# Development of a Novel Control Scheme for Grid-Following Converter under Asymmetrical Faults

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation and Incitement

#### 1.2. Literature Review

^{−}). However, this scheme also needed angle information to confirm the safe operation of the converter and it did not confirm better utilization of the converter’s current capacity. In [14], the authors proposed a control scheme for the static synchronous compensator (STATCOM) under unbalanced conditions. This scheme also involved the true angle difference between the voltage sequence phasors. It computed the current for each phase and identified that the maximum of these should be less than or equal to the current limit of the converter.

#### 1.3. Contribution and Paper Organization

- Simplified and accurate current limiting scheme for unbalanced faults, which fulfills the requirements of recent grid codes while ensuring the maximum current limit of the converter.
- Ensuring better utilization of the converter’s capacity during unbalanced faults.
- A robust control scheme for the negative sequence current injection without a dedicated PLL.
- Sequence extraction scheme in αβ-domain based on the delay sampling method.
- Comparison of the priority injection schemes for different types of faults.

## 2. Layout of Test Network

## 3. Control Schemes

#### 3.1. Conventional Control Scheme

_{q}) is zero. Thus:

^{+}) ranges from 2 to 6. The range of the proportional constant is defined in German grid code (VDE-AR-N 4110). A summary of this code can be found in [16]:

_{d}is less than i

^{max}

_{NC}(maximum allowed current in normal conditions). This is to have some margin for the reactive power support in normal conditions:

#### 3.2. Proposed Control Scheme

#### 3.2.1. Sequence Extraction Scheme

^{−2Ts}operator was introduced. The output of the delayed operator was used as the delayed signal in (15). The layout diagram is given in Figure 8 and the expressions for the discrete domain are given in (16).

_{s}) is at least five times the controller step time; but, in this case, more harmonic injections are expected.

#### 3.2.2. Reference Current Generation Scheme

^{-}∆v

_{n}. For this purpose, the expression given below in (18) was derived.

_{αβ,n}

^{*}is calculated from (18), it comes to be i

_{qn}

^{*}= k

^{−}∆v

_{n}, which is according to the grid codes. To verify that the injected current in the negative sequence corresponds to the reactive power, the following expressions were derived.

#### 3.2.3. Priority and Limit Selection

_{dp}, i

_{qp}, i

_{dn}and i

_{qn}are the horizontal and vertical projections of the positive and negative current phasors in the synchronous rotating frame of reference.

^{−j}

^{(ωt+}

^{θp}

^{)}and applying the definition of (21) to (20), then the new expression is as given in (22).

_{dn}= 0 in (23) leads to a simpler expression that is given in (24).

_{qp}, i

_{dp}can be put to zero and the cos term can be defined as equal to one (maximum limit).

_{dp}, the term involving i

_{dp}is taken as maximum (sin(δ) to 1). The term i

_{qp}cos(δ) is a critical one, which decides the better use of the converter’s current capacity. If the numeric addition of positive and negative sequence current phasors is limited to the maximum current capacity, then cos(δ) should be taken as one; however, this scenario does not give the better utilization of the converter’s current capacity. On the other hand, if the cos(δ) is taken as zero then the maximum utilization of the converter’s current capacity is ensured but, in this case, the maximum current in the faulty phase may go up to 5% higher than the maximum converter’s current limit. In order to get better performance, this value is selected as ¼ (cos(δ) to 1/4) in these calculations. These values are selected to simplify the expression for the i

_{dp}and also to get the accurate current limit. Keeping in view the above discussion, the current limits for NQP are given in (25) and for the QNP are given in (26).

_{qn}is considered to be in phase with the i

_{qp}while computing the limits for i

_{qp}and, for i

_{dp}the major projection of i

_{qn}is projected on the i

_{dp}. In this way, simpler expressions can be computed for the current limits in unbalanced conditions. This scheme works well irrespective of the type of fault, the severity of the fault, and the reference real and reactive powers. Moreover, it is not affected by the low-pass filters and the performance limitations of the PLL.

