# Virtual Inertia-Based Inverters for Mitigating Frequency Instability in Grid-Connected Renewable Energy System: A Review

^{*}

## Abstract

**:**

## 1. Introduction

- RES exhibits low or non-existent inertial responses which lead to frequency instability [8].
- In the event of a fault and sudden load change, the system frequency deviates from the nominal frequency [9].
- The frequency nadir and rate of change of frequency (RoCoF) are expected to be higher in the event of a fault or sudden load change, which activates the load-shedding controller to trip frequency relay [10].

## 2. Implementation of VI-Based Inverters

- Reduction in frequency nadir and frequency deviation from nominal frequency (f
_{n}) - Less overshoot and faster transient or respond time
- Less RoCoF and less steep gradient
- Faster recovery time to the nominal frequency

#### 2.1. VSM

- Step 1:
- The voltages at point of common coupling (PCC) between the output of VSM and grid are measured to compute the phase currents of the VISMA in real-time.
- Step 2:
- The computed currents are utilized as reference currents for a current-controlled inverter.
- Step 3:
- The pulse width modulation (PWM) modulator drives the inverter.

_{ref}) is sent to the hysteresis current controller. This implementation has numerical instability, especially in the higher order of the SM model. In contrast, for voltage references, the voltage amplitude and phase angle are directly utilized for the generation of PWM to drive the converter. This method is very similar to synchronverter implementation. The power reference is based on the active and reactive power references generated from active and reactive power controllers to drive the PWM via a voltage reference calculator. Table 1 presents the merits and demerits of a general VSM. Table 2 shows the recent researches and implementations of VSM in various applications, such as RES, microgrid and smart grid.

#### 2.2. VSG

_{d}and V

_{q}are defined as the d-axis and q-axis components of the measured grid voltage (v). The q-axis current reference (${I}_{q}^{*}$) and the reactive power (Q) is defined as zero, assuming that only the active power is being controlled. This is because the regulation of grid frequency involves the manipulation of active power only. Hence, based on the described terminology, VSG is a current-controlled voltage source inverter, with VI. VSG is popular and used by the European VSYNC research group. It is also widely validated through real-time simulations, field tests, remote microgrid, wind systems, and other applications. The design of VSG control strategies can be categorized into two types, either addressing via output or topology. For the output variant, the VSG can be further sub-divided into the controlled current source and a controlled voltage source. The foundation of VSG is based on SG as the voltage source. Figure 9 illustrates the control strategy of a generic VSG which consists of both active power (P) and reactive power (Q) calculation blocks to generate reference current (I

_{ref}) for the PWM control. Figure 10 and Figure 11 show the detailed mathematical modelling of active power loop (APL) and reactive power loop (RPL) respectively.

- Step 1:
- The grid voltage (V) at PCC between the output of VSG and the grid is measured and sent to the processing unit, which contains the VSG algorithm.
- Step 2:
- The processing unit uses the SM model to compute the stator current of the VSG.
- Step 3:
- Current controller sends the gate signal to inverter based on the calculated reference current (I
_{ref}).

_{I}and K

_{D}. It minimizes RoCoF and power flow through ESS, neural-network-based controller, and adaptive dynamic programming (ADP), since the ESS injects and absorbs active power (P) and reactive power (Q) actively while AI-based controller enables adaptive moment of inertia (J) and damping factor (D) VSG topology has extended and improved over the years. The frequency nadirs and peaks in the system can be further minimized by utilizing higher energy and power exchange through VI system or vice versa. Active and reactive power dynamic decoupling technique for VSG is vital for medium- and low-voltage microgrids [46]. A self-adaptable reactive power-voltage controller to resolve the sharing problem of reactive power in the parallel VSG. It is executed by using the difference in reactive power to adjust the reactive power-voltage control coefficient [47].

#### 2.3. Synchronverter

_{,}regulate the generated and consumed real power and regulate the reactive power if it is connected to grid. Synchronverter is modeled by using SG swing equations [61]. Equations (3), (4) and (6) are fundamental equations, used to mathematically describe the dynamic of the SG. Equation (7) defines the vectors of three-phase stator flux ($\phi $), voltage (v), current (i), $\tilde{\mathrm{cos}\theta}$, and $\tilde{\mathrm{sin}\theta}$. The field excitation current is denoted by i

_{f}while mutual-inductance between stator and field winding is denoted by M

_{f}. T

_{e}, e, P, Q, i

_{f}, and $\dot{\theta}$ are electromagnetic torque, back electromotive force (EMF) or synchronverter inner generated voltage, active power, reactive power, field current, and Virtual angular speed of the machine, respectively. $\tilde{\mathrm{cos}\theta}$ and $\tilde{\mathrm{sin}\theta}$ are vectors defined as the three-phase angle difference with equal spacing of 120° or $2\pi /3$ in radian.

