# Voltage-Based Hybrid Algorithm Using Parameter Variations and Stockwell Transform for Islanding Detection in Utility Grids

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## Abstract

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## 1. Introduction

- An islanding detection method (IDM) based on the use of voltage signals is proposed in this paper.
- Features extracted from the voltage signal using the ST and rate of change in RMS voltage are used to define a voltage-based islanding recognition factor (IRFV).
- Islanding events are discriminated from the faulty and operational events using simple decision rules based on the peak magnitude of IRFV.
- Proposed IDM is effective to detect islanding events with minimum NDZ.
- Proposed IDM is more effective compared to the method based on the rate of change in voltage and a discrete wavelet transform (DWT)-based method.

## 2. Test Grid of IEEE-13 Nodes

#### 2.1. Solar PV System

_{ph}: photo-current of PV cell, I

_{0}: saturation current of PV cell, A: curve fitting factor of a solar cell, R

_{sh}: shunt resistance of PV cell, R

_{s}: series resistance of PV cell, q: electron charge (1.602 × 10

^{−19}C), k: Boltzmann constant (1.38 × 10

^{−23}J/K), V

_{mp}: voltage corresponding to maximum power point tracking (MPPT), I

_{mp}: current corresponding to MPPT. The following parameters are used to design solar PV system at standard test conditions (STC) for each module: V

_{oc}= 64.2 V; I

_{sc}= 5.96 A; V

_{mp}= 54.7 V; I

_{mp}= 5.58 A; R

_{s}= 0.037998 Ω; R

_{sh}= 993.51 Ω; I

_{0}= 1.1753 × 10

^{−8}A; diode quality factor (Q

_{d}) = 1.3; I

_{ph}= 5.9602 A [18,19].

#### 2.2. Wind Power Plant

_{s}= 0.023 pu, L

_{s}= 0.18 pu, R

_{r}= 0.016 pu, L

_{r}= 0.016 pu, L

_{m}= 2.9 pu. A proportional integral (PI) controller is employed for control of the converter used to integrate DFIG to the test grid. The grid side and rotor side convertors are operated at pulse width modulation (PWM) carrier frequencies of 2700 and 1620 Hz in respective order. The maximum pitch angle is considered equal to 27°, and the maximum rate of change in pitch angle is considered equal to 10°/s. The pitch controller gain is considered equal to 150. Gains of reactive power and voltage regulator are considered equal to 0.05 and 20 in respective order [20,21].

## 3. Proposed Voltage-Based Algorithm for Identification of Islanding Events

- Record the voltage waveform and root mean square (RMS) values of the voltage (VR) at IRL node.
- Decompose the voltage signal using Stockwell transform at a sampling frequency of 3.84 kHz and designate the output matrix as SV. Equation (7) described in Section 3.1 is used to compute SV. Detailed mathematical formulation of Stockwell transform are reported in [22,23,24].
- Compute the median of the columns of the matrix SV and assigned symbol median-based islanding recognition factor (MIRF), which is defined in the Equation (2).$$\mathrm{MIRF}=median\left(SV\right)$$
- Compute the rate of change in RMS voltage (ROCOV) and assign the symbol voltage rate of change in islanding recognition factor (VRCIRF). This is achieved by differentiating the voltage signal with respect to time. VRCIRF is defined in the Equation (3).$$\mathrm{VRCIRF}=\frac{d\left(VR\right)}{dt}$$
- Compute the voltage-based islanding recognition factor (IRFV) by multiplying the MIRF and VRCIRF element to element, as detailed below. Here, WFV is the voltage-based weight factor. WFV is considered equal to the 1000 for this study.$$\mathrm{IRFV}=\mathrm{MIRF}\times \mathrm{VRCIRF}\times \mathrm{WFV}$$
- Set the threshold magnitudes TMV1 and TMV2 equal to 50 and 300, respectively, for the IRFV. If peak magnitude of IRFV is less than TMV1, then the event is an operational event. For peak magnitudes of IRFV between the TMV1 and TMV2, the event is islanding. However, if the peak magnitude of IRFV is greater than the TMV2 then the event is faulty in nature.