## 4. Results and Discussions

_{a}”.

_{a}control schemes.

#### 4.1. Numerical Example

_{p}= 0.6 and v

_{n}= 0.29, the reference real power (p

^{*}) is 0.95 and q* = 0, k

^{±}= 2. The pre-fault reactive current will be zero in this case. The maximum current limit (i

^{max}) is 1.2 p.u. To calculate the reference reactive current, use the expression given in (17).

_{dp}

^{*}= 1.58; i

_{qp}

^{*}= −0.8; i

_{qn}

^{*}= −0.58

#### 4.1.1. BCI Scheme

_{qn}

^{lim}is zero.

_{qn}

^{lim}= 0; i

_{qn}

^{**}= 0; i

_{qp}

^{lim}= i

^{max}= ±1.2; i

_{qp}

^{**}= −0.8;

_{dp}

^{lim}= ±0.895; i

_{dp}

^{**}= 0.895;

_{p}= 1.2; i

_{n}= 0; i = i

_{p}+ i

_{n}= 1.2

#### 4.1.2. QNP Priority with Proposed Scheme

_{qp}

^{lim}= i

^{max}= ±1.2; i

_{qp}

^{**}= −0.8; i

_{qn}

^{lim}= ±0.4; i

_{qn}

^{**}= −0.4;

_{dp}

^{lim}= ±0.4; i

_{dp}

^{**}= 0.4;

_{p}= 0.8944; i

_{n}= 0.4; i = i

_{p}+ i

_{n}= 1.295

#### 4.1.3. NQP Priority with Proposed Scheme

_{qn}

^{lim}= ±1.2; i

_{qn}

^{**}= −0.58; i

_{qp}

^{lim}= ±0.62; i

_{qp}

^{**}= −0.62;

_{dp}

^{lim}= ±0.36; i

_{dp}

^{**}= 0.36;

_{p}= 0.715; i

_{n}= 0.58; i = i

_{p}+ i

_{n}= 1.295

#### 4.1.4. NQP Priority with PNSI_{a} Scheme

_{qn}

^{lim}= ±1.2; i

_{qn}

^{**}= −0.58; i

_{qp}

^{lim}= ±0.62; i

_{qp}

^{**}= −0.62;

_{dp}

^{lim}= 0.0; i

_{dp}

^{**}= 0.0;

_{p}= 0.62; i

_{n}= 0.58; i = i

_{p}+ i

_{n}= 1.2

#### 4.2. Simulation Results

_{a}scheme was activated. It is also important to mention that the PNSI

_{a}also had the NQP priority scheme in this study. Moreover, for the simulation results, the reference real power was 0.95 p.u and the reference reactive power was zero.

^{±}was chosen as 2 for these simulations.

#### 4.2.1. Single Line to Ground Fault (SLG)

_{n}/v

_{p}). Less UF means more uniform voltage among the phases. According to subplot Figure 10e, the proposed scheme results in less UF factor compared to the BCI scheme. It is also important to mention here that in case of high impedance faults, the different priority schemes give the same result. This is due to the lower reactive current requirement arising from lower ∆v

_{p}and ∆v

_{n}. However, with the increasing severity of the fault, the priority schemes have different responses, which will be discussed for the line-to-line fault and double line-to-ground faults.

#### 4.2.2. Line-to-Line Fault (LL)

_{a}schemes, respectively. The maximum amplitudes are given in Table 2. Moreover, subplot Figure 11b shows that almost every control scheme was able to confirm the safe operation of the converter. As far as the comparison for the PNSI

_{a}scheme is concerned, it is clear from the subplot Figure 11b, that the PNSI

_{a}scheme injected more current in the healthy phase and less current in one of the faulty phases compared to the NQP priority scheme with the proposed control. Similarly, from subplot Figure 11c, it is clear that the PNSI

_{a}scheme injected a lower total current compared to the proposed scheme. This is because the PNSI

_{a}scheme confirmed the converter’s safe operation by limiting the maximum point of the elliptical trajectory to the maximum current and considering the numeric addition of sequence phasors; however, the proposed scheme did not consider both the phasors exactly in phase. This is the reason why the numeric addition of the positive and negative sequence current phasors was more than the maximum current limit of the converter for the QNP and NQP, although the maximum phase current was still within the converter’s current limit. This means that the PNSI

_{a}scheme did not use the full capacity of the converter, but the newly proposed scheme was able to use it efficiently.

