverter [95]. The synchronverter is a complex nonlinear system that has all the bad and good characteristics of an SG, e.g., loss of stability caused by under-excitation in addition to the oscillations around the synchronous frequency (hunting). However, the parameters in a synchronverter such as inertia friction coefficient, field inductance, mutual inductance, or parameters that are impossible to change in a real SG could be chosen or even changed or varied when the system is operational. Figure 18 shows the diagram of a synchronverter and the dynamics of an SG can be depicted in the following equations:

()

where M_f, i_f, and e are the maximum mutual inductance between the stator windings and the field windings, field excitation current, and the reference voltage from the controller, respectively.

and

are represented by equations (16) and (17). The notation < -,- > denotes the inner product in

()

From the control diagram, we see the two major loops in synchronverter, frequency drooping loop and voltage drooping loop. The frequency drooping loop is related to the frequency changes like in SG and it is responsible for managing the power output. In the frequency drooping loop, the difference between angular frequency reference ω_ref (which is equal to the nominal angular frequency of the grid ω_g) and the virtual angular speed ω_v is calculated and multiplied by the damping factor D_P and then added to the mechanical torque T_m (T_m is obtained from the reference active power P_ref). The result is compared with the electromagnetic torque T_e which is calculated by (12) and finally divided by the moment of inertia J.

In the voltage drooping loop, the tracking error between the reference reactive power Q_ref and the reactive power Q that is calculated by (15) is added to the result of the multiplication of D_P and the difference between the reference voltage V_ref and grid voltage V_g as mentioned in Figure 18. Then the resulting signal is multiplied by the gain 1/K to obtain the excitation flux. In the end, it is possible to calculate and generate (e) by (14) and apply it to the PWM for generating the switching signals.

4.4. Power Synchronization Controller

This is a VSM topology that aims to give the system a self-synchronization. Two principal loops are in this method, active power control loop and voltage control loop [96]. The active power loop controls the phase angle deviation Δθ and the phase angle θ is generated by the addition of the phase angle deviation Δθ and the reference angle deviation θ_ref (Δθ + θ_ref). The voltage control loop regulates ΔE and generates E by ΔE + E_ref. e is given by equation (18) and finally applied to the PWM block, as mentioned in Figure 19.

()

This topology is weak facing an over-current event and it has a large steady-state error due to the absence of the current control loop. However, in [97, 98], the authors added a current control loop to the system and performed it in a weak grid operation and fault ride through (FRT) capability. The purpose of FRT is to enhance the stability and reliability of the electrical grid, as well as to ensure the uninterrupted supply of electricity to consumers, even when the grid experiences minor disturbances [99]. For example, if there is a sudden drop in voltage due to a fault in the grid, a power generation system with FRT capability will adjust its operation to ride through the fault without disconnecting from the grid.

4.5. Synchronous Voltage Controller (Sync VC)

Based on emulating the SG, a new approach in [100] was proposed and it is termed Sync VC. Unlike the synchronous power controller, SyncVC has two control loops with current and voltage regulation. In addition, the emulation of SG is achieved by the voltage control loop and it is called voltage-based VSM, contrary to the power-based VSM, where the emulation is realized on the power loop. In this topology, a d-axis control loop is applied to control i_d and v_d and generate virtual inertia and virtual PLL. Furthermore, a q-axis control loop is used to regulate the voltage magnitude. The following equations describe the voltage control loops:

()

Figure 20 shows the diagram of Sync VC. In the d-axis, the current error (i_dref − i_d) is treated by a PI controller which gives V_ref. Then V_dref − V_d is calculated and passes in a virtual PLL to generate the phase angle. The low-pass filter (LPF) 1/(s + ω_v) is equivalent to 1/Js + D_P and plays the role of the virtual rotor. So, it generates virtual inertia, damping effect, and attenuating PWM switching effects as the first objective. The q-axis control loop plays the role of the automatic voltage controller (automatic voltage regulation (AVR)) (see Figures 20(a), 20(b), and 20(c)). As a result, two operation modes are possible: (i) constant reactive power control mode i_d − Q bus, for maintaining constant reactive power to the feeder, and (ii) constant voltage control mode i_d − V bus, for maintaining constant voltage to the feeder. In the first mode i_d − Q, the error (i_ref − Q) passes in an LPF and then regulated by a PI control to adjust the voltage amplitude of the Sync VC. The second mode (i_d − V) is composed of a cascade of double loops where the first loop controls the feeder voltage amplitude and the second controls the q-axis voltage. The LPF 1/(s + ω_r) is equivalent to 1/(sL_f + R_f) and mimics the dynamic RL excitation circuit.

4.6. Fifth-Order VSM Topology

A high-order model of VSM (5th order) is presented in [101, 102]. That means it considers all static and dynamic characteristics of an SG. Figure 21 shows a diagram of this VSM. Equations (20)–(22) are the dynamic equations of the model.

()

where V_g, R_s, and L_s are the grid voltage, stator resistance, and stator inductance, respectively.

The 5th-order VSM takes the three-phase voltage V as its input and produces the three-phase current i as its output. The measured voltage grid is the input of the control circuit that generates the reference current i_ref. The inverter’s input is generated from the hysteresis by tracking the current error between i_ref and the measured current i and then passing by the PWM. The regulating mechanical torque is responsible for regulating and controlling the active power. However, the reactive power generated by the system is not controlled but it is adjusted by the grid’s SGs. This technique allows bidirectional power flow which is suitable for energy power storage systems such as ESSs.

4.7. VSM With Low-Order Model

In [103], a low-order model of VSM has been utilized to emulate the inertia characteristics of an SG. It has the capability to respond to frequency changes. In Figure 22, a diagram of this topology is presented. We see clearly the simplicity of the system. The control system is composed of two main blocks, the PLL block and the reference current generator block. The PLL block has an output Δω and the RoCoF equals Δω/dt. The proposed VSM works as a current control source to emulate the inertia. The reference current generator block generates the reference current using the equations below:

()

4.8. VSM0H

VSM0H is a VSM topology proposed by a group from the UK National Grid [104]. This topology regulates the frequency and voltage in proportion to the active and reactive power demand, respectively. In addition, no PI controller or inner current control loop are used and it has no PLL. Figure 23 shows a diagram of the VSM0H topology and equations (27)–(29) are its dynamic equations.

()

where τs is the time constant.

The active and reactive power are determined using I_dq and V_dq, after which they are processed through a Boxcar filter. After one cycle, the frequency and voltage are calculated. The signal is then fed into the inverter through a PWM process. This technique enhances the natural damping in a SG and a VSM-dominated grid. This technique does not have inertia, so it could not react properly with the RoCoF but it is fast and could well manage the frequency nadir. The VSM0H has the ability of operating in a grid of 100% RES penetration, so it could perfectly work with the deloading method.

4.9. Universal VSM

This is a method that could work in grid-connected mode, islanded mode, or even during fault [105]. The principle of this technique is the management of the ESSs and the MPPT of the RESs to generate inertia. Hence, this system has the ability to change the functioning mode without the need of switching operations. Moreover, this method gives the system the black-start ability and by using a dq current control, the system will have an over-current protection. The diagram of the universal VSM is shown in Figure 24 and its dynamic equations are as follows:

()

From Figure 24, the frequency regulation is assured by the virtual governor in proportion to I_q. However, the voltage is regulated by the AVR in proportion to I_d−v.

4.10. ISE Lab VSM

A simplified VSM topology has been proposed by a research group at Osaka University in Japan termed ISE Lab VSM [106]. It is a high-order model system. However, unlike 5th-order VSM and synchronverter, it uses only the swing of the SG and it has a voltage mode control. It is clear in Figure 25, where a diagram of the ISE Lab VSM is illustrated, that the active power P and the reactive power Q are regulated by the modulation of θ and E [107]. Additionally, ω_v is computed using the swing equation (44), while equations (42) and (43) represent the droop and governor equations, respectively, with K_p and K_q as the droop gains. P₀ and Q₀ are the preset active and reactive power, respectively, and they are calculated by electricity system operators’ (ESOs’) requirements and the rating of VSM [108].

()

4.11. Algebraic Model of VSM

An algebraic VSM model, based on the steady-state phasor diagram of SG to produce current reference, was proposed by a research team from Kawasaki Heavy Industries (KHI) [109]. This technique ignores the dynamic equations of SG and utilizes Park’s differential equations combined with a current-controller inverter to model the generator. In addition, a current control loop is added for over-current protection.

()

and Y are defined as next:

()

Equations (34) and (35) represent the dynamics of governor and AVR, respectively, and the diagram of the algebraic model of VSM is illustrated in Figure 26.

4.12. Discussion

In the context of VSMs, there are several technical requirements and characteristics that are essential for their effective operation and integration into modern power grids [110, 111]. These requirements and characteristics help determine the suitability of a particular VSM topology for specific applications. While there are no rigid prerequisites for VSMs, some technical requirements proposed by ESOs have gained prominence [112–114]:

1.
Seamless operation in grid-connected and islanded mode: One of the fundamental requirements for VSMs is the ability to seamlessly transition between grid-connected and islanded (standalone) modes of operation. This capability ensures the uninterrupted supply of power even when the grid experiences disruptions or faults.
2.
Inherent over-current protection: VSMs should incorporate inherent over-current protection mechanisms to safeguard the system against excessive current flow, which can lead to equipment damage or grid instability.
3.
Dynamic voltage and frequency support: VSMs must possess the capability to provide dynamic support for grid voltage and frequency. They should be able to adjust their operating parameters to help regulate and stabilize voltage and frequency during transient disturbances.
4.
FRT capability: FRT, as mentioned earlier, is crucial for VSMs. It enables them to withstand and remain connected to the grid during short-term voltage or frequency disturbances, contributing to grid stability and reliability. Different regions and grid operators may have specific FRT requirements and standards that RE systems must adhere to, depending on the local grid conditions and regulations. These standards specify the performance and behavior of RE systems during grid disturbances to maintain grid stability and reliability.
5.
Black-start capability: Black-start capability is essential for power generation systems, including VSMs, to initiate and restore grid operations from a blackout condition. It ensures the ability to restart and synchronize with the grid when necessary.

When assessing various VSM topologies, it becomes evident that different topologies offer different features and capabilities.

Frequency support: All VSM topologies provide frequency support, which is a primary function of VSMs in emulating the behavior of SGs.

Voltage control/AVR: While all topologies incorporate some form of closed-loop control for voltage regulation and AVR, low-order VSMs typically do not include AVR functionality.

Seamless operation: Among the discussed topologies, only the universal VSM offers seamless operation in both grid-connected and islanded modes, making it suitable for a wider range of applications.

Over-current protection: Some topologies, such as the ISE Lab VSM and VSM0H, lack inherent over-current protection, which may necessitate additional protective measures.

FRT and frequency detection: Each topology exhibits unique characteristics when it comes to FRT and frequency detection. These distinctions can influence their suitability for specific grid conditions and requirements.