_{m}) is a control input while the electromagnetic torque (T

_{e}) depends on the i and $\theta $. Hence, the state variables of the synchronverter are the following: i (the inductor currents), v (the capacitor voltages), θ (virtual angle), and $\dot{\theta}$ (a virtual angular speed). The moment of inertia is denoted by J, 1/s is the integrator, D

_{p}is the damping factor for active power loop, D

_{q}is the damping factor for reactive power loop, K is the regulator coefficient of reactive power, Q

_{SET}is the set point of reactive power, $\dot{\theta}$

_{r}is the reference angular velocity, $\dot{\theta}$

_{m}is the measured feedback angular velocity, V

_{r}is the reference r.m.s voltage, and V

_{m}is the measured feedback grid voltage.

_{m}and M

_{f}i

_{f}. To operate the synchronverter, the controller is designated to generate the control signals T

_{m}and M

_{f}i

_{f}in a way that system stability is maintained and the desired values of real and reactive power are obeyed. The synchronverter is controlled by two (dual) channels, similar to the synchronous generator. The two channels are real power and reactive power. The frequency droop control loop controls the real power, while the voltage droop controls the reactive power. The frequency droop compares the $\dot{\theta}$ with the ${\dot{\theta}}_{r}$ which normally equals the nominal angular frequency of the grid (${\dot{\theta}}_{m}$). This difference is multiplied with a gain to the active mechanical torque, T

_{m}. The mechanical friction coefficient and the frequency drooping coefficient is denoted as D

_{p}. This frequency loop regulates $\dot{\theta}$ of the SG and creates the phase angle (θ) for the control signal (e).

_{q}). It regulates the M

_{f}i

_{f}which is proportional to the amplitude of the voltage generated. In general, a synchronverter has power part and electronic part. The power part is the conventional inverter structure with switching devices (metal–oxide–semiconductor field-effect transistor (MOSFET) or insulated-gate bipolar transistor (IGBT)), gate driver, power sources, inductor-capacitor-inductor (LCL) filter, and other electronic components to convert DC to AC. On the contrary, the electronic part of synchronverter is a control unit comprising of sensors, analogue to digital converter (ADC), and measurement devices, interfaced to a microcontroller, DSP, or any computing devices. The function of the electronic part is to control the gate signal of switching devices in the power part via PWM. The modeling of synchronverter is based on the dynamic characteristic of an SG. The mathematical model ranges from second to seventh order. The higher is the order, the more accurate is the modeling, but with higher complexity and longer calculation time. Hence, the third order is most popular due to its balance between accuracy and complexity.

## 3. Applications of VI-Based Inverters

#### 3.1. Grid-Connected RES

#### 3.2. HVDC Transmission

#### 3.3. ESS

#### 3.4. Microgrid

#### 3.5. EV

## 4. Comparison of VI-Based Inverters

_{a}is the mechanical time constant, and P

_{d}is the damping power. For VSG, P

_{O}is the initial power, P

_{VSG}is the output power, $d\mathsf{\Delta}\omega /dt$ is the RoCoF, Kω is the inertia emulation characteristic, and ${K}_{D}$ is the damping factor constant. For synchronverter, P

_{SET}is the desired active power setpoint, D

_{P}is the damping factor, and f

_{ref}is the reference frequency.

## 5. Future Research

- The definition of a new grid code and standards: Grid code and standards should enable the integration of large-scale RES into the power grid, by enforcing VI emulation. The frequency regulation should be contributed by RES, and grid-forming inverter should be mandatory.
- The revision of existing reserve policy: Further technical studies and economic analysis are recommended to revise the current policy to adjust proper frequency reserve margin. It is to suit the high penetration of RES in balancing between cost and performance.
- The development of new storage technologies for frequency regulation: Both supercapacitor and ultracapacitor are promising storage technologies that are applicable to VI emulation.