_{a}schemes, followed by the QNP and BCI schemes, respectively. Hence, based on the UF and better utilization of the converter, it can be concluded that the proposed control scheme with NQP priority injection is more suitable compared to the rest of the schemes.

#### 4.2.3. Double Line to Ground Fault (DLG)

_{a}schemes gave better results, followed by the QNP and BCI schemes, respectively.

_{a}schemes had less UF compared to the QNP and BCI. Overall, the performance of the control schemes for the DLG fault was similar to their performance for the LL fault.

_{a}scheme. The key parameters were the healthy phase overvoltage, voltage unbalance factor, maximum current injection in the healthy and faulty phase(s), the converter’s current limitation, and the maximum utilization of the converter. Different color bars are used in order to define the performance of the schemes for a particular parameter. Green is for the best performance followed by light green, orange, and red, respectively.

_{a}fulfill the recent grid codes, the difference between the two schemes is in the current limitation calculation. From these results, it can be confirmed that the PNSI

_{a}limits the current based on the numeric addition of the positive and negative sequence current phasors, due to which, it is unable to use the converter’s current capacity effectively in case of asymmetrical faults; however, the proposed scheme is able to use the converter’s current capacity effectively. Hence, better utilization of the converter is ensured by the proposed current limiting scheme. Moreover, unlike the PNSI

_{a}scheme, the newly proposed scheme does not need to consider the angle of the positive sequence current phasor. From a grid perspective, the NQP priority scheme is better than the QNP priority scheme. Like the PNSI

_{a}scheme, the results presented in [6,7,8,9] show that the numeric sum of the positive and negative sequence current phasors is equal to the maximum current capacity of the converter, which means that the presented schemes are unable to use the maximum current capacity of the converter effectively. The proposed scheme provides better utilization of the converter’s current capacity, and it also does not need the true angular difference between the positive and negative sequences.

## 5. Conclusions

_{a}scheme, and other schemes presented in the literature. The results show its advantage over these schemes. Moreover, the two priority schemes were also compared; it was found that the NQP priority scheme gives better performance compared to the QNP scheme under different faulty conditions.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbol | Description |

k^{+-} | Proportional constant for positive and negative sequence injection |

∆v_{p} | Change in magnitude of the positive sequence voltage phasor |

∆v_{n} | Change in magnitude of the negative sequence voltage phasor |

∆i_{qp} | Change in reactive current injection for positive sequence |

∆i_{qn} | Change in reactive current injection for negative sequence |

v_{g} | Grid’s voltage |

R_{g} | Grid’s resistance |

L_{g} | Grid’s inductance |

L_{f} | Filter’s inductance |

C_{f} | Filter’s capacitance |

v_{dc} | DC link voltage |

v_{abc}^{*} | Converter’s reference voltage |

v_{pcc} | Three-phase voltage at Point of Common Coupling (PCC) |

i_{abc} | Three-phase feed in current by the converter |

f | Fundamental frequency |

ω | Angular frequency (2пf) |

ω_{PLL} | Angular frequency for phase-locked loop |

p* | Reference real power of the converter |

q* | Reference reactive power of the converter |

v_{αβ} | Alpha-Beta (αβ) components of measured voltage |

v_{dq} | dq-components of measured voltage phasor |

i_{dq} | dq-components of measured current phasor |

i_{dq}^{*} | dq-components of the reference current |

v_{dq}^{*} | dq-components of the reference voltage |

θ | Initial phase angle of the voltage phasor |

θ_{p} | Initial phase angle of the positive sequence voltage phasor |

ω_{p} | Angular frequency of positive sequence voltage phasor |

θ_{n} | Initial phase angle of the negative sequence voltage phasor |

v_{p} | Magnitude of the positive sequence voltage phasor |

v_{n} | Magnitude of the negative sequence voltage phasor |

v_{αβ,p} | αβ-components of the positive sequence voltage |

v_{αβ,n} | αβ-components of the negative sequence voltage |

v_{dq,p} | dq-components of the positive sequence voltage |

i_{dq,p}^{*} | dq-components of the reference current for the positive sequence |