In conclusion, selecting the most suitable VSM topology requires careful alignment with the grid’s specific needs and operational conditions. Each VSM topology offers distinct advantages and limitations, making it crucial to evaluate them against technical requirements, such as response time, stability, and compatibility with existing infrastructure. By thoroughly assessing these factors, grid operators can make informed decisions that enhance grid stability and performance in high-RES environments. Table 5 provides a summary of the FRT and frequency detection characteristics, as well as the major advantages and drawbacks of each topology, aiding in the selection process for the most suitable VSM topology based on specific grid scenarios and operational requirements.

Table 5. Characteristics and some major advantages and drawbacks of VSM topologies [9].

VSM topology	Frequency detection	FRT	Advantage	Drawback	References
Inducverter	Yes	Yes	Soft-synchronizing and autosynchronizing capability	Limited fast-fault current injection	[94]
Synchronverters	Yes	Yes	The same dynamics as SG observed from the grid	Numerical instability	[113–116]
Power synchronization controller	Yes	Yes	Emulates the self-synchronizing capability of SGs	Large steady-state error	[96, 117, 118]
Synchronous voltage controller	Yes	Not investigated	Emulates SG dynamics in voltage loop	Instability during fault	[100]
5th-order VSM	No	Not investigated	Fast employments	Numerical instability	[119, 120]
Low-order VSM	Yes	Not investigated	PLL emulation of the SG’s swing equation	Susceptible to noise from frequency derivative term	[107, 121–123]
Virtual synchronous machine zero inertia	No	Not investigated	Simple control structure	No inherent over-current protection	[124, 125]
Universal VSM	Yes	Yes	Seamless operation in all operating modes	No experimental validation	[105, 126, 127]
ISE Lab VSM	No	Yes	Simpler replication of SG dynamics	Power oscillations	[128]
Algebraic model of VSM	Yes	Not investigated	Phasor’s representation of the SG	Need to change the control paradigm between grid and islanded modes	[109]

5. Some Issues of Inertia Implementation

In this field of research, there exist diverse challenges, mechanisms for modeling, and prospects for incorporating RES [129]. Adequate comprehension of these challenges is essential to progress in this sphere. Some stochastic frameworks to model inertia and power frequency response support are presented in [130–132]. Implementing VSMs and enhancing inertia presents several technical challenges, which are discussed in this section.

5.1. Time Delays

In theory, there is no time delay in power converters and power control to respond and deliver power to the grid [133]. However, in practice, a communication and power conversion time delay is introduced, which could cause a bad functioning of the frequency control system and destabilize the entire system [134]. The time delay is caused by communications and power control of the power converter [135].

5.1.1. Communication Time Delay

It is the time of transmissions between the control center and power converters. Optimizing the distance between control centers and power converters is essential. In large power systems, a decentralized approach, as proposed in [136], may be more effective. But in practice, it still exists and it must be considered in system dimensioning [137].

5.1.2. Power Control of Individual Power Converter Time Delay

It is the time needed to switch between modes, e.g., from deloading mode to MPPT mode. Some techniques and schemes were proposed to reduce it [136]. The utilization of ESSs is one of the most effective solutions. However, it has other concerns like the high cost and life cycle [138].

5.2. Placement of Inertia

Time-varying inertia profiles and locations of inertia may have a big impact on a large power system. One of the most important concerns of the utilization of ESSs is their placements [139]. The optimal placement of ESS units is a big challenge to the inertia emulation system. Reference [140] proposed an optimization program based on the maximization of the damping ratio of every power system mode and minimizing the oscillation between generators.

5.3. Adaptive Inertia

In a power grid, frequency deviations and the RoCoF are not constant during frequency events. Therefore, inertia should also vary to ensure an appropriate response. Figure 27 [17] presents a comparison between adaptive and constant inertia during a frequency event. Additionally, studies [149] and [150] propose control system schemes that achieve fast frequency recovery with reduced oscillations. These control systems emulate inertia according to frequency deviations and RoCoF. An algorithm for searching continuously the optimal inertia is presented in [143]. The main drawback of these algorithms is the nonlinearity of the adaptive inertia which causes a negative impact on the stability of the power grid [144].

5.4. Market Design for Inertia Service

Nowadays, inertia is not considered an extremely important property in the majority of power systems. That is what makes the inertia emulation still an experimental field [145]. So, the market of inertia emulation needs to be well-designed and optimized to integrate it and make it function perfectly [146]. Considering inertia as a frequency regulation control ancillary service will highly help the integration of inertia emulation market in the power system. In addition, the compatibility of inertia ancillary service with the other ancillary services is highly required.

6. AI as a Solution to Enhance Inertia

AI is pervading all fields of human activities. In addition, the power grid is going to be more intelligent for managing all the new sources and load characteristics. AI has the ability to predict stability issues and different perturbations in the power system [147]. Furthermore, the drawbacks of some VSM topologies and problems could be solved. To reach the sustainable development of society, RESs are considered the unique solution [17]. So, to manage all the challenges that come with it, the grid must be more intelligent in all its sectors from generation to consumption. As a result, AI can give a good help and a huge step for the smart grid.

Reference [157] introduces the implementation of a neural network (NN) to regulate the active and reactive power delivered to the grid. This system is able to work in both inductive and noninductive power networks. The proposed NN has two hidden layers and seven nodes per each hidden layer. The prediction of the next step output vector is the NN output. The voltage magnitude of the inverter is the only element in the control input vector. The inverter reactive and real power, the reactive power error, the real power error, the frequency error, and the inverter phase angle are all included in the NN/plant output vector. The state space model of the system in the discontinuous domain is represented in equations (38) and (39) and the diagram of this technique is shown in Figure 28.

()

X, F, U, and Y are the state vector, the derivative state vector, the input vector, and the output vector, respectively. G is the output vector in terms of the input vector.

A radial basis function (RBF) to improve frequency stability and overcome the shortcomings of VSMs is presented in [149]. This system determines the VSM stability margin, frequency adjustment time, power circuit cutoff frequency, grid connection standards, the reasonable range of virtual inertia J, and the damping coefficient D_P. The proposed RBF NN has one hidden layer based on the Gauss function. This AI system is designed to determine the virtual inertia J. So, the control block diagram (see Figure 29) has J as an output. The instantaneous angular velocity ω and its derivative (dω/dt) are the input vector.

Generally, VSMs take care only of stability issues. In contrast, reference [150] presented a double artificial neural network (ANNt and ANNLC) to consider both the stability and the reliability of the system by estimating the lifetime consumption (LC) of the power device. Figure 30 represents the diagram control of this technique and the following equation is the overall cost function for H optimization with inertia and reliability.

()

where α is the weighting factor for balancing the importance between the two terms. The input parameter of ANNLC is the inertia constant H and LC is the output of the system. The ANNt input parameters are the power injection P_inj and the ambient temperature T_a. P_inj is given by the VSM simulation model with multiple selections of the H. ANNt generates the mean junction temperature T_jm and cycle amplitude ΔT_j as an output vector. This technique will help for an optimally designed virtual inertia in the future.

Reference [151] proposed an NN-based integral sliding mode backstepping control to enable the free switch between the connected mode and the islanded mode of the inverter. The system also estimates the measurement uncertainties to offset their influences. That will ameliorate the system performances with a reduced power oscillation, a smoother frequency transition, and improved control accuracy and dynamic performance. Figure 31 presents the diagram of this method. The following equations define the output and the inputs of the RBF NN observer:

()

where d is the output of the RBF NN observer, and h is the output of the Gaussian function.

As renewable integration continues, the relevance of AI-based solutions will grow, allowing for predictive and real-time adjustments in VSM control and ESS discharge. The SWOT analysis (see Table 6) highlighted that while AI offers adaptability and precision, it introduces challenges related to resource intensity (high computational, energy, and financial demands), as well as cybersecurity concerns, necessitating further study.

Table 6. SWOT analysis of AI solutions.

SWOT analysis of AI solutions
Internal factors	Strengths • Enhanced frequency regulation. • Adaptability and flexibility. • Multiobjective approach.	Weaknesses • Complexity and resource intensity. • Training data dependency.
External factors	Opportunities • Technological advancements. • Integration with renewable energy and smart grid.	Threats • Regulation and standards compliance. • Cybersecurity risks. • Acceptance and adoption.

7. Practical Case Studies and Applications

The inertia enhancement strategies discussed in this review, including VSMs, ESSs, SCs, and WTs, are not merely theoretical, they are currently employed in power grids worldwide. These methods are vital for maintaining stability in grids with high levels of RES integration. However, as RES penetration increases, the requirements for these systems grow, creating the need for faster and more precise control. In this context, AI emerges as a revolutionary solution, offering predictive capabilities and rapid response times that traditional control methods struggle to match.

The following case studies present existing inertia solutions and illustrate how AI could further enhance these applications through improved real-time control and forecasting.

7.1. Case Study 1: Denmark’s High-RES Grid With SCs and WTs

Denmark’s Western Power Grid, which connects to Norway, Sweden, and Germany, has a high integration of RE, predominantly wind, leading to a system with low inertia. This configuration presents frequency stability challenges, particularly during disturbances. To counter frequency instability resulting from high-RES penetration, SCs are strategically placed. These SCs help support rotational inertia by either injecting or absorbing energy to stabilize frequency during disruptions. For instance, when a generator disconnects, SCs release rotational energy to slow the frequency drop. Similarly, during periods of excess power, SCs absorb energy to prevent frequency rise, thus supporting system stability. Simulations indicate that adding SCs raised the frequency nadir from 49.35 Hz to 49.5 Hz under specific disturbance conditions [152].

This case study demonstrates that while SCs enhance stability, system complexity increases with greater RES integration. AI integration would enable scalability, allowing for enhanced real-time and predictive control. By forecasting frequency fluctuations and dynamically adjusting SC and turbine outputs, AI could enhance the reliability of Denmark’s grid, advancing it toward a more resilient and intelligent future.

7.2. Case Study 2: Great Britain’s National Grid With VSMs and Battery ESSs

Great Britain’s National Grid employs VSMs and battery-based ESSs to counteract the inertia loss due to RES integration. The VSMs are optimally tuned with specific damping and droop settings to simulate synchronous inertia, while battery ESSs provide rapid frequency response by discharging during grid disturbances. This combined approach has notably enhanced grid resilience, underscoring the benefits of integrating VSMs and ESSs for inertia support.

Recent modifications to the balancing mechanism (BM) have amplified battery ESS roles in maintaining grid stability, leading to a 47% increase in battery dispatch across the network. This increase follows the National Grid ESO’s reintroduction of bulk dispatch for battery units, enabling multiple batteries to be dispatched simultaneously. Previously, units with higher-rated power were prioritized for ease of dispatch, but bulk dispatch now allows proportional participation of all battery units, increasing the grid’s flexibility and responsiveness [153].