#### 3.1. Stockwell Transform

#### 3.2. Decision Tree Rules

## 4. Results and Discussion

#### 4.1. Healthy Condition without Any Disturbance

#### 4.2. Recognition of Islanding Events

#### 4.2.1. Islanding with Wind and Solar Energy Production

#### 4.2.2. Islanding with Wind Energy Production

#### 4.2.3. Islanding with Solar Energy Production

#### 4.3. Faulty Events

#### 4.3.1. Single-Phase-to-Ground Fault

#### 4.3.2. Two-Phase Fault

#### 4.3.3. Two-Phase-to-Ground Fault

#### 4.3.4. Three-Phase Fault with Ground

#### 4.4. Operational Events

#### 4.4.1. Outage of Wind Power Plant from Test Grid

#### 4.4.2. Outage of Solar Power Plant from Test Grid

#### 4.4.3. Synchronization of SPP to Grid

#### 4.4.4. Synchronization of WPP to Grid

#### 4.4.5. Feeder Operation

#### 4.4.6. Capacitor Switching

#### 4.4.7. Load Switching

## 5. Identification of Non-Detection Zone

## 6. Classification of Events

## 7. Performance Comparison of Algorithm

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Healthy condition (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based islanding recognition factor (IRF) (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 4.**Islanding event in the presence of both wind and solar power generation (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 5.**Islanding event in the presence of wind power generation (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 6.**Islanding event in the presence of solar power generation (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 7.**Single-phase-to-ground fault (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 8.**Two-phase fault (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 9.**Two-phase-to-ground fault (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 10.**Three-phase fault with ground (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 11.**Outage of wind power plant from test grid (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 12.**Outage of solar power plant from test grid (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 13.**Synchronization of solar power plant (SPP) to grid (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 14.**Synchronization of wind power plant (WPP) to grid (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 15.**Feeder operation (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 16.**Capacitor switching (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 17.**Load switching (

**a**) voltage signal (

**b**) root means square value of voltage (

**c**) median-based IRF (

**d**) rate of change in voltage-based IRF (

**e**) islanding recognition factor based on voltage.

**Figure 18.**Discrimination of islanding event from the faulty and operational events using voltage-based IRF.

Nodes of Test Distribution Grid | Load Connected at Various Nodes of Test Distribution Grid | Capacitor Banks at Various Nodes of Test Distribution Grid (kVAr) | |
---|---|---|---|

kW | kVAr | ||

634 | 400 | 290 | |

645 | 170 | 125 | |

646 | 230 | 132 | |

652 | 128 | 86 | |

671 | 1155 | 660 | |

675 | 843 | 462 | 600 |

692 | 170 | 151 | |

611 | 170 | 80 | 100 |

632–671 | 200 | 116 | |

680 | |||

650 |

Transformer | Transformer MVA Rating | kV-HV Winding Transformer | kV-LV Winding Transformer | HV Winding | LV Winding | ||
---|---|---|---|---|---|---|---|

R (Ω) | X (Ω) | R (Ω) | X (Ω) | ||||

Grid-ICT | 10 | 115 | 4.16 | 29.095 | 211.60 | 0.1142 | 0.8306 |

T-Feeder | 5 | 4.16 | 0.48 | 0.011 | 3.0159 | 0.011 | 3.0159 |

T-WPP | 5 | 4.16 | 0.575 | 0.3807 | 2.7688 | 0.0510 | 0.0042 |

T-SPP | 5 | 4.16 | 0.260 | 0.001 | 1.1310 | 0.001 | 1.1310 |

ΔP (kW) | Voltage (pu) | |||||||
---|---|---|---|---|---|---|---|---|

0.88 | 0.90 | 0.92 | 0.94 | 0.96 | 0.98 | 1.0 | 1.1 | |

−10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

−8 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |

−6 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |

−4 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |

−2 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |

0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

2 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |

4 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |

6 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |

8 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |

10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

12 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

S. No. | Type of Event | Peak Magnitude of IRFV |
---|---|---|

1 | Healthy condition without any disturbance. | 0.03 |

2 | Islanding event in the presence of both wind and solar power generation. | 105.04 |

3 | Islanding event in the presence of wind power generation. | 141.63 |

4 | Islanding event in the presence of solar power generation. | 242.60 |

5 | Single-phase-to-ground fault. | 598.12 |

6 | Two-phase fault. | 587.70 |

7 | Two-phase-to-ground fault. | 561.05 |

8 | Three-phase fault with ground. | 399.40 |

9 | Outage of wind power plant. | 2.09 |

10 | Outage of solar power plant. | 3.14 |

11 | Synchronization of SPP. | 32.81 |

12 | Synchronization of WPP. | 26.49 |

13 | Feeder operation. | 23.15 |

14 | Capacitor switching. | 33.25 |

15 | Load switching. | 0.351 |

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## Share and Cite

**MDPI and ACS Style**

Mahela, O.P.; Sharma, Y.; Ali, S.; Khan, B.; Garg, A.R.
Voltage-Based Hybrid Algorithm Using Parameter Variations and Stockwell Transform for Islanding Detection in Utility Grids. *Informatics* **2021**, *8*, 21.
https://doi.org/10.3390/informatics8020021

**AMA Style**

Mahela OP, Sharma Y, Ali S, Khan B, Garg AR.
Voltage-Based Hybrid Algorithm Using Parameter Variations and Stockwell Transform for Islanding Detection in Utility Grids. *Informatics*. 2021; 8(2):21.
https://doi.org/10.3390/informatics8020021

**Chicago/Turabian Style**

Mahela, Om Prakash, Yagya Sharma, Shoyab Ali, Baseem Khan, and Akhil Ranjan Garg.
2021. "Voltage-Based Hybrid Algorithm Using Parameter Variations and Stockwell Transform for Islanding Detection in Utility Grids" *Informatics* 8, no. 2: 21.
https://doi.org/10.3390/informatics8020021