i_{αβ,n}^{*} | αβ-components of the reference current for the negative sequence |

i_{αβ} | αβ-components of the measured current |

i_{αβ}^{**} | αβ-components of the reference current after applying the priority and current limit scheme |

V_{p} | Positive sequence voltage phasor |

V_{n} | Negative sequence voltage phasor |

a | Unity phasor with an angle of 120° |

T_{s} | Unit sample time |

i^{max} | Magnitude of maximum current |

i_{x}^{lim} | Limit value for the current of type “x” |

i_{p} | Positive sequence current phasor’s magnitude |

i_{n} | Negative sequence current phasor’s magnitude |

i | Phasor of measured current |

φ_{p,n} | Initial angle of the corresponding current phasor |

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**Figure 9.**Phasor diagram for the resultant current and its sequence components [5].

**Figure 10.**Performance comparison of different schemes for SLG Fault. (

**a**) instantaneous three phase voltages (phase to neutral) at PCC, (

**b**) instantaneous three phase converter’s currents, (

**c**) magnitude of positive and negative sequence current phasor, (

**d**) reference current components for positive and negative sequences, (

**e**) magnitude of positive and negative sequence voltage phasor along with unbalanced factor.

**Figure 11.**Performance comparison of different schemes for LL Fault. (

**a**) instantaneous three phase voltages (phase to neutral) at PCC, (

**b**) instantaneous three phase converter’s currents, (

**c**) magnitude of positive and negative sequence current phasor, (

**d**) reference current components for positive and negative sequences, (

**e**) magnitude of positive and negative sequence voltage phasor along with unbalanced factor.

**Figure 12.**Performance comparison of different schemes for DLG Fault. (

**a**) instantaneous three phase voltages (phase to neutral) at PCC, (

**b**) instantaneous three phase converter’s currents, (

**c**) magnitude of positive and negative sequence current phasor, (

**d**) reference current components for positive and negative sequences, (

**e**) magnitude of positive and negative sequence voltage phasor along with unbalanced factor.

Grid | |||||

Voltage (L-L) | Frequency | Short Circuit Power | X/R | ||

400 V | 50 Hz | 800 kVA | 5 | ||

Filter | |||||

Inductance (L_{f}) | Capacitance (C_{f}) | ||||

0.38 mH | 95 uF | ||||

Transformer | |||||

Type | Rated Power | Voltage | Rated Frequency | Reactance | Resistance |

Y∆1 | 200 kVA | 400/260 V | 50 Hz | 0.03 p.u | 0.0012 p.u |

Inverter | |||||

Rated Power | Rated Voltage (L-L) | DC link voltage (v_{dc}) | |||

100 kVA | 260 V | 425 V |

Fault Type | Parameter | NQP ≈ | PNSI_{a}≈ | QNP ≈ | BCI ≈ | Reduction with NQP (%) | Reduction with PNSI_{a} (%) | Reduction with QNP (%) | |||
---|---|---|---|---|---|---|---|---|---|---|---|

SLG | Phase over voltage (p.u) | 1.06 | 1.06 | 1.06 | 1.09 | 2.75 | 2.75 | 2.75 | |||

Voltage unbalance factor | 0.32 | 0.32 | 0.32 | 0.37 | 13.51 | 13.51 | 13.51 | ||||

Peak current in healthy phase(s) | 0.79 | 0.79 | 0.79 | 1.21 | 34.71 | 37.41 | 37.41 | ||||