AI integration could further transform battery ESS operation and grid stability. Predictive AI algorithms could enable ESS units to anticipate demand peaks or RES output variations, facilitating proactive energy dispatch that minimizes curtailment and maximizes grid support. For instance, AI could predict grid stress events and coordinate ESS discharges to preemptively stabilize frequency, optimizing battery utilization across multiple assets in real time. Furthermore, AI could improve market responsiveness by analyzing price signals and dynamically adjusting ESS dispatch in line with real-time grid conditions and historical demand data, enabling operators to capitalize on high-value opportunities while balancing supply and demand [154].

7.3. Case Study 3: California’s High Solar Penetration and ESS Integration

In California, high solar penetration has necessitated extensive ESS deployment to prevent overgeneration and support grid stability [155]. Solar output often exceeds demand, particularly during midday in spring and fall. ESS thus plays a critical role in preventing solar power curtailment by storing excess energy and discharging it during peak demand periods. These battery ESSs provide synthetic inertia, discharging rapidly to stabilize frequency during load variations and mitigating reverse power flow common in high-penetration PV scenarios [156].

To handle solar variability and improve grid flexibility, the Los Angeles Department of Water and Power (LADWP) has deployed large-scale battery systems and pumped hydro storage, supporting load leveling, peak shaving, and frequency regulation, all crucial for managing solar power’s intermittency [157]. Research by Southern California Edison highlights the role of ESS in voltage regulation, which helps California’s grid accommodate increasing PV penetration more effectively by stabilizing frequency [156].

AI integration within California’s ESS framework holds the potential to enhance these capabilities. AI-driven predictive algorithms can optimize ESS discharge and charge cycles based on real-time grid status and demand forecasts. By anticipating periods of high solar output or demand, AI can dynamically adjust ESS operations, thereby improving frequency stabilization and reducing curtailment reliance. AI can also enable advanced demand response (DR) by coordinating distributed ESS units to autonomously address grid disturbances, supporting both voltage and frequency regulation. This approach not only reduces grid instability risks but also extends ESS lifespan by optimizing usage patterns.

These cases demonstrate that while inertia enhancement methods are widely implemented, the demand for stability in high-RES grids calls for advanced solutions like AI. With predictive control and rapid response capabilities, AI is well-positioned to become a critical component of inertia management. Gradually implementing AI-driven solutions will contribute to the development of smart grids. In this way, AI not only addresses current inertia needs but also establishes a foundation for resilient, intelligent power grids aligned with a sustainable, smart energy vision. Inertia enhancement techniques are also highly complementary to grid modernization efforts, such as smart grids and DR programs, which provide the real-time adaptability and infrastructure needed to integrate AI with existing grid assets.

Smart grids enable real-time monitoring and adaptive control of grid resources, facilitating inertia emulation through VSMs, ESSs, and advanced control algorithms. VSMs, for instance, can be managed via smart grid communication protocols to emulate inertia based on real-time grid conditions. DR programs help manage load during frequency disturbances by reducing or shifting demand to balance generation and load, indirectly supporting grid inertia. Smart grids provide the communication infrastructure necessary to coordinate various inertia sources, while DR can react to rapid frequency changes, reducing the need for high physical inertia. Together, these advancements ensure that both generation and load respond to grid conditions, enabling a more flexible and resilient power system.

8. Conclusion

This comprehensive review analyzes inertia enhancement strategies for high-RES power grids, emphasizing the growing need for stability and adaptability. By examining VSMs, ESSs, WTs, and SCs, the study sheds light on each method’s technical capabilities and limitations. Key among the contributions is the forward-looking perspective on integrating AI to optimize inertia emulation, offering benefits in predictive and real-time control not attainable through traditional approaches. Practical case studies throughout the review illustrate how these techniques are already applied in high-RES power systems, and a comparative analysis of VSM topologies provides a clear reference for practitioners selecting the most suitable methods.

The study concludes that as RES penetration intensifies, so does the need for intelligent, responsive solutions. AI integration is positioned as a critical enabler, enhancing VSM and ESS applications by predicting grid fluctuations and dynamically adapting system responses to improve stability. Future research directions may focus on developing adaptive AI-driven VSM controllers for real-time response and exploring hybrid inertia solutions to further enhance resilience. These insights align with global sustainability goals and pave the way for designing intelligent, robust power grids capable of meeting the complex demands of a decentralized, RE landscape.

Nomenclature

E_kin: The kinetic energy [J]
ω_r: The rated velocity of the rotor [m/s]
J: The moment of inertia [kg·m²]
H_gen: The power system’s global inertia [s]
H_sys: The inertia constant of the system [s]
f_nom: The nominal frequency [Hz]
H_gen: The inertia constant of the generator [s]
S_gen: The rated power of the synchronous generator SG [VA]
S_sys: The rated power of all the system [VA]
E_gen: The kinetic energy of the SG [J]
V_cdc: DC-link voltage [V]
C_cdc: DC-link capacitance [F]
ω_r: Rotor angular frequency [rad/s]
V_del: Voltage deloaded [V]
V_MPP: The voltage at the maximum power point [V]
Δf: Frequency error [Hz]
ΔP: Power error [W]
P_inertia: Inertial power [W]
ω_g: Grid angular frequency [rad/s]
H: Inertia constant [s]
T_m: The mechanical torque [N.m]
T_e: Electrical torque [N.m]
D_p: Damping coefficient
ω_v: Virtual angular frequency [rad/s]
ω_slip: Slip frequency [rad/s]
θ: Phase angle [rad]
P: Active power [W]
P_ref: Active power reference [W]
Q: Reactive power [VAR]
Q_ref: Reactive power reference [VAR]
M_f: Maximum mutual inductance [H]
V_g: Grid voltage [V]
R_s: Stator resistance [Ω]
L_s: Stator inductance [H]
Δ_SOC: State of charge deviation [W]
K_SOC: State of charge gain [W]
τs: Time constant [s]

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

No funding was received.

