Renewable energy is connected to the grid through the inverter, which in turn reduces the inertia and stability of the power grid itself. The traditional grid-connected inverter does not have the function of voltage regulation and frequency regulation and can therefore no longer adapt to the new development. The virtual synchronous generator (VSG) has the function of voltage regulation and frequency regulation, which has more prominent advantages than traditional inverters. Based on the principle of VSG, the relationship between the frequency characteristics and the energy storage capacity of the feedforward branch-based virtual synchronous machine (FVSG) is derived when the input power and grid frequency change. Reveal the relationship between the virtual inertia coefficient, damping coefficient, and frequency characteristics of VSG and energy storage capacity. An energy storage configuration method that meets the requirements of frequency variation characteristics is proposed. A mathematical model is established, and the Matlab/Simulink simulation software is used for modeling. The simulation results verify the relationship between the inertia coefficient, damping coefficient, and energy storage demand of the FVSG.

With the rapid development and innovation of what is often called “new energy,” represented by photovoltaic and wind power, these resources have been more widely used and worked into power grids over recent years [

Geng et al. [

Meng et al. [

This paper first proposes a feed-forward branch-based virtual synchronous generator (FVSG) system for the optimisation of the robustness of conventional VSGs. The relationship between the frequency characteristics and parameters of the FVSG, the inertia and damping coefficients, and the capacity and charging/discharging characteristics of the energy storage unit are then all analysed in the presence of input power disturbances and grid frequency variations. The corresponding relationships are derived to give the optimal configuration parameters of the energy storage unit. The results of the study can be used for the design of FVSG parameters and the capacity configuration of energy storage devices.

The synchronous generator has a rotor and has a particular inertia, so the system’s frequency will not change abruptly in a short time. The VSG introduces virtual inertia moment control in the control algorithm of the inverter to simulate the rotor inertia of the synchronous generator. The mechanical rotation equation of the synchronous generator is shown in equation [_{s} is the mechanical torque input by the generator; _{e} is the electromagnetic torque of the generator;

The mechanical power of the synchronous generator is defined as equation

The electromagnetic power of the synchronous generator is defined as equation

The equation can be obtained from equation to

The VSG simulates the rotor motion equation of the synchronous generator mainly by controlling the control algorithm of the inverter. It can simulate the moment of inertia and damping characteristics of the synchronous generator and realize the stability and droop characteristics of the output voltage and frequency of the virtual synchronous generator. The schematic diagram of the virtual synchronization machine is shown in

In the figure: _{out} is the output power; _{in} is the input power; _{es} is the charging and discharging power of the energy storage device; _{a}, _{b} and _{c} are the output three-phase phase voltages; _{ga}, _{gb}, and _{gc} are the three-phase phase voltages of the grid; _{dc} is the input DC bus voltage.

When the number of pole pairs of the VSG is considered to be 1, the angular frequency of the induced electromotive force is the same as the mechanical angular frequency of the rotor rotating, and the equation can be obtained from the equation

Use _{in0} to represent the rated input power of the VSG, and _{out0} to represent the rated output power of the VSG.

Let

Equations can be obtained when the VSG operates under the rated steady-state operating conditions.

Equation can be obtained from equations to

The active output power of the generator can be expressed as equation
_{a}, _{b} and _{c}; _{g} represents the effective value of _{ga}, _{gb} and _{gc}. Let _{0} represents the rated of value of _{a}, _{b} and _{c};

Since

When _{g} are constant, because of

Let

The variation of the VSG angle of attack can be expressed as equation

Equations are the small-signal time-domain mathematical models of the VSG. Laplace transform can be used to obtain the small-signal frequency-domain mathematical model of VSG, as shown in equations to

According to equations to, the transfer function block diagram of VSG can be obtained as shown in

A robust optimal control method of FVSG is proposed. In the case of input power and grid frequency disturbance, the VSG can maintain relative stability, and the transient process is smooth without oscillation. After the feedforward branch is added to the controller of the VSG, the control block diagram is shown in

In the figure,

The increased feedforward gain does not affect the power linearization process. Therefore, the FVSG and the traditional VSG have the same synchronization coefficient