Peak current in faulty phase | 1.19 | 1.19 | 1.18 | 1.2 | |||||||

Positive sequence converter current | (0.58 − 0.4i) ≈ |0.7| | (0.58 − 0.4i) ≈ |0.7| | (0.58 − 0.4i) ≈ |0.7| | (1.15 − 0.36i) ≈ |1.2| | |||||||

Negative sequence converter current | − 0.51i ≈ |0.51| | − 0.51i ≈ |0.51| | − 0.51i ≈ |0.51| | − 0.0i ≈ |0.0| | |||||||

Numeric sum of pos. and neg. seq. currents | 1.21 | 1.21 | 1.21 | 1.2 | |||||||

LL | Phase over voltage (p.u) | 0.97 | 0.96 | 1.02 | 1.13 | 14.16 | 15.04 | 9.74 | |||

Voltage unbalance factor | 0.59 | 0.59 | 0.61 | 0.65 | 9.23 | 9.23 | 6.15 | ||||

Peak current in healthy phase(s) | 0.28 | 0.52 | 0.23 | 1.2 | 76.67 | 56.67 | 80.83 | ||||

Peak current in each faulty phase | 1.04 | 1.16 | 0.77 | 1.17 | 1.04 | 1.17 | 1.2 | ||||

Positive sequence converter current | (0.27 − 0.42i) ≈ |0.5| | (0.0 − 0.44i) ≈ |0.44| | (0.37 − 0.64i) ≈ |0.73| | (1.06 − 0.56i) ≈ |1.2| | |||||||

Negative sequence converter current | − 0.78i ≈ |0.78| | − 0.76i ≈ |0.76| | − 0.57i ≈ |0.57| | − 0.0i ≈ |0.0| | |||||||

Numeric sum of pos. and neg. seq. currents | 1.28 | 1.2 | 1.3 | 1.2 | |||||||

DLG | Phase over voltage (p.u) | 1.03 | 1.0 | 1.06 | 1.15 | 10.43 | 13.04 | 7.83 | |||

Voltage unbalance factor | 0.47 | 0.47 | 0.49 | 0.52 | 9.62 | 9.62 | 5.77 | ||||

Peak current in healthy phase(s) | 0.32 | 0.54 | 0.58 | 1.2 | 73.33 | 55 | 51.67 | ||||

Peak current in each faulty phase | 0.97 | 1.22 | 0.68 | 1.19 | 1.02 | 1.22 | 1.2 | ||||

Positive sequence converter current | (0.37 − 0.65i) ≈ |0.75| | (0.0 − 0.67i) ≈ |0.67| | (0.4 − 0.81i) ≈ |0.91| | (0.93 − 0.76i) ≈ |1.2| | |||||||

Negative sequence converter current | − 0.55i ≈ |0.55| | − 0.53i ≈ |0.53| | − 0.39i ≈ |0.39| | − 0.0i ≈ |0.0| | |||||||

Numeric sum of pos. and neg. seq. currents | 1.3 | 1.2 | 1.3 | 1.2 | |||||||

Compliance with recent grid codes | ✓ | ✓ | ✓ | ✗ |

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## Share and Cite

**MDPI and ACS Style**

Abubakar, M.; Renner, H.; Schürhuber, R.
Development of a Novel Control Scheme for Grid-Following Converter under Asymmetrical Faults. *Energies* **2023**, *16*, 1276.
https://doi.org/10.3390/en16031276

**AMA Style**

Abubakar M, Renner H, Schürhuber R.
Development of a Novel Control Scheme for Grid-Following Converter under Asymmetrical Faults. *Energies*. 2023; 16(3):1276.
https://doi.org/10.3390/en16031276

**Chicago/Turabian Style**

Abubakar, Muhammad, Herwig Renner, and Robert Schürhuber.
2023. "Development of a Novel Control Scheme for Grid-Following Converter under Asymmetrical Faults" *Energies* 16, no. 3: 1276.
https://doi.org/10.3390/en16031276