Open Research

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

1 Wildi T., Electrical Machines, Drives, and Power Systems, 2006, Pearson Educacion.
Google Scholar
2 Lin B., Wang H., Zhang Y., and Wen B., Real-time Power System Generator Tripping Control Based on Deep Reinforcement Learning, International Journal of Electrical Power & Energy Systems. (2022) 141, https://doi.org/10.1016/j.ijepes.2022.108127.
10.1016/j.ijepes.2022.108127
Web of Science® Google Scholar
3 Heylen E., Teng F., and Strbac G., Challenges and Opportunities of Inertia Estimation and Forecasting in Low-Inertia Power Systems, Renewable and Sustainable Energy Reviews. (2021) 147, https://doi.org/10.1016/j.rser.2021.111176.
10.1016/j.rser.2021.111176
Web of Science® Google Scholar
4 Lew D., Bartlett D., Groom A. et al., Secrets of Successful Integration: Operating Experience with High Levels of Variable, Inverter-Based Generation, IEEE Power and Energy Magazine. (2019) 17, no. 6, 24–34, https://doi.org/10.1109/MPE.2019.2930855, 2-s2.0-85074196275.
10.1109/MPE.2019.2930855
Google Scholar
5 Hadjipaschalis I., Poullikkas A., and Efthimiou V., Overview of Current and Future Energy Storage Technologies for Electric Power Applications, Renewable and Sustainable Energy Reviews. (2009) 13, no. 6-7, 1513–1522, https://doi.org/10.1016/j.rser.2008.09.028, 2-s2.0-64249151091.
10.1016/j.rser.2008.09.028
Web of Science® Google Scholar
6 Mccartan T., Rate of Change of Frequency Grid Code Modification Report to NIAUR, EIRGRID, North Ireland. (2012) SONI limited.
Google Scholar
7 Guerrero J. M., Vasquez J. C., Matas J., De Vicuña L. G., and Castilla M., Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach toward Standardization, IEEE Transactions on Industrial Electronics. (2011) 58, no. 1, 158–172, https://doi.org/10.1109/TIE.2010.2066534, 2-s2.0-78650181509.
10.1109/TIE.2010.2066534
Web of Science® Google Scholar
8 Energy P., Rate of Change of Frequency (ROCOF)-review of TSO and Generator Submissions Final Report, Commission for Energy Regulation (CER), 2013, Surrey, UK.
Google Scholar
9 Muftau B. and Fazeli M., The Role of Virtual Synchronous Machines in Future Power Systems: A Review and Future Trends, Electric Power Systems Research. (2022) 206, https://doi.org/10.1016/j.epsr.2022.107775.
10.1016/j.epsr.2022.107775
Web of Science® Google Scholar
10 Fernández-Guillamón A., Gómez-Lázaro E., Muljadi E., and Molina-García Á., Power Systems with High Renewable Energy Sources: A Review of Inertia and Frequency Control Strategies over Time, Renewable and Sustainable Energy Reviews. (2019) 115, https://doi.org/10.1016/j.rser.2019.109369, 2-s2.0-85071919439.
10.1016/j.rser.2019.109369
Web of Science® Google Scholar
11 Ratnam K. S., Palanisamy K., and Yang G., Future Low-Inertia Power Systems: Requirements, Issues, and Solutions-A Review, Renewable and Sustainable Energy Reviews. (2020) 124, https://doi.org/10.1016/j.rser.2020.109773.
10.1016/j.rser.2020.109773
PubMed Web of Science® Google Scholar
12 Al-Shetwi A. Q., Sustainable Development of Renewable Energy Integrated Power Sector: Trends, Environmental Impacts, and Recent Challenges, Science of the Total Environment. (2022) 822, https://doi.org/10.1016/j.scitotenv.2022.153645.
10.1016/j.scitotenv.2022.153645
PubMed Web of Science® Google Scholar
13 Prakash V., Bhakar R., Tiwari H. P., Pain H. W., Bian Y., and Li F., Primary Frequency Response in Future Low Carbon Scenario: Opportunities & Challenges, 2016 International Conference on Recent Advances and Innovations in Engineering (ICRAIE), December 2016, IEEE, 1–6, https://doi.org/10.1109/ICRAIE.2016.7939502, 2-s2.0-85021631673.
10.1109/ICRAIE.2016.7939502
Google Scholar
14 Prakash V., Sharma K. C., and Bhakar R., Optimal Generation Mix for Frequency Response Adequacy in Future Power System, Energy and Built Environment. (2021) 2, no. 3, 243–250, https://doi.org/10.1016/j.enbenv.2020.06.010.
10.1016/j.enbenv.2020.06.010
Google Scholar
15 Ahmad T., Zhang H., and Yan B., A Review on Renewable Energy and Electricity Requirement Forecasting Models for Smart Grid and Buildings, Sustainable Cities and Society. (2020) 55, https://doi.org/10.1016/j.scs.2020.102052.
10.1016/j.scs.2020.102052
Web of Science® Google Scholar
16 Feilat E. A., Azzam S., and Al-Salaymeh A., Impact of Large PV and Wind Power Plants on Voltage and Frequency Stability of Jordan’s National Grid, Sustainable Cities and Society. (2018) 36, 257–271, https://doi.org/10.1016/j.scs.2017.10.035, 2-s2.0-85032669491.
10.1016/j.scs.2017.10.035
Web of Science® Google Scholar
17 Robert F. C., Sisodia G. S., and Gopalan S., A Critical Review on the Utilization of Storage and Demand Response for the Implementation of Renewable Energy Microgrids, Sustainable Cities and Society. (2018) 40, 735–745, https://doi.org/10.1016/j.scs.2018.04.008, 2-s2.0-85047397686.
10.1016/j.scs.2018.04.008
Web of Science® Google Scholar
18 Twaha S. and Ramli M. A., A Review of Optimization Approaches for Hybrid Distributed Energy Generation Systems: Off-Grid and Grid-Connected Systems, Sustainable Cities and Society. (2018) 41, 320–331, https://doi.org/10.1016/j.scs.2018.05.027, 2-s2.0-85048482843.
10.1016/j.scs.2018.05.027
Web of Science® Google Scholar
19 Fang J., Li H., Tang Y., and Blaabjerg F., On the Inertia of Future More-Electronics Power Systems, IEEE Journal of Emerging and Selected Topics in Power Electronics. (2019) 7, no. 4, 2130–2146, https://doi.org/10.1109/JESTPE.2018.2877766, 2-s2.0-85055700929.
10.1109/JESTPE.2018.2877766
Web of Science® Google Scholar
20 Fang J., Lin P., Li H., Yang Y., and Tang Y., An Improved Virtual Inertia Control for Three-phase Voltage Source Converters Connected to a Weak Grid, IEEE Transactions on Power Electronics. (2019) 34, no. 9, 8660–8670, https://doi.org/10.1109/TPEL.2018.2885513, 2-s2.0-85058164308.
10.1109/TPEL.2018.2885513
Web of Science® Google Scholar
21 Bhowmik P., Chandak S., and Rout P. K., Frequency Superimposed Energy Bifurcation Technology for a Hybrid Microgrid, Sustainable Cities and Society. (2019) 45, 607–618, https://doi.org/10.1016/j.scs.2018.12.027, 2-s2.0-85059185286.
10.1016/j.scs.2018.12.027
Web of Science® Google Scholar
22 High Penetration of Power Electronic Interfaced Power Sources, ENTSO-E Guidance Document for National Implementation for Network Codes on Grid Connection. (2017) Technical Report, Belgium.
Google Scholar
23 Yan R., Saha T. K., and Modi N., Frequency Response and its Enhancement Using Synchronous Condensers in Presence of High Wind Penetration, 2015 IEEE Power & Energy Society General Meeting, July 2015, IEEE, 1–5, https://doi.org/10.1109/PESGM.2015.7285801, 2-s2.0-84956868666.
10.1109/PESGM.2015.7285801
Google Scholar
24 Kundur P. S. and Malik Om P., Power System Stability and Control, 2022, McGraw-Hill Education.
Google Scholar
25 Nguyen H. T., Yang G., Nielsen A. H., and Jensen P. H., Frequency Stability Improvement of Low Inertia Systems Using Synchronous Condensers, 2016 IEEE International Conference on Smart Grid Communications (SmartGridComm), November 2016, IEEE, 650–655, https://doi.org/10.1109/SmartGridComm.2016.7778835, 2-s2.0-85010202023.
10.1109/SmartGridComm.2016.7778835
Google Scholar
26 Tielens P., Operation and Control of Power Systems with Low Synchronous Inertia, PhD, ARENBERG DOCTORAL SCHOOL, Faculty of Engineering Science. (2017) .
Google Scholar
27 Xv K., Jia J., Xie B., Yang N., Wang R., and Xie Y., Power Grid Inertia Promotion Strategy Considering Synchronous Condenser Support, 2023 6th International Conference on Energy, Electrical and Power Engineering (CEEPE), May 2023, IEEE, 672–677.
Google Scholar
28 Spahic E., Varma D., Beck G., Kuhn G., and Hild V., Impact of Reduced System Inertia on Stable Power System Operation and an Overview of Possible Solutions, 2016 IEEE Power and Energy Society General Meeting (PESGM), July 2016, IEEE, 1–5.
Google Scholar
29 Nuhic M., Kkuni K. V., and Ramachandran J., Comparative Study of Hybrid Synchronous Condenser Incorporating Battery Energy Storage System for Ancillary Service Provision, 19th Wind Integration Workshop, 2020.
Google Scholar
30 Liu K., Qu Y., Kim H. M., and Song H., Avoiding Frequency Second Dip in Power Unreserved Control during Wind Power Rotational Speed Recovery, IEEE Transactions on Power Systems. (2018) 33, no. 3, 3097–3106, https://doi.org/10.1109/TPWRS.2017.2761897, 2-s2.0-85031800465.
10.1109/TPWRS.2017.2761897
Web of Science® Google Scholar
31 Australian Energy Market Commission, EPR0059, AEMC 2017, Frequency Control Frameworks Review, 2017.
Google Scholar
32 Riesz J. and Palermo J., International Review of Frequency Control Adaptation, Australian Energy Market Operator. (2016) .
Google Scholar
33 Lalor G., Mullane A., and O’Malley M., Frequency Control and Wind Turbine Technologies, IEEE Transactions on Power Systems. (2005) 20, no. 4, 1905–1913, https://doi.org/10.1109/TPWRS.2005.857393, 2-s2.0-28244449042.
10.1109/TPWRS.2005.857393
Web of Science® Google Scholar
34 Kayikçi M. and Milanovic J. V., Dynamic Contribution of DFIG-Based Wind Plants to System Frequency Disturbances, IEEE Transactions on Power Systems. (2009) 24, no. 2, 859–867, https://doi.org/10.1109/TPWRS.2009.2016062, 2-s2.0-67349262621.
10.1109/TPWRS.2009.2016062
Web of Science® Google Scholar
35 Arani M. F. M. and El-Saadany E. F., Implementing Virtual Inertia in DFIG-Based Wind Power Generation, IEEE Transactions on Power Systems. (2013) 28, no. 2, 1373–1384, https://doi.org/10.1109/TPWRS.2012.2207972, 2-s2.0-84886446794.
10.1109/TPWRS.2012.2207972
Web of Science® Google Scholar
36 Morren J., De Haan S. W., Kling W. L., and Ferreira J. A., Wind Turbines Emulating Inertia and Supporting Primary Frequency Control, IEEE Transactions on Power Systems. (2006) 21, no. 1, 433–434, https://doi.org/10.1109/TPWRS.2005.861956, 2-s2.0-32144457162.
10.1109/TPWRS.2005.861956
Web of Science® Google Scholar
37 Ekanayake J. and Jenkins N., Comparison of the Response of Doubly Fed and Fixed-Speed Induction Generator Wind Turbines to Changes in Network Frequency, IEEE Transactions on Energy Conversion. (2004) 19, no. 4, 800–802, https://doi.org/10.1109/TEC.2004.827712, 2-s2.0-10244250325.
10.1109/TEC.2004.827712
Web of Science® Google Scholar
38 Blaabjerg F. and Ma K., Future on Power Electronics for Wind Turbine Systems, IEEE Journal of emerging and selected topics in power electronics. (2013) 1, no. 3, 139–152, https://doi.org/10.1109/JESTPE.2013.2275978, 2-s2.0-84938933299.
10.1109/JESTPE.2013.2275978
Web of Science® Google Scholar
39 Blaabjerg F., Liserre M., and Ma K., Power Electronics Converters for Wind Turbine Systems, IEEE Transactions on Industry Applications. (2012) 48, no. 2, 708–719, https://doi.org/10.1109/TIA.2011.2181290, 2-s2.0-84859044676.
10.1109/TIA.2011.2181290
Web of Science® Google Scholar
40 PROGRESS REPORT FUTURE POWER SYSTEM SECURITY PROGRAM, 2017, www.aemo.com.au.
Google Scholar
41 Lukic S. M., Cao J., Bansal R. C., Rodriguez F., and Emadi A., Energy Storage Systems for Automotive Applications, IEEE Transactions on Industrial Electronics. (2008) 55, no. 6, 2258–2267, https://doi.org/10.1109/TIE.2008.918390, 2-s2.0-56649107722.
10.1109/TIE.2008.918390
Web of Science® Google Scholar
42 Kassakian J. G. and Jahns T. M., Evolving and Emerging Applications of Power Electronics in Systems, IEEE Journal of Emerging and Selected Topics in Power Electronics. (2013) 1, no. 2, 47–58, https://doi.org/10.1109/JESTPE.2013.2271111, 2-s2.0-84893608364.
10.1109/JESTPE.2013.2271111
Web of Science® Google Scholar
43 Karanki S. B., Geddada N., Mishra M. K., and Kumar B. K., A DSTATCOM Topology with Reduced DC-link Voltage Rating for Load Compensation with Nonstiff Source, IEEE Transactions on Power Electronics. (2012) 27, no. 3, 1201–1211, https://doi.org/10.1109/TPEL.2011.2163946, 2-s2.0-84856887545.
10.1109/TPEL.2011.2163946
Web of Science® Google Scholar