The inertial and frequency modulation responses of FVSG are shown in

Considering only the influence of input power disturbance on frequency, without considering the impact of grid frequency variation, the equation can be obtained by making

The equation indicates that the system adjusts the FVSG power angle by adjusting the frequency

The oscillation angular frequency

It can be seen from the equation that the larger the moment of inertia

In the case of overdamping, let

The maximum value of

Similarly, when Critical damping, the maximum value of

Similarly, when underdamped, the maximum value of

It can be seen from equations that the larger the moment of inertia

Considering only the influence of grid frequency disturbance on FVSG frequency, without considering the influence of input power change, let

The equation is a typical second-order system. The oscillation angular frequency

The adjustment time in the case of overdamping and critical damping is relatively long and is not considered.

When underdamped, the adjustment time _{s} can be approximately expressed as an equation with an allowable error of 2%.

The energy storage device is directly related to the input power of the FVSG and the grid frequency disturbance, as well as the inertia coefficient and damping coefficient of the FVSG. The configuration of FVSG energy storage parameters is mainly to determine the inertia coefficient and damping coefficient according to the actual demand. The demand for energy storage is then determined based on the parameters of the FVSG, input power, and grid frequency disturbance. The following is mainly analyzed from two aspects of input power and grid frequency disturbance.

When only analyzing the influence of input power disturbance on frequency, without considering the impact of grid frequency disturbance, let

The equation can be obtained from

Thus, the charging and discharging power of the energy storage device can be obtained as in equation

The equation can be obtained from the work below:

According to the physical meaning of inertia, the equation can be obtained

Equation is the standard second-order transfer function model. The following analysis is divided into 3 cases according to different damping ratios, and the case of negative damping (

When the system is overdamped (

The equation can be written as such
_{1 }= 1/_{1}, _{2 }= 1/_{2}.

The equation can be expressed as a cascade of two first-order systems when the damping coefficient is much larger than 1, when the pole _{2} is far from the imaginary axis and can be neglected. Therefore, the transfer function model shown in the equation above can be simplified to a first-order system as shown in equation below:

Generally, the step response reaches 95% to 98% of the steady-state value after a_{1} (where a takes the value of 3 to 4) time. Therefore, it can be considered that in the overdamped case, the regulation time of VSG, which is the response time required for energy storage, is shown in the equation below:

When

Therefore, it is known that when the input power is disturbed, the maximum charge and discharge energy of the energy storage device is also the minimum capacity of the energy storage device, and the minimum capacity of the required configuration of the energy storage capacity is shown in the equation.

When the system is critically damped (

Thus, the mathematical model can be expressed as an equation

Similar to the case of over-damping, the regulation time of the system at this time

When

When the system is underdamped (0<

Let

The time to reach the steady-state value for the first time is shown in the equation

The regulation time of the system is shown in the equation
_{s1}, _{s2} are the times of 95% and 98% overshoot, respectively, which are also the response times required by the energy storage device. The maximum charge/discharge energy of the energy storage device is obtained when the steady-state value is reached for the first time. The energy absorbed by the energy storage device throughout the step process, which is the area of the shaded part when the steady-state is reached as shown in

In the case of over-damping, critical damping, and under-damping, the inertia coefficient J is less than, equal to, and greater than

When only the influence of input power disturbance on frequency is analyzed, and the influence of grid frequency disturbance is not considered, let in

The equation can be obtained from the following:

According to the physical meaning of inertia, equation can be obtained as the following:

The charging and discharging of the energy from and of energy storage device consists of two main components: one is the difference between the output power of the FVSG and the input power after reaching the new steady-state due to the change in the frequency of the grid, and its charging and discharging power value is _{in} of the FVSG, so that

If it cannot be regulated by the input power, this part of the energy storage capacity demand is

The equation is the second-order transfer function model. The following analysis is performed in 3 cases according to different damping ratios, and the case of negative damping (ζ < 0) is not considered because it is unstable.

When the system is overdamped (

When

Therefore it is known that when the grid frequency changes, the maximum charge and discharge energy of the energy storage device is also the minimum capacity of the energy storage device. The minimum capacity of the required configuration of the energy storage capacity needs to satisfy the equation.