#### 5.1. Current Challenges and Limitations

_{P}) and integral gain (K

_{I}) must be robust. It is to ensure that transient response, settling time, overshoots, and oscillations are satisfactory. The robustness of the PI controller is limited because operating environments such as temperature, weather, power surge, sudden load change, and occurrence of faults may affect the performance. The PI controller is not adaptive and does not learn over time. It is required to fine-tune the controllers to ensure the system is stable for every new model. The current limitation of existing VI technique is the requirement of fine-tuning for the frequency droop coefficient, inertia constant, and load frequency controller parameters. The tuning process cannot guarantee the frequency stability of microgrid with low inertia. System reliability should be emphasized to continuously access the robustness of frequency regulation [94]. Generally, VI-based inverter is a relatively new design for a modern power system. Due to its new conceptual design and architecture, there are still many unexplored areas yet to be resolved.

#### 5.2. ESS for VI System

#### 5.3. Current Market and Commercialized VI Service

^{2}[100]. This SI unit represents the behavior of present SM and suitable for the application of VI. The cost of inertia can be defined as cost per kg m

^{2}to indicate how much the cost will it be for every single unit of kg m

^{2}inertia. VI is also crucial for any power which requires high reliability and stability. This includes modern data centers, hospitals, server centers, and power grids which require an uninterruptible and stable power supply. Any commercial inverter can be improved by emulating VI to become VI-based converter to be power grid ready. The EV requires bidirectional converter (DC to AC) and VI is potential to stabilize the power transfer.

#### 5.4. Industrial Implementation of VI-Based Inverters

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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Merits | Demerits |
---|---|

- Suppress grid disturbances - Automatic synchronization and power-sharing ability - For both stand-alone and microgrid operation - Conceptual simplicity | - Long TET because of Park Transformation - Numerical instability - Complex PLL implementation |

Type of Application | Ref. | Type of VSM/VISMA | Highlights of the Control Strategy |
---|---|---|---|

DC Microgrids | [33] | VSM for DC Microgrids | VSM is designed to improve the inertia of DC microgrid and reduce the fluctuation of the DC bus voltage. |

MMC | [34] | VSM for MMC | VSM control strategy is applied for MMC to operate and control it as an SG. |

General | [32] | Enhanced VSM | The enhanced VSM (eVSM) exhibits larger inertia which eliminates the requirement of a large DC-link element or BESS. |

Microgrid | [35] | VSM with EES for a stand-alone microgrid | ESS is integrated by VSM-based inverter to the grid and a double second-order generalized integrator PLL to regulate frequency during transient conditions. |

Load | [36] | Load VSM | Load virtual synchronous machine topology and corresponding control strategy to mimic the characteristics of an SM. |

General | [37] | Optimal design of the VI and damping coefficient | H2 norm objective function is utilized to calculate the coefficient values for VSM. |

Smart grids | [38] | VSM for distributed control of power converters in smart grids | A VSM is designed to provide smart grid support and allow a seamless transition between grid-connected or islanded operation. |

Merits | Demerits |
---|---|

- Enable load sharing among parallel-connected units - Unlike SG, the parameter of VSG (H and D) can be controlled in real-time - Fast response in tracking steady-state frequency - No magnetic saturation and eddy current losses - Can act as a motor - Simple implementation - Typical current-source implementation with inherent overcurrent protection | - Long execution time because of Park Transformation - Instability due to the presence of PLL especially in weak grid - The presence of frequency derivative introduced noise - Unable to implement in islanded mode since it is not a grid forming unit - It emulates inertia during frequency variation, not input power variation |

Type of Application | Ref. | Type of VSG | Highlights of the Control Strategy |
---|---|---|---|

General | [43] | Fuzzy Secondary Controller (FSC) | Fuzzy logic control (FLC) algorithm, which is a type of artificial intelligence (AI) method is applied for VSG control. |

[49] | Power decoupling control strategy | Active power and reactive power are independently controlled for the enhanced decoupling strategy for VSGs. | |

[45] | Adaptive Control for VSG | The inertia and damping coefficient of VSG is adjusted flexibly to achieve better dynamic performance. | |

Wind Energy | [50] | VI Control Strategy in Microgrid | The state information of the generator and ESS are utilized for VI control to regulate output frequency in a direct and accurate manner. |

[51] | VSG with Short-Term Energy Storage | The VSG is integrated with short-term minute-level energy storage. | |