44 Wang H. and Blaabjerg F., Reliability of Capacitors for DC-link Applications in Power Electronic Converters—An Overview, IEEE Transactions on Industry Applications. (2014) 50, no. 5, 3569–3578, https://doi.org/10.1109/TIA.2014.2308357, 2-s2.0-84907459155.
10.1109/TIA.2014.2308357
Web of Science® Google Scholar
45 Fang J., Li H., Tang Y., and Blaabjerg F., Distributed Power System Virtual Inertia Implemented by Grid-Connected Power Converters, IEEE Transactions on Power Electronics. (2018) 33, no. 10, 8488–8499, https://doi.org/10.1109/TPEL.2017.2785218, 2-s2.0-85039767578.
10.1109/TPEL.2017.2785218
Web of Science® Google Scholar
46 Hossain M. J., Pota H. R., Mahmud M. A., and Aldeen M., Robust Control for Power Sharing in Microgrids with Low-Inertia Wind and PV Generators, IEEE Transactions on Sustainable Energy. (2015) 6, no. 3, 1067–1077, https://doi.org/10.1109/TSTE.2014.2317801, 2-s2.0-85028215994.
10.1109/TSTE.2014.2317801
Web of Science® Google Scholar
47 Kim Y. S., Kim E. S., and Moon S. I., Frequency and Voltage Control Strategy of Standalone Microgrids with High Penetration of Intermittent Renewable Generation Systems, IEEE Transactions on Power Systems. (2016) 31, no. 1, 718–728, https://doi.org/10.1109/TPWRS.2015.2407392, 2-s2.0-84925114961.
10.1109/TPWRS.2015.2407392
Web of Science® Google Scholar
48 Duckwitz D. and Fischer B., Modeling and Design of $df/dt$-Based Inertia Control for Power Converters, IEEE Journal of Emerging and Selected Topics in Power Electronics. (2017) 5, no. 4, 1553–1564, https://doi.org/10.1109/JESTPE.2017.2703814, 2-s2.0-85037046876.
10.1109/JESTPE.2017.2703814
Web of Science® Google Scholar
49 Fang J., Zhang R., Li H., and Tang Y., Frequency Derivative-Based Inertia Enhancement by Grid-Connected Power Converters with a Frequency-Locked-Loop, IEEE Transactions on Smart Grid. (2019) 10, no. 5, 4918–4927, https://doi.org/10.1109/TSG.2018.2871085, 2-s2.0-85053600746.
10.1109/TSG.2018.2871085
Web of Science® Google Scholar
50 Cao J. and Emadi A., A New Battery/ultracapacitor Hybrid Energy Storage System for Electric, Hybrid, and Plug-In Hybrid Electric Vehicles, IEEE Transactions on Power Electronics. (2011) 27, no. 1, 122–132, https://doi.org/10.1109/TPEL.2011.2151206, 2-s2.0-83655192802.
10.1109/TPEL.2011.2151206
Web of Science® Google Scholar
51 Yu J., Fang J., and Tang Y., Inertia Emulation by Flywheel Energy Storage System for Improved Frequency Regulation, 2018 IEEE 4th Southern Power Electronics Conference (SPEC), December 2018, IEEE, 1–8.
Google Scholar
52 Chen Z. H. O. U., Yu H.-jie, Qiu W.-qiang, Yang Bo, Yi-bin T. A. O., and Zhen-zhi L. I. N., Flywheel Energy Storage System for Power Quality Improvement Application: A Review, 4th International Conference on Automation, Mechanical and Electrical Engineering (AMEE 2019), 2019, Xiamen, China, 232–238, https://doi.org/10.12783/dtetr/amee2019/33463.
10.12783/dtetr/amee2019/33463
Google Scholar
53 Kesgin M. G., Han P., Taran N., and Ionel D. M., Overview of Flywheel Systems for Renewable Energy Storage with a Design Study for High-Speed Axial-Flux Permanent-Magnet Machines, 2019 8th International Conference on Renewable Energy Research and Applications (ICRERA), November 2019, IEEE, 1026–1031, https://doi.org/10.1109/ICRERA47325.2019.8996526.
10.1109/ICRERA47325.2019.8996526
Google Scholar
54 Esparcia E. A., Castro M. T., Odulio C. M. F., and Ocon J. D., A Stochastic Techno-Economic Comparison of Generation-Integrated Long Duration Flywheel, Lithium-Ion Battery, and Lead-Acid Battery Energy Storage Technologies for Isolated Microgrid Applications, Journal of Energy Storage. (2022) 52, https://doi.org/10.1016/j.est.2022.104681.
10.1016/j.est.2022.104681
Web of Science® Google Scholar
55 Mohamed M. M., El Zoghby H. M., Sharaf S. M., and Mosa M. A., Optimal Virtual Synchronous Generator Control of Battery/supercapacitor Hybrid Energy Storage System for Frequency Response Enhancement of Photovoltaic/diesel Microgrid, Journal of Energy Storage. (2022) 51, https://doi.org/10.1016/j.est.2022.104317.
10.1016/j.est.2022.104317
Web of Science® Google Scholar
56 Mahdavi M. S., Gharehpetian G. B., and Moghaddam H. A., Enhanced Frequency Control Method for Microgrid-Connected Flywheel Energy Storage System, IEEE Systems Journal. (2021) 15, no. 3, 4503–4513, https://doi.org/10.1109/JSYST.2020.3010029.
10.1109/JSYST.2020.3010029
Web of Science® Google Scholar
57 García-Pereira H., Blanco M., Martínez-Lucas G., Pérez-Díaz J. I., and Sarasúa J. I., Comparison and Influence of Flywheels Energy Storage System Control Schemes in the Frequency Regulation of Isolated Power Systems, IEEE Access. (2022) 10, 37892–37911, https://doi.org/10.1109/ACCESS.2022.3163708.
10.1109/ACCESS.2022.3163708
Web of Science® Google Scholar
58 Zhao Z., Xiao H., and Yang Y., Improved Coordinated Control Strategy of Hybrid Energy Storages in PV Power Smoothing, Energy Procedia. (2018) 145, 151–156, https://doi.org/10.1016/j.egypro.2018.04.026, 2-s2.0-85056530050.
10.1016/j.egypro.2018.04.026
Google Scholar
59 Sami I., Ullah N., Muyeen S. M., Techato K., Chowdhury M. S., and Ro J. S., Control Methods for Standalone and Grid Connected Micro-hydro Power Plants with Synthetic Inertia Frequency Support: A Comprehensive Review, IEEE Access. (2020) 8, 176313–176329, https://doi.org/10.1109/ACCESS.2020.3026492.
10.1109/ACCESS.2020.3026492
Web of Science® Google Scholar
60 Suul J. A., Variable Speed Pumped Storage Hydropower Plants for Integration of Wind Power in Isolated Power Systems, Renewable Energy, 2009, IntechOpen, https://doi.org/10.5772/7354.
Google Scholar
61 Gu H., Yan R., and Saha T. K., Minimum Synchronous Inertia Requirement of Renewable Power Systems, IEEE Transactions on Power Systems. (2018) 33, no. 2, 1533–1543, https://doi.org/10.1109/TPWRS.2017.2720621, 2-s2.0-85023746401.
10.1109/TPWRS.2017.2720621
Web of Science® Google Scholar
62 Liu Y., Yang S., Zhang S., and Peng F. Z., Comparison of Synchronous Condenser and STATCOM for Inertial Response Support, 2014 IEEE Energy Conversion Congress and Exposition (ECCE), 2014, IEEE, 2684–2690, https://doi.org/10.1109/ECCE.2014.6953761, 2-s2.0-84934274715.
10.1109/ECCE.2014.6953761
Google Scholar
63 Igbinovia F. O., Fandi G., Muller Z., and Tlusty J., Reputation of the Synchronous Condenser Technology in Modern Power Grid, 2018 International Conference on Power System Technology (POWERCON), 2018, IEEE, 2108–2115, https://doi.org/10.1109/POWERCON.2018.8601540, 2-s2.0-85058696187.
10.1109/POWERCON.2018.8601540
Google Scholar
64 Ruttledge L., Miller N. W., O’Sullivan J., and Flynn D., Frequency Response of Power Systems with Variable Speed Wind Turbines, IEEE Transactions on Sustainable Energy. (2012) 3, no. 4, 683–691, https://doi.org/10.1109/TSTE.2012.2202928, 2-s2.0-84883215624.
10.1109/TSTE.2012.2202928
Web of Science® Google Scholar
65 Holdsworth L., Ekanayake J. B., and Jenkins N., Power System Frequency Response from Fixed Speed and Doubly Fed Induction Generator-based Wind Turbines, Wind Energy. (2004) 7, no. 1, 21–35, https://doi.org/10.1002/we.105, 2-s2.0-3342969237.
10.1002/we.105
Web of Science® Google Scholar
66 Conroy J. F. and Watson R., Frequency Response Capability of Full Converter Wind Turbine Generators in Comparison to Conventional Generation, IEEE Transactions on Power Systems. (2008) 23, no. 2, 649–656, https://doi.org/10.1109/TPWRS.2008.920197, 2-s2.0-43849097550.
10.1109/TPWRS.2008.920197
Web of Science® Google Scholar
67 Beres R. N., Wang X., Liserre M., Blaabjerg F., and Bak C. L., A Review of Passive Power Filters for Three-phase Grid-Connected Voltage-Source Converters, IEEE Journal of Emerging and Selected Topics in Power Electronics. (2016) 4, no. 1, 54–69, https://doi.org/10.1109/JESTPE.2015.2507203, 2-s2.0-84962241692.
10.1109/JESTPE.2015.2507203
Web of Science® Google Scholar
68 Kjaer S. B., Pedersen J. K., and Blaabjerg F., A Review of Single-phase Grid-Connected Inverters for Photovoltaic Modules, IEEE Transactions on Industry Applications. (2005) 41, no. 5, 1292–1306, https://doi.org/10.1109/TIA.2005.853371, 2-s2.0-26844560797.
10.1109/TIA.2005.853371
Web of Science® Google Scholar
69 Rodriguez P., Luna A., Munoz-Aguilar R. S., Etxeberria-Otadui I., Teodorescu R., and Blaabjerg F., A Stationary Reference Frame Grid Synchronization System for Three-phase Grid-Connected Power Converters under Adverse Grid Conditions, IEEE Transactions on Power Electronics. (2012) 27, no. 1, 99–112, https://doi.org/10.1109/TPEL.2011.2159242, 2-s2.0-83655190880.
10.1109/TPEL.2011.2159242
Web of Science® Google Scholar
70 Rodriguez P., Luna A., Ciobotaru M., Teodorescu R., and Blaabjerg F., Advanced Grid Synchronization System for Power Converters under Unbalanced and Distorted Operating Conditions, IECON 2006-32nd Annual Conference on IEEE Industrial Electronics, 2006, IEEE, 5173–5178, https://doi.org/10.1109/IECON.2006.347807, 2-s2.0-50249106454.
10.1109/IECON.2006.347807
Google Scholar
71 Peralta D., Cañizares C., and Bhattacharya K., Practical Modeling of Flywheel Energy Storage for Primary Frequency Control in Power Grids, 2018 IEEE Power & Energy Society General Meeting (PESGM), 2018, IEEE, 1–5, https://doi.org/10.1109/PESGM.2018.8585844, 2-s2.0-85060785917.
10.1109/PESGM.2018.8585844
Google Scholar
72 Cheema K. M., Chaudhary N. I., Tahir M. F. et al., Virtual Synchronous Generator: Modifications, Stability Assessment and Future Applications, Energy Reports. (2022) 8, 1704–1717, https://doi.org/10.1016/j.egyr.2021.12.064.
10.1016/j.egyr.2021.12.064
Web of Science® Google Scholar
73 Alatrash H., Mensah A., Mark E., Haddad G., and Enslin J., Generator Emulation Controls for Photovoltaic Inverters, IEEE Transactions on Smart Grid. (2012) 3, no. 2, 996–1011, https://doi.org/10.1109/TSG.2012.2188916, 2-s2.0-84861897482.
10.1109/TSG.2012.2188916
Web of Science® Google Scholar
74 You S., Liu Y., Tan J. et al., Comparative Assessment of Tactics to Improve Primary Frequency Response without Curtailing Solar Output in High Photovoltaic Interconnection Grids, IEEE Transactions on Sustainable Energy. (2019) 10, no. 2, 718–728, https://doi.org/10.1109/TSTE.2018.2846233, 2-s2.0-85048484690.
10.1109/TSTE.2018.2846233
Web of Science® Google Scholar
75 Mishra S., Zarina P. P., and Sekhar P. C., A Novel Controller for Frequency Regulation in a Hybrid System with High PV Penetration, 2013 IEEE Power & Energy Society General Meeting, 2013, IEEE, 1–5, https://doi.org/10.1109/PESMG.2013.6672143, 2-s2.0-84893202875.
10.1109/PESMG.2013.6672143
Google Scholar
76 Zarina P. P., Mishra S., and Sekhar P. C., Exploring Frequency Control Capability of a PV System in a Hybrid PV-Rotating Machine-Without Storage System, International Journal of Electrical Power & Energy Systems. (2014) 60, 258–267, https://doi.org/10.1016/j.ijepes.2014.02.033, 2-s2.0-84897540130.
10.1016/j.ijepes.2014.02.033
Web of Science® Google Scholar
77 Rahmann C. and Castillo A., Fast Frequency Response Capability of Photovoltaic Power Plants: The Necessity of New Grid Requirements and Definitions, Energies. (2014) 7, no. 10, 6306–6322, https://doi.org/10.3390/en7106306, 2-s2.0-84908884619.
10.3390/en7106306
Web of Science® Google Scholar
78 Moutis P., Vassilakis A., Sampani A., and Hatziargyriou N. D., DC Switch Driven Active Power Output Control of Photovoltaic Inverters for the Provision of Frequency Regulation, IEEE Transactions on Sustainable Energy. (2015) 6, no. 4, 1485–1493, https://doi.org/10.1109/TSTE.2015.2450539, 2-s2.0-84960240326.
10.1109/TSTE.2015.2450539
Web of Science® Google Scholar
79 Zarina P. P., Mishra S., and Sekhar P. C., Deriving Inertial Response from a Non-inertial PV System for Frequency Regulation, 2012 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), 2012, IEEE, 1–5, https://doi.org/10.1109/PEDES.2012.6484409, 2-s2.0-84876016810.
10.1109/PEDES.2012.6484409
Google Scholar
