# Overview on Grid-Forming Inverter Control Methods

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Terminology

## 3. Functional Principle of Synchronous Machines

_{f}and another part related to the reactive current I

_{r}. Both effects occur with a delay of the open-circuit time constant (T

_{d0}′). The first part reflects the reference transfer behavior of the excitation voltage U

_{f}to the synchronous generated voltage

_{d}′ is active. During the process, the reactance decays to the synchronous value x

_{d}. This transition is illustrated in Figure 1.

_{0}and ϑ is the rotation angle. The damping parameter D represents the mechanical damping according to friction and windage.

_{i}. For the whole paper, the generator convention is adopted [14] (pp. 20–27) as commonly used for power sources.

## 4. Grid-Forming Inverter Control Methods

#### 4.1. Droop-Based Grid-Forming Control Methods (e.g. Selfsync)

_{0}and U

_{0}denote the nominal values. In a similar way, reference [17] deals with the stand-alone operation of static inverters and suggests a method in which a voltage and frequency drop behavior in relation to the output reactive and active power is imposed. The purpose is to achieve load sharing among power sources without explicit communication. Likewise, in [18] droops are deployed in combination with a virtual flux control. In the meantime, a multitude of droop-based approaches have been published [19].

_{e}, T

_{m}), in order to eliminate oscillations, due to harmonics, and to obtain a more-smooth reaction. Afterwards, the value is fed back to generate the internal inverter voltage. A reasonable improvement compared to the normal droop control can be gained by an angle feedforward proportional to the active power flow, which was first introduced in [20] or [21] and is referenced as Selfsync. We concentrate on this approach in the following elaboration.

_{q}corresponds to (x

_{d}− x

_{d}′). Consequently, the reactive power droop can be interpreted as impedance evolution similar to that of the synchronous machine (see Figure 1): In the first moment only the filter impedance of the inverter is active and due to the imposed droop, the impedance in the reactive current path is adjusted to a higher stationary (synchronous) value. The time constant T

_{e}is in accordance to the open-circuit time constant T

_{d0}′ of the synchronous machine. It should be noted that the reactive power is used here. Strictly speaking, the relation between the reactive current and the voltage amplitude is not precisely linear here, due to voltage variations. Therefore, these conclusions are only valid around the nominal operating voltage. On the other hand, it is possible to normalize the droop parameter by the output voltage. By doing so, the reactive power droop changes to a reactive current droop.

_{m}/k

_{p}is equivalent to the inertia time constant and 1/k

_{p}is equal to the mechanical feedback damping parameter D. As an extension to the basic functionality, forward damping is achieved, due to the angle feedforward. This damping is much more effective against oscillation, as it bypasses the integrator. Consequently, a better stability and transient performance was observed when using such a technique. The damper windings have a similar effect, since they inherently produce a counter torque according to the slip (deviation from the synchronous rotation) of the machine.

_{m}is chosen according to the acceleration time of the grid (~10 s). Hence, it is a measure for the inertia contribution in relation to the nominal power of the grid-forming unit. The time constant for the voltage amplitude is chosen lower. The droop parameters k

_{p}and k

_{q}mean that, at nominal power, the frequency or voltage drop is 5% and 10%, respectively. Additionally, an adequate feedforward damping is achieved with a value around 5 pu.

_{p,d}is similar to the angle feedforward by k

_{p}′. The effect of k

_{q,d}is that the reactance of the reactive current path is virtually further increased in relation to the rate of current change during a transient process. The consequence is that the time development of the reactance is not so smooth and more dynamic.

#### 4.2. Power Synchronization Loop

_{E}defines the negative gain for the impedance L

_{i,}so that in a steady state, the new value is (ωL

_{i}/(1+K

_{E})) and T

_{E}is responsible for the continuous time delay with which the impedance is adapted. This can be deduced from the transfer function from the resulting current flow to the provided voltage drop. The closed voltage amplitude loop can therefore be restated (Figure 9) under the assumption that I

_{a}has only a very small influence on the voltage amplitude at the point of common coupling.

#### 4.3. Voltage Controlled Inverter (VCI)

_{p}/2πK

_{i}) equally to that of the Selfsync approach. Here, K

_{Prim}equals the feedback damping factor D and (1+K

_{P}K

_{Prim})/K

_{I}is the inertia time constant.