[52] | Inertia estimation of VSG-controlled Type 4 WTGs | The wind turbine generator is controlled by VSG based on motion equation concept. | |

HVDC | [53] | VSG Control Strategy for HVDC | VSG control is adapted for voltage-source converter-based multiterminal high-voltage direct current |

Frequency protection | [54] | PSO-based VSG | Particle swarm optimization (PSO) is applied to optimize VI constant of VSG. |

Microgrid | [44] | Extended VSG for Microgrid | The H∞ control method is applied to tune the virtual parameters of VSG. |

[55] | Robust VI Control by H infinity control method | A robust H∞ based VI controller is designed to minimize the frequency deviations of an islanded microgrid. | |

[56] | VSG with digital frequency protection | VSG is designed to stabilize the system frequency with digital frequency protection to interface with small and large scales of power systems. | |

[57] | Optimized VSG Control by PSO | PSO is utilized to optimize the values of virtual inertia constant and virtual damping factor. | |

[41] | A hybrid AC/DC microgrid control system based on a VSG | An improved VSG with a pre-synchronization controller is applied for hybrid AC to DC microgrid system. |

Merits | Demerits |
---|---|

- Self-synchronizing to the grid frequency without any additional controller, unless there is a large disturbance - Scalable by parallel connection in sharing real and reactive power - Technological maturity-control synchronverter is the same way as controlling a synchronous generator - Robust and dynamic control of PQ and voltage phase as well frequency - Does not require PLL for self-synchronizing synchronverter - Frequency derivative which known for noise is not presented | - No overcurrent protection due to voltage-source implementation - Differential equation complexity causes numerical instability - Voltage-source control has no inherent protection against severe grid transient - Require external protection for safe operation |

Type of Application | Ref. | Type of Synchronverter | Highlights of Control Strategy |
---|---|---|---|

General | [66] | Hot seamless transfer | Additional seamless transfer branch to enable single-phase synchronverter acts as an uninterrupted power source |

[62] | Self-synchronized synchronverter | Modification on synchronverter which does not require PLL to synchronize itself to the grid. Instead of PLL, virtual impedance is utilized. | |

[71] | Self-synchronized synchronverter with enhanced dynamics and current limitation | The droop ratio is decoupled from the damping coefficient and a PR current inner loop is added. | |

[64] | Bounded frequency and voltage | Integration of bounded frequency and voltage to ensure synchronverter always operates in a stable region. | |

[72] | Modified self-synchronized synchronverter | A filter has been used in filter-based current feeding loops to eliminate the power ripples. | |

Solar PV | [65] | Grid-connected PV inverters without PLL | Self-synchronizing inverter without the need of PLL is able to interface the solar PV system to the utility grid. |

[67] | Bounded droop control | It provides the synchronverter with power limitation and more flexible design process. | |

[16] | Grid integration of PV system using synchronverter | Interface solar photovoltaic module was connected as DC source to the inverter. The inverter was connected to the grid without any transformer. | |

HVDC | [73] | Synchronverter-based emulation and control of HVDC | Control strategy for HVDC based on synchronverter |

Renewable Power Generation Systems | [74] | Flexible droop characteristics | The controller has flexibility since it avoids the constraint between the damping and droop characteristics in power regulating loop. |

Wind Farm | [17] | Self-synchronization of wind farm in MMC-based HVDC | Synchronverter is implemented on the wind energy conversion system converter to synchronize them to the Modular MMC-based HVDC system. |

ESS | [75] | Grid-connected ESS using synchronverters | Lithium-ion batteries as ESS is connected to the power grid via synchronverters. It improves the stability of the grid and supplies power during high demand. |

Power system | [70] | Synchronverter for damping inter-area oscillations in two-area power systems | Synchronverter is utilized to improve the damping of inter-area oscillations and transient stability of a power system. |