80 Zarina P. P., Mishra S., and Sekhar P. C., Photovoltaic System Based Transient Mitigation and Frequency Regulation, 2012 Annual IEEE India Conference (INDICON), 2012, IEEE, 1245–1249, https://doi.org/10.1109/INDCON.2012.6420809, 2-s2.0-84874134720.
10.1109/INDCON.2012.6420809
Google Scholar
81 Xin H., Liu Y., Wang Z., Gan D., and Yang T., A New Frequency Regulation Strategy for Photovoltaic Systems without Energy Storage, IEEE Transactions on Sustainable Energy. (2013) 4, no. 4, 985–993, https://doi.org/10.1109/TSTE.2013.2261567, 2-s2.0-84884588860.
10.1109/TSTE.2013.2261567
Web of Science® Google Scholar
82 Al-Shetwi A. Q., Issa W. K., Aqeil R. F. et al., Active Power Control to Mitigate Frequency Deviations in Large-Scale Grid-Connected PV System Using Grid-Forming Single-Stage Inverters, Energies. (2022) 15, no. 6, https://doi.org/10.3390/en15062035.
10.3390/en15062035
Web of Science® Google Scholar
83 Sun Y. Z., Zhang Z. S., Li G. J., and Lin J., Review on Frequency Control of Power Systems with Wind Power Penetration, 2010 International Conference on Power System Technology, 2010, IEEE, 1–8, https://doi.org/10.1109/POWERCON.2010.5666151, 2-s2.0-78751562985.
10.1109/POWERCON.2010.5666151
Google Scholar
84 Wu Z., Gao W., Gao T. et al., State-of-the-art Review on Frequency Response of Wind Power Plants in Power Systems, Journal of Modern Power Systems and Clean Energy. (2018) 6, no. 1, 1–16, https://doi.org/10.1007/s40565-017-0315-y, 2-s2.0-85040826619.
10.1007/s40565-017-0315-y
Web of Science® Google Scholar
85 Taghizadeh M., Hoseintabar M., and Faiz J., Frequency Control of Isolated WT/PV/SOFC/UC Network with New Control Strategy for Improving SOFC Dynamic Response, International Transactions on Electrical Energy Systems. (2015) 25, no. 9, 1748–1770, https://doi.org/10.1002/etep.1925, 2-s2.0-84942254159.
10.1002/etep.1925
Web of Science® Google Scholar
86 Hosseini E. and Shahgholian G., Output Power Levelling for DFIG Wind Turbine System Using Intelligent Pitch Angle Control, Automatika. (2017) 58, no. 4, 363–374, https://doi.org/10.1080/00051144.2018.1455017, 2-s2.0-85056089537.
10.1080/00051144.2018.1455017
Web of Science® Google Scholar
87 Jing Y., Sun H., Zhang L., and Zhang T., Variable Speed Control of Wind Turbines Based on the Quasi-Continuous High-Order Sliding Mode Method, Energies. (2017) 10, no. 10, https://doi.org/10.3390/en10101626, 2-s2.0-85044528986.
10.3390/en10101626
Web of Science® Google Scholar
88 Çelik E., Kurt E., and Öztürk N., Wind Turbine Speed Control of a Contactless Piezoelectric Wind Energy Harvester, International Journal of Electronics. (2020) 107, no. 2, 226–238, https://doi.org/10.1080/00207217.2019.1643039.
10.1080/00207217.2019.1643039
Web of Science® Google Scholar
89 Bonfiglio A., Invernizzi M., Labella A., and Procopio R., Design and Implementation of a Variable Synthetic Inertia Controller for Wind Turbine Generators, IEEE Transactions on Power Systems. (2019) 34, no. 1, 754–764, https://doi.org/10.1109/TPWRS.2018.2865958, 2-s2.0-85059111391.
10.1109/TPWRS.2018.2865958
Web of Science® Google Scholar
90 Magnus D. M., Scharlau C. C., Pfitscher L. L., Costa G. C., and Silva G. M., A Novel Approach for Robust Control Design of Hidden Synthetic Inertia for Variable Speed Wind Turbines, Electric Power Systems Research. (2021) 196, https://doi.org/10.1016/j.epsr.2021.107267.
10.1016/j.epsr.2021.107267
Web of Science® Google Scholar
91 Gonzalez-Longatt F., Chikuni E., and Rashayi E., Effects of the Synthetic Inertia from Wind Power on the Total System Inertia after a Frequency Disturbance, 2013 IEEE International Conference on Industrial Technology (ICIT), 2013, IEEE, 826–832, https://doi.org/10.1109/PowerAfrica.2012.6498636, 2-s2.0-84877304228.
10.1109/PowerAfrica.2012.6498636
Google Scholar
92 Boyle J., Littler T., and Foley A. M., Frequency Regulation and Operating Reserve Techniques for Variable Speed Wind Turbines, 2021 IEEE Madrid PowerTech, 2021, IEEE, 1–5, https://doi.org/10.1109/PowerTech46648.2021.9495072.
10.1109/PowerTech46648.2021.9495072
Google Scholar
93 Tarnowski G. C., Kjar P. C., Sorensen P. E., and Ostergaard J., Variable Speed Wind Turbines Capability for Temporary Over-production, 2009 IEEE Power & Energy Society General Meeting, 2009, IEEE, 1–7, https://doi.org/10.1109/PES.2009.5275387, 2-s2.0-71849111103.
10.1109/PES.2009.5275387
Google Scholar
94 Ashabani M., Freijedo F. D., Golestan S., and Guerrero J. M., Inducverters: PLL-Less Converters with Auto-Synchronization and Emulated Inertia Capability, IEEE Transactions on Smart Grid. (2016) 7, no. 3, 1660–1674, https://doi.org/10.1109/TSG.2015.2468600, 2-s2.0-84941352435.
10.1109/TSG.2015.2468600
Web of Science® Google Scholar
95 Zhong Q. C. and Weiss G., Synchronverters: Inverters that Mimic Synchronous Generators, IEEE Transactions on Industrial Electronics. (2011) 58, no. 4, 1259–1267, https://doi.org/10.1109/TIE.2010.2048839, 2-s2.0-79952651962.
10.1109/TIE.2010.2048839
Web of Science® Google Scholar
96 Zhang L., Harnefors L., and Nee H. P., Power-synchronization Control of Grid-Connected Voltage-Source Converters, IEEE Transactions on Power Systems. (2010) 25, no. 2, 809–820, https://doi.org/10.1109/TPWRS.2009.2032231, 2-s2.0-77951667637.
10.1109/TPWRS.2009.2032231
Web of Science® Google Scholar
97 Zhang L., Harnefors L., and Nee H. P., Interconnection of Two Very Weak AC Systems by VSC-HVDC Links Using Power-Synchronization Control, IEEE Transactions on Power Systems. (2011) 26, no. 1, 344–355, https://doi.org/10.1109/TPWRS.2010.2047875, 2-s2.0-79151475005.
10.1109/TPWRS.2010.2047875
Web of Science® Google Scholar
98 Zhang L., Harnefors L., and Nee H. P., Modeling and Control of VSC-HVDC Links Connected to Island Systems, IEEE Transactions on Power Systems. (2011) 26, no. 2, 783–793, https://doi.org/10.1109/TPWRS.2010.2070085, 2-s2.0-79955528007.
10.1109/TPWRS.2010.2070085
Web of Science® Google Scholar
99 Al-Shetwi A. Q., Sujod M. Z., Blaabjerg F., and Yang Y., Fault Ride-Through Control of Grid-Connected Photovoltaic Power Plants: A Review, Solar Energy. (2019) 180, 340–350, https://doi.org/10.1016/j.solener.2019.01.032, 2-s2.0-85060107254.
10.1016/j.solener.2019.01.032
Web of Science® Google Scholar
100 Ashabani M. and Jung J., Synchronous Voltage Controllers: Voltage-Based Emulation of Synchronous Machines for the Integration of Renewable Energy Sources, IEEE Access. (2020) 8, 49497–49508, https://doi.org/10.1109/ACCESS.2020.2976892.
10.1109/ACCESS.2020.2976892
Web of Science® Google Scholar
101 Chen Y., Hesse R., Turschner D., and Beck H. P., Improving the Grid Power Quality Using Virtual Synchronous Machines, 2011 International Conference on Power Engineering, Energy and Electrical Drives, 2011, IEEE, 1–6, https://doi.org/10.1109/PowerEng.2011.6036498, 2-s2.0-82955210389.
10.1109/PowerEng.2011.6036498
Google Scholar
102 Beck H. P. and Hesse R., Virtual Synchronous Machine, 2007 9th International Conference on Electrical Power Quality and Utilisation, 2007, IEEE, 1–6, https://doi.org/10.1109/EPQU.2007.4424220, 2-s2.0-51149117207.
10.1109/EPQU.2007.4424220
Google Scholar
103 Van Wesenbeeck M. P. N., De Haan S. W. H., Varela P., and Visscher K., Grid Tied Converter with Virtual Kinetic Storage, 2009 IEEE Bucharest PowerTech, 2009, IEEE, 1–7, https://doi.org/10.1109/PTC.2009.5282048, 2-s2.0-74949122733.
10.1109/PTC.2009.5282048
Google Scholar
104 Yu M., Roscoe A. J., Booth C. D. et al., Use of an Inertia-Less Virtual Synchronous Machine within Future Power Networks with High Penetrations of Converters, 2016 Power Systems Computation Conference (PSCC), 2016, IEEE, 1–7, https://doi.org/10.1109/PSCC.2016.7540926, 2-s2.0-84986575830.
10.1109/PSCC.2016.7540926
Google Scholar
105 Fazeli M. and Holland P., Universal and Seamless Control of Distributed Resources-Energy Storage for All Operational Scenarios of Microgrids, IEEE Transactions on Energy Conversion. (2017) 32, no. 3, 963–973, https://doi.org/10.1109/TEC.2017.2689505, 2-s2.0-85029491611.
10.1109/TEC.2017.2689505
Web of Science® Google Scholar
106 Sakimoto K., Miura Y., and Ise T., Stabilization of a Power System with a Distributed Generator by a Virtual Synchronous Generator Function, 8th International Conference on Power Electronics-ECCE Asia, 2011, IEEE, 1498–1505, https://doi.org/10.1109/ICPE.2011.5944492, 2-s2.0-80052081192.
10.1109/ICPE.2011.5944492
Google Scholar
107 Liu J., Miura Y., Bevrani H., and Ise T., Enhanced Virtual Synchronous Generator Control for Parallel Inverters in Microgrids, IEEE Transactions on Smart Grid. (2017) 8, no. 5, 2268–2277, https://doi.org/10.1109/TSG.2016.2521405, 2-s2.0-84958611727.
10.1109/TSG.2016.2521405
Web of Science® Google Scholar
108 Alipoor J., Miura Y., and Ise T., Stability Assessment and Optimization Methods for Microgrid with Multiple VSG Units, IEEE Transactions on Smart Grid. (2018) 9, no. 2, 1462–1471, https://doi.org/10.1109/TSG.2016.2592508, 2-s2.0-85042492664.
10.1109/TSG.2016.2592508
Web of Science® Google Scholar
109 Hirase Y., Abe K., Sugimoto K., and Shindo Y., A Grid-connected Inverter with Virtual Synchronous Generator Model of Algebraic Type, IEEJ Transactions on Power and Energy. (2012) 132, no. 4, 371–380, https://doi.org/10.1541/ieejpes.132.371, 2-s2.0-84866879530.
10.1541/ieejpes.132.371
Google Scholar
110 Al-Shetwi A. Q., Hannan M. A., Jern K. P., Mansur M., and Mahlia T. M. I., Grid-connected Renewable Energy Sources: Review of the Recent Integration Requirements and Control Methods, Journal of Cleaner Production. (2020) 253, 119831–122020, https://doi.org/10.1016/j.jclepro.2019.119831.
10.1016/j.jclepro.2019.119831
Web of Science® Google Scholar
111 Al-Shetwi A. Q. and Sujod M. Z., Grid-connected Photovoltaic Power Plants: A Review of the Recent Integration Requirements in Modern Grid Codes, International Journal of Energy Research. (2018) 42, no. 5, 1849–1865, https://doi.org/10.1002/er.3983, 2-s2.0-85040710922.
10.1002/er.3983
Web of Science® Google Scholar
112 Jouini T., Markovic U., and Gros D., New Options for Existing System Services and Needs for New System Services, MIGRATE project Deliv. (2018) 3, 1–105.
Google Scholar
113 Enhanced Frequency Response Frequently Asked Questions, 2016, National Grid, UK, https://www2.nationalgrid.com/Enhanced-Frequency-Response.aspx.
Google Scholar
114 National grid Eso, Stability Pathfinder: Technical Performance and Assessment Criteria, 2019.
Google Scholar
115 Zhong Q. C., Nguyen P. L., Ma Z., and Sheng W., Self-synchronized Synchronverters: Inverters without a Dedicated Synchronization Unit, IEEE Transactions on Power Electronics. (2013) 29, no. 2, 617–630, https://doi.org/10.1109/TPEL.2013.2258684, 2-s2.0-84883223382.
10.1109/TPEL.2013.2258684
Web of Science® Google Scholar
116 Dong S., Jiang J., and Chen Y. C., Analysis of Synchronverter Self-Synchronization Dynamics to Facilitate Parameter Tuning, IEEE Transactions on Energy Conversion. (2020) 35, no. 1, 11–23, https://doi.org/10.1109/TEC.2019.2945958.
10.1109/TEC.2019.2945958
Web of Science® Google Scholar
117 Zhang W., Remon D., and Rodriguez P., Frequency Support Characteristics of Grid-interactive Power Converters Based on the Synchronous Power Controller, IET Renewable Power Generation. (2017) 11, no. 4, 470–479, https://doi.org/10.1049/iet-rpg.2016.0557, 2-s2.0-85019053918.
10.1049/iet-rpg.2016.0557
CAS Web of Science® Google Scholar
118 Zhang W., Cantarellas A. M., Rocabert J., Luna A., and Rodriguez P., Synchronous Power Controller with Flexible Droop Characteristics for Renewable Power Generation Systems, IEEE Transactions on Sustainable Energy. (2016) 7, no. 4, 1572–1582, https://doi.org/10.1109/TSTE.2016.2565059, 2-s2.0-84988704580.
10.1109/TSTE.2016.2565059
Web of Science® Google Scholar
119 Hesse R., Turschner D., and Beck H. P., Micro Grid Stabilization Using the Virtual Synchronous Machine (VISMA), Proceedings of the International Conference on Renewable Energies and Power Quality (ICREPQ’09), 2009, Valencia, Spain, 15–17.