#### 4.4. Virtual Synchronous Machine (VSM)

_{pf}in order to reflect that change.

_{0}and 2π are condensed into a single time constant T

_{a}= 2H and a forward damping constant K

_{df}is introduced, which can be dimensioned to effectively dampen oscillations between generators.

#### 4.5. Virtual Oscillator Control (VOC)

_{i}and κ

_{v}serve as scaling factors for the interface between the real hardware and the virtual oscillator. The inductance and the capacitance of the oscillating circuit are chosen in such a way that the resonant frequency matches the nominal frequency ω

_{0}.

_{0}and the nominal reactive power Q

_{0}. The block diagram of the VOC as the averaged model is shown in Figure 16. The linearized Q/U-loop reduces to a PT1 element similar to the electromagnetic behavior of the synchronous machine. In this way, 1/K corresponds to (x

_{d}− x

_{d}′) and Z/K corresponds to the time constant T

_{d0}′.

#### 4.6. Matching Control

_{g}is the nominal or grid frequency and U

_{DC}is the dc-link voltage. The control law incorporates both the dc-voltage regulation and the synchronization to the grid.

_{J}is the inertia emulation coefficient, K

_{T}is responsible for the DC-link voltage tracking and K

_{D}is the damping coefficient.

#### 4.7. PLL-Based Modified Current-Controlled Methods

_{e}being the electrical power between two voltage sources with amplitude U,E and angle ϑ

_{1,2}over the inductive impedance X

_{i}

_{p}and assuming the mechanical power P

_{m}in Equation (17) to be zero, the similarity of the PLL structure and Equation (17) becomes visible:

_{i}, K

_{d}to

_{p}for additional damping and to improve the frequency detection speed, see Figure 19. However, the design of the PLL gain factors follows the same approach.

_{i}:

_{PCC}being the measured terminal voltage amplitude and U being the inverters voltage amplitude.

_{PCC}. In turn, the changes in the amplitude of U

_{PCC}are determined by the reactive current flow, as seen in Figure 8.

_{0}, which equals U

_{PCC}in idle mode or could be adjusted in terms of outer control loops. Consequently, the provided voltage amplitude is given as a function of the reactive current deviation ΔI

_{r}from the nominal or initial value:

#### 4.8. Direct Power Control (DPC)

_{c}is the phase angle shift related to the PLL angle θ

_{pll}. Hence, a retarded adjustment of the controlled angle ϑ

_{c}is undermined, when the PLL follows the grid voltage too quickly. Thus, for analyzing the overall control performance, the dynamics of the PLL is of great importance. A closer look into the PLL and its parameterization is not given in the Reference.

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Transient evolution of the impedance after a current step (derived from [13] (p. 244)).

**Figure 7.**Power synchronization control loop according to [27].

**Figure 10.**Frequency controller of the voltage controlled inverter VCI according to [30].

**Figure 13.**Elimination of the impedance by the integrator action with the appropriate time constant.

**Figure 15.**Illustration of the virtual oscillator circuit according to [43].

**Figure 17.**Functional principle of matching control according to [46].

**Figure 19.**Phase locked loop (PLL) structure for calculation of an additional active power setpoint for inertial response of inverters according to [53].

**Figure 20.**Generalized transfer function between active power and voltage angle of PLL-based inertial response methods.

**Figure 21.**Generalized transfer function between reactive power and voltage amplitude of inverters with modified grid current control.

**Figure 22.**Direct power control according to [69].

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

T_{m} | k_{p}·10 s |

k_{p} | 0.05 pu |

T_{e} | 1 s |

k_{q} | 0.1 pu |

k_{p}’ | 5 pu |

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**MDPI and ACS Style**

Unruh, P.; Nuschke, M.; Strauß, P.; Welck, F. Overview on Grid-Forming Inverter Control Methods. *Energies* **2020**, *13*, 2589.
https://doi.org/10.3390/en13102589

**AMA Style**

Unruh P, Nuschke M, Strauß P, Welck F. Overview on Grid-Forming Inverter Control Methods. *Energies*. 2020; 13(10):2589.
https://doi.org/10.3390/en13102589

**Chicago/Turabian Style**

Unruh, Peter, Maria Nuschke, Philipp Strauß, and Friedrich Welck. 2020. "Overview on Grid-Forming Inverter Control Methods" *Energies* 13, no. 10: 2589.
https://doi.org/10.3390/en13102589