When the system is critically damped (

When

When the system is underdamped (0<

When the steady-state value is reached, the maximum charge/discharge energy of the energy storage device is obtained. The energy absorbed by the energy storage device throughout the step process is the area of the shaded part in

In the case of over-damping, critical damping and under-damping, the inertia coefficient

In summary, although different

Damping ratio | Minimum design capacity of energy storage equipment | |
---|---|---|

Input power disturbance | Grid frequency change | |

Over-damping | Equation | Equation |

Critical damping | Equation | Equation |

Under-damping | Equation | Equation |

In order to verify the relationship between the charging and discharging power and capacity parameters of the energy storage device and the inertia coefficient and damping coefficient FVSG. Use Matlab/Simulink to build a simulation model. The relevant parameter settings are shown in

Parameter | Unit | Value | ||
---|---|---|---|---|

Overdamped |
Critical damping |
Underdamped |
||

kg·m^{2} |
268 | 268 | 546 | |

N·m·s | 84682 | 1068 | 1068 | |

W·rad^{−1} |
1 × 10^{7} |
|||

_{0} |
rad·s^{−1} |
10 |
||

_{0} |
kV | 6.6 |

In the simulation of charging and discharging energy, when the FVSG input power is disturbed,

The under-damped parameters in

It can be seen from the

The simulation curve of the frequency response when the input power is disturbed is shown in

The simulation results in

When the grid frequency is disturbed, the critical damping parameters in

The simulation results in

The parameters of _{max} equation.

The simulation results in

The minimum energy storage device design should meet the maximum value of charging and discharging energy to ensure the maximum charging and discharging demand required when output power disturbances or grid frequency changes occur.

The parameters of

It can be seen from

As can be seen from

In the actual selection of parameters, it is also necessary to combine with the actual situation, a comprehensive cost-effective consideration, and the selection of appropriate parameters together.

In this paper, the relationship among frequency characteristics, inertia coefficient, damping coefficient, and energy storage capacity of FVSG is deduced in detail. Matlab/Simulink carries out the simulation verification. Research indicates:

FVSG robustness is optimised to maintain its relative stability during input power perturbations and grid frequency changes, improving the adaptiveness of the parameters.

Changing the inertia and damping coefficients has a greater impact on the fluctuation of the output power. The smaller the inertia coefficient and the larger the damping coefficient, the better the stability of the output power. Combined with economic considerations, the FVSG has better immunity to interference at a damping factor of 0.707.

In order to improve the immunity of the FVSG, the inertia and damping coefficients need to be increased, as well as a larger capacity of the energy storage device. When the energy storage capacity of the FVSG is insufficient, the output of the FVSG will not be controlled as expected and will cause voltage fluctuations. Therefore, the actual design has to meet the minimum charge and discharge requirements of the FVSG.

_{s}

Mechanical torque

_{e}

Electromagnetic torque

Damping coefficient

Moment of inertia

_{in}

Input power

_{out}

Output power

_{in0}

Rated input power

_{out0}

Rated output power

_{es}

The charging and discharging power of the energy storage device

Mechanical angular frequency

Rated angular frequency

Grid frequency

Difference between output corner frequency and rated corner frequency

Difference between actual input power and rated input power

Difference between actual output power and rated output power

_{a}, u

_{b}, u

_{c}

Output three-phase voltage

_{ga}, u

_{gb}, u

_{gc}

Three-phase voltage of the grid

_{dc}

DC bus voltage

Valid values for _{a}_{b}_{c}

_{g}

Valid values for _{ga}_{ga}_{gc}

_{0}

Ratings for _{a}_{b}_{c}

Rated power angle

Feedforward gain

Charge and discharge energy of energy storage device

Synchronization factor

This paper is completed under the careful guidance of my tutor. The teacher’s profound professional knowledge, rigorous academic attitude, excellent work style, tireless noble ethics, noble kind of self-discipline and leniency, and approachable and straightforward personality charm have a far-reaching impact on me. Not only did I set a lofty academic goal and master the basic research methods, but it also made me understand many ways to deal with people and circumstances. From the topic selection to the completion of this paper, each step is completed under the tutor’s guidance, and the teacher has devoted a lot of effort. I want to express my high respect and heartfelt thanks to the teacher!