Parameter | VSM | VSG | Synchronverter |
---|---|---|---|

Converter type | VSC | ||

Inverter type | Current-controlled | Voltage-controlled | |

Based on | SM | SG | |

Model order | Up to seventh order | Up to second order | |

Complexity | High | Medium | |

Grid mode | Yes | ||

Standalone mode | Not applicable | Yes | |

Grid viewpoint | Different than SG | As an SG | |

Dependency on the tracking of ref. I or V | Yes | No | |

Cost | High | ||

General mathematical model | $\frac{d{\omega}_{VSM}}{dt}=\frac{{P}^{*}}{{T}_{a}}-\frac{P}{{T}_{a}}-\frac{{P}_{d}}{{T}_{a}}$ | ${P}_{VSG}={P}_{0}+K\omega \frac{d\mathsf{\Delta}\omega}{dt}+{K}_{D}\mathsf{\Delta}\omega $ | ${P}_{set}+{D}_{p}({f}_{ref}-{f}_{grid})-{P}_{0}=J\omega \frac{d\omega}{dt}$ |

Algorithm Implementation Complexity | Moderate—higher order of SG model | Hard—parameters difficult to adjust and dependent on unstable PLL | Easy—second-order SG model and can operate with or without PLL |

Readiness for commercial and industrial inverter | Ready for full commercialization: ABB, Schneider Electric, FREQCON | ||

Readiness for the grid or power system operator | Hydro-Québec TransÉnergie’s (HQT’s) Canada; National Grid Electricity System Operator (NGESO), Great Britain; Electric Reliability Council of Texas grid; South African Grid Code | ||

Research and Development (R&D) Funding | SYNDEM | VSYNC project (EU), 2007; IEPE Group; ISE Lab; Kawasaki Heavy Industries (KHI) | Synchronverter- European Commission, Q3 Energie GmbH & Co. |

Type of Inverter | Grid-Forming | Grid-Following |
---|---|---|

VI-based Inverters | Synchronverter and VSM | VSG |

Function | Supporting the grid | Following the grid |

Source behavior from grid viewpoint | Voltage source | Current source |

Set grid voltage and frequency | Yes | No (Follow the grid) |

Provide active and reactive power to the load via voltage | Yes | Inject active and reactive power |

Response | Slow response due to large inertia | Fast response to the intermittent |

Inertial response | Yes | No |

Buffer | Yes | No |

Instable due to intermittent irradiance (PV) or wind | No | Yes |

Support weak grid operation | Yes | No |

Islanding | Yes | No |

Deviation from the nominal frequency | Higher | Lower |

RoCoF | Similar | |

Peak power injection during disturbance | Smaller | Larger |

Injection of active power | Not application | Yes |

The manipulation of frequency of voltage | Yes | Not application |

Order of Model | Model Implementation | Reference Voltage | Reference Current | Reference Power (P&Q) | Merit | Demerit | |
---|---|---|---|---|---|---|---|

Direct PWM | V&I Controllers | ||||||

Seventh-order model | Electric, magnetic, swing equation of stator and rotor winding | Possible | Possible | VSM | N/A | Full representation of SG dynamics with all parameters | Highly complex and high computational burden |

Fifth- or fourth-order model | Electric, magnetic, swing equation of stator winding | VSM | Possible | VSM | N/A | Best balance between complexity and computational burden | Only stator winding is considered compared to seventh-order model |

Second-order model | Swing equation and voltage amplitude is given by the reactive power controller | Synchronverter | Ongoing research | Conceptual | VSG | Most common scheme of converter implementation for a simple and close imitation | Lack of some parameters compared to seventh-order model |

First-order model | Inertial emulation by power response calculated from grid voltage tracking | N/A | N/A | Possible | VSYNC and VSG | Simplest and fastest implementation | Incapable of isolated operation and insufficient modeling |

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## Share and Cite

**MDPI and ACS Style**

Yap, K.Y.; Sarimuthu, C.R.; Lim, J.M.-Y. Virtual Inertia-Based Inverters for Mitigating Frequency Instability in Grid-Connected Renewable Energy System: A Review. *Appl. Sci.* **2019**, *9*, 5300.
https://doi.org/10.3390/app9245300

**AMA Style**

Yap KY, Sarimuthu CR, Lim JM-Y. Virtual Inertia-Based Inverters for Mitigating Frequency Instability in Grid-Connected Renewable Energy System: A Review. *Applied Sciences*. 2019; 9(24):5300.
https://doi.org/10.3390/app9245300

**Chicago/Turabian Style**

Yap, Kah Yung, Charles R. Sarimuthu, and Joanne Mun-Yee Lim. 2019. "Virtual Inertia-Based Inverters for Mitigating Frequency Instability in Grid-Connected Renewable Energy System: A Review" *Applied Sciences* 9, no. 24: 5300.
https://doi.org/10.3390/app9245300