The system impedance instability, high-order harmonics, and frequency offset are main fault characteristics of wind power system. Moreover, the measurement angle of faulty phase is affected by rotation speed frequency component, which causes traditional directional protections based on angle comparison between voltage and current to operate incorrectly. In this paper, a time-domain protection for connected to wind power plant based on model matching is proposed, which compares the calculated current and the measured current to identify internal faults and external faults. Under external faults, the calculated current and measured current waveform are quite similar because the protected transmission lines is equivalent to a lumped parameter model and the model itself is not damaged. However, the similarity of calculated current and measured current is quite low, due to destroyed integrity of model under internal faults. Additionally, Hausdorff distance is introduced to obtain the similarity of the calculated current and measured current. Since the proposed protection scheme is applied in time domain, it is independent from current frequency offsets of wind energy system, high-order harmonics, and system impedance variations. Comprehensive case studies are undertaken through Power Systems Computer Aided Design (PSCAD), while simulation results verify the accuracy and efficiency of the proposed approach in fault identification.

Renewable energy, such as wind and solar, is increasingly used for power generation because of the importance of sustainable energy supply and environmental protection in the economic and social development around the world [

Thus far, some new researches on the development of modern power system protection and control are widely concerned [

The traditional protection is adversely affected by wind turbine control strategy which can vary the voltage and current after faults occur, hence numerous references studies the fault characteristics of transmission lines with wind turbine [

This paper proposes a protection method based on model matching and Hausdorff distance. The transmission line is equivalent to π model in this paper. Under external faults, the calculated current and measured current waveform are quite similar, because the protected transmission lines are equivalent to a lumped parameter model and the model itself is not damaged. However, the similarity of calculated current and measured current is quite low, due to destroyed integrity of model under internal faults. Moreover, Hausdorff distance is introduced to obtain the similarity of the calculated current and measured current. Simulation results verify the accuracy and efficiency of the proposed approach in fault identification. The main contributions of this manuscript can be summarized into the following four aspects:

Action characteristics of traditional directional protection based on angle comparison of voltage are analysed, and it shows that measurement angle based on Fourier transform is affected by rotation speed frequency component, which causes traditional directional protections using angle comparison between voltage and current to operate incorrectly.

A time-domain protection for connected to wind power plant based on model matching is proposed, which is not affected by rotation speed frequency component. Theoretically, it is not affected by the frequency deviation of current on wind power system, high-order harmonics, and impedance variations.

The proposed method has a high accuracy and efficiency in fault identification, which is not affected by fault locations, fault types, and noise. It is suitable for field operation because the sampling frequency is lower.

Hausdorff distance is introduced to obtain the similarity of the calculated current and measured current. Hausdorff distance can be carried out in a shorter time window and has a high efficiency in signal processing.

In this paper, Section 1 introduces related research in recent years. Section 2 analyses short-circuit current characteristics for doubly-fed induction generator (DFIG) and its influence on directional protection. Section 3 introduces time-domain protection based on model matching. Section 4 introduces Hausdorff distance. Section 5 establishes system model by