Google Scholar
120 Chen Y., Hesse R., Turschner D., and Beck H. P., Dynamic Properties of the Virtual Synchronous Machine (VISMA), Renewable Energy and Power Quality Journal. (2011) 1, no. 9, 755–759, https://doi.org/10.24084/repqj09.444, 2-s2.0-84973228547.
10.24084/repqj09.444
Google Scholar
121 Mo O., D’Arco S., and Suul J. A., Evaluation of Virtual Synchronous Machines with Dynamic or Quasi-Stationary Machine Models, IEEE Transactions on Industrial Electronics. (2016) 64, no. 7, 5952–5962, https://doi.org/10.1109/TIE.2016.2638810, 2-s2.0-85028805310.
10.1109/TIE.2016.2638810
Web of Science® Google Scholar
122 Van Thong V., Woyte A., Albu M. et al., Virtual Synchronous Generator: Laboratory Scale Results and Field Demonstration, 2009 IEEE Bucharest PowerTech, 2009, IEEE, 1–6, https://doi.org/10.1109/PTC.2009.5281790, 2-s2.0-74949132544.
10.1109/PTC.2009.5281790
Google Scholar
123 Chen M. and Xiao X., Hierarchical Frequency Control Strategy of Hybrid droop/VSG-Based Islanded Microgrids, Electric Power Systems Research. (2018) 155, 131–143, https://doi.org/10.1016/j.epsr.2017.10.011, 2-s2.0-85031798256.
10.1016/j.epsr.2017.10.011
Web of Science® Google Scholar
124 Roscoe A. J., Yu M., Ierna R. et al., A VSM (Virtual Synchronous Machine) Convertor Control Model Suitable for RMS Studies for Resolving System Operator/owner Challenges, 15th Wind Integration Workshop, 2016.
Google Scholar
125 Castillo L. R. and Roscoe A., Experimental Validation of a Novel Inertia-Less VSM Algorithm, 2018 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), 2018, IEEE, 1–5, https://doi.org/10.1109/ISGT.2018.8403384, 2-s2.0-85050697076.
10.1109/ISGT.2018.8403384
Google Scholar
126 Fazeli M., Holland P. M., and Baruwa M., Grid-Less Power Systems: A Vision for Future Structure of Power Networks, IEEE Access. (2020) 8, 159120–159131, https://doi.org/10.1109/ACCESS.2020.3020455.
10.1109/ACCESS.2020.3020455
Web of Science® Google Scholar
127 Nasser N. and Fazeli M., Buffered-Microgrid Structure for Future Power Networks: A Seamless Microgrid Control, IEEE Transactions on Smart Grid. (2021) 12, no. 1, 131–140, https://doi.org/10.1109/TSG.2020.3015573.
10.1109/TSG.2020.3015573
Web of Science® Google Scholar
128 Alipoor J., Miura Y., and Ise T., Voltage Sag Ride-Through Performance of Virtual Synchronous Generator, IEEJ Journal of Industry Applications. (2015) 4, no. 5, 654–666, https://doi.org/10.1541/ieejjia.4.654, 2-s2.0-85018434671.
10.1541/ieejjia.4.654
Google Scholar
129 Kumar K. A., Kushwaha P., Prakash V., Bhakar R., Tiwari H., and Sharma K. G., Inertia Emulation Trends in Low Carbon Power System, 2019 8th International Conference on Power Systems (ICPS), December 2019, IEEE, 1–6, https://doi.org/10.1109/ICPS48983.2019.9067707.
10.1109/ICPS48983.2019.9067707
Google Scholar
130 Prakash V., Bhakar R., Tiwari H., and Sharma K. C., System Inertia Prediction for Primary Frequency Response Adequacy under Uncertain Wind Generation, 2018 8th IEEE India International Conference on Power Electronics (IICPE), December 2018, IEEE, 1–6, https://doi.org/10.1109/IICPE.2018.8709539, 2-s2.0-85065870447.
10.1109/IICPE.2018.8709539
Google Scholar
131 Prakash V., Bhakar R., Tiwari H., and Sharma K. C., Inertia and Primary Frequency Response Assessment under Uncertain Photovoltaic Generation, 2018 8th IEEE India International Conference on Power Electronics (IICPE), December 2018, IEEE, 1–6, https://doi.org/10.1109/IICPE.2018.8709511, 2-s2.0-85065872920.
10.1109/IICPE.2018.8709511
Google Scholar
132 Kushwaha P., Prakash V., and Bhakar R., A Novel Framework to Assess Synthetic Inertia & Primary Frequency Response Support from Energy Storage Systems, Sustainable Energy, Grids and Networks. (2023) 34, https://doi.org/10.1016/j.segan.2023.101052.
10.1016/j.segan.2023.101052
Web of Science® Google Scholar
133 Hoke A. F., Shirazi M., Chakraborty S., Muljadi E., and Maksimovic D., Rapid Active Power Control of Photovoltaic Systems for Grid Frequency Support, IEEE Journal of Emerging and Selected Topics in Power Electronics. (2017) 5, no. 3, 1154–1163, https://doi.org/10.1109/JESTPE.2017.2669299, 2-s2.0-85029489634.
10.1109/JESTPE.2017.2669299
Web of Science® Google Scholar
134 Fang J., Li X., Tang Y., and Hongchang L., Improvement of Frequency Stability in Power Electronics-Based Power Systems, 2017 Asian Conference on Energy, Power and Transportation Electrification (ACEPT), 2017, IEEE, 1–6, https://doi.org/10.1109/ACEPT.2017.8168614, 2-s2.0-85046000897.
10.1109/ACEPT.2017.8168614
Google Scholar
135 Guerrero J. M., Chandorkar M., Lee T. L., and Loh P. C., Advanced Control Architectures for Intelligent Microgrids—Part I: Decentralized and Hierarchical Control, IEEE Transactions on Industrial Electronics. (2013) 60, no. 4, 1254–1262, https://doi.org/10.1109/TIE.2012.2194969, 2-s2.0-84870551218.
10.1109/TIE.2012.2194969
Web of Science® Google Scholar
136 Sangwongwanich A., Yang Y., and Blaabjerg F., High-performance Constant Power Generation in Grid-Connected PV Systems, IEEE Transactions on Power Electronics. (2016) 31, no. 3, 1822–1825, https://doi.org/10.1109/TPEL.2015.2465151, 2-s2.0-84949501366.
10.1109/TPEL.2015.2465151
Web of Science® Google Scholar
137 Sangwongwanich A., Yang Y., Blaabjerg F., and Wang H., Benchmarking of Constant Power Generation Strategies for Single-phase Grid-Connected Photovoltaic Systems, 2016 IEEE Applied Power Electronics Conference and Exposition (APEC). (2016) 54, no. 1, 370–377, https://doi.org/10.1109/APEC.2016.7467899, 2-s2.0-84973667639.
10.1109/APEC.2016.7467899
Google Scholar
138 Fathi A., Shafiee Q., and Bevrani H., Robust Frequency Control of Microgrids Using an Extended Virtual Synchronous Generator, IEEE Transactions on Power Systems. (2018) 33, no. 6, 6289–6297, https://doi.org/10.1109/TPWRS.2018.2850880, 2-s2.0-85049152262.
10.1109/TPWRS.2018.2850880
Web of Science® Google Scholar
139 Borsche T. S., Liu T., and Hill D. J., Effects of Rotational Inertia on Power System Damping and Frequency Transients, 2015 54th IEEE Conference on Decision and Control (CDC), 2015, IEEE, 5940–5946, https://doi.org/10.1109/CDC.2015.7403153, 2-s2.0-84962013861.
10.1109/CDC.2015.7403153
Google Scholar
140 Poolla B. K., Bolognani S., and Dörfler F., Optimal Placement of Virtual Inertia in Power Grids, IEEE Transactions on Automatic Control. (2017) 62, no. 12, 6209–6220, https://doi.org/10.1109/TAC.2017.2703302.
10.1109/TAC.2017.2703302
Web of Science® Google Scholar
141 Alipoor J., Miura Y., and Ise T., Power System Stabilization Using Virtual Synchronous Generator with Alternating Moment of Inertia, IEEE journal of Emerging and selected topics in power electronics. (2015) 3, no. 2, 451–458, https://doi.org/10.1109/JESTPE.2014.2362530, 2-s2.0-84929173198.
10.1109/JESTPE.2014.2362530
Web of Science® Google Scholar
142 Li D., Zhu Q., Lin S., and Bian X. Y., A Self-Adaptive Inertia and Damping Combination Control of VSG to Support Frequency Stability, IEEE Transactions on Energy Conversion. (2017) 32, no. 1, 397–398, https://doi.org/10.1109/TEC.2016.2623982, 2-s2.0-85015028883.
10.1109/TEC.2016.2623982
Web of Science® Google Scholar
143 Torres M. A., Lopes L. A. C., Moran L. A., and Espinoza J. R., Self-tuning Virtual Synchronous Machine: A Control Strategy for Energy Storage Systems to Support Dynamic Frequency Control, IEEE Transactions on Energy Conversion. (2014) 29, no. 4, 833–840, https://doi.org/10.1109/TEC.2014.2362577, 2-s2.0-84913594252.
10.1109/TEC.2014.2362577
Web of Science® Google Scholar
144 Poolla B. K., Groß D., Borsche T., Bolognani S., and Dörfler F., Virtual Inertia Placement in Electric Power Grids, Energy Markets and Responsive Grids: Modeling, Control, and Optimization. (2018) 281–305, https://doi.org/10.1007/978-1-4939-7822-9_12.
10.1007/978-1-4939-7822-9_12
Google Scholar
145 Ela E., Gevorgian V., Tuohy A., Kirby B., Milligan M., and O’Malley M., Market Designs for the Primary Frequency Response Ancillary Service—Part I: Motivation and Design, IEEE Transactions on Power Systems. (2014) 29, no. 1, 421–431, https://doi.org/10.1109/TPWRS.2013.2264942, 2-s2.0-84891539635.
10.1109/TPWRS.2013.2264942
Web of Science® Google Scholar
146 Ela E., Gevorgian V., Tuohy A., Kirby B., Milligan M., and O’Malley M., Market Designs for the Primary Frequency Response Ancillary Service—Part II: Case Studies, IEEE Transactions on Power Systems. (2014) 29, no. 1, 432–440, https://doi.org/10.1109/TPWRS.2013.2264951, 2-s2.0-84891547030.
10.1109/TPWRS.2013.2264951
Web of Science® Google Scholar
147 Shi Z., Yao W., Li Z. et al., Artificial Intelligence Techniques for Stability Analysis and Control in Smart Grids: Methodologies, Applications, Challenges and Future Directions, Applied Energy. (2020) 278, https://doi.org/10.1016/j.apenergy.2020.115733.
10.1016/j.apenergy.2020.115733
Web of Science® Google Scholar
148 Saadatmand S., Nia M. S. S., Shamsi P., Ferdowsi M., and Wunsch D. C., Neural Network Predictive Controller for Grid-Connected Virtual Synchronous Generator, 2019 North American Power Symposium (NAPS), 2019, IEEE, 1–6, https://doi.org/10.2139/ssrn.3562136.
10.1109/NAPS46351.2019.9000386
Google Scholar
149 Yao F., Zhao J., Li X., Mao L., and Qu K., RBF Neural Network Based Virtual Synchronous Generator Control with Improved Frequency Stability, IEEE Transactions on Industrial Informatics. (2021) 17, no. 6, 4014–4024, https://doi.org/10.1109/TII.2020.3011810.
10.1109/TII.2020.3011810
Web of Science® Google Scholar
150 Xu Q., Dragicevic T., Xie L., and Blaabjerg F., Artificial Intelligence-Based Control Design for Reliable Virtual Synchronous Generators, IEEE Transactions on Power Electronics. (2021) 36, no. 8, 9453–9464, https://doi.org/10.1109/TPEL.2021.3050197.
10.1109/TPEL.2021.3050197
Web of Science® Google Scholar
151 Teng Q., Xu D., Yang W., Li J., and Shi P., Neural Network-Based Integral Sliding Mode Backstepping Control for Virtual Synchronous Generators, Energy Reports. (2021) 7, 1–9, https://doi.org/10.1016/j.egyr.2020.11.032.
10.1016/j.egyr.2020.11.032
Web of Science® Google Scholar
152 Nguyen H. T., Yang G., Nielsen A. H., and Jensen P. H., Frequency Stability Improvement of Low Inertia Systems Using Synchronous Condensers, 2016 IEEE International Conference on Smart Grid Communications (SmartGridComm), 2016, IEEE, 650–655, https://doi.org/10.1109/SmartGridComm.2016.7778835, 2-s2.0-85010202023.
10.1109/SmartGridComm.2016.7778835
Google Scholar
153 Great Britain’s Battery Fleet Dispatching 47% More Energy after Changes Brought in by ESO, 2024, https://www.energy-storage.news/great-britains-battery-fleet-dispatching-47-more-energy-after-changes-brought-in-by-eso/.
Google Scholar
154 Flexitricity, UK’s Largest Battery Ready to Balance the Grid, 2024, https://www.flexitricity.com/resources/press-release/uks-largest-battery-ready-balance-grid.
Google Scholar
155 Denholm P., Clark K., and O’Connell M., Emerging Issues and Challenges in Integrating High Levels of Solar into the Electrical Generation and Transmission System, 2016, National Renewable Energy Laboratory, Golden, CO.
Google Scholar
156 Mather B. and Neal R., Integrating High Penetrations of PV into Southern California: Year 2 Project Update, 2012 38th IEEE Photovoltaic Specialists Conference, 2012, IEEE, 000737–000741, https://doi.org/10.1109/PVSC.2012.6317711, 2-s2.0-84869466988.
10.1109/PVSC.2012.6317711
Google Scholar
157 Planning G., Los Angeles Department of Water and Power-Energy Storage Development Plan, 2014.
Google Scholar
158 Shuai Z., Huang W., Shen C., Ge J., and Shen Z. J., Characteristics and Restraining Method of Fast Transient Inrush Fault Currents in Synchronverters, IEEE Transactions on Industrial Electronics. (2017) 64, no. 9, 7487–7497, https://doi.org/10.1109/TIE.2017.2652362, 2-s2.0-85025121851.
10.1109/TIE.2017.2652362
Web of Science® Google Scholar

Citing Literature

All articles

The Power Grid Inertia With High Renewable Energy Sources Integration: A Comprehensive Review

Abstract

1. Introduction

2. Inertia in Conventional Power Grid

3. Techniques to Enhance the Inertia

3.1. Synchronous Condensers (SCs)

3.2. WTs

3.3. Storage Energy Systems

3.3.1. DC-Link Capacitor

3.3.2. Ultracapacitor

3.3.3. Batteries

3.3.4. Flywheels

3.3.5. Hydropower

4. Virtual Synchronous Machines (VSMs)

4.1. Deloading Technique

4.1.1. For PV Power Plant

4.1.2. For Wind Power Plants

4.2. Inducverters

4.3. Synchronverters

4.4. Power Synchronization Controller

4.5. Synchronous Voltage Controller (Sync VC)

4.6. Fifth-Order VSM Topology

4.7. VSM With Low-Order Model

4.8. VSM0H

4.9. Universal VSM

4.10. ISE Lab VSM

4.11. Algebraic Model of VSM

4.12. Discussion

5. Some Issues of Inertia Implementation

5.1. Time Delays

5.1.1. Communication Time Delay

5.1.2. Power Control of Individual Power Converter Time Delay

5.2. Placement of Inertia

5.3. Adaptive Inertia

5.4. Market Design for Inertia Service

6. AI as a Solution to Enhance Inertia

7. Practical Case Studies and Applications

7.1. Case Study 1: Denmark’s High-RES Grid With SCs and WTs

7.2. Case Study 2: Great Britain’s National Grid With VSMs and Battery ESSs

7.3. Case Study 3: California’s High Solar Penetration and ESS Integration

8. Conclusion

Nomenclature

Conflicts of Interest

Funding

Open Research

Data Availability Statement

References

Citing Literature

Figures

References

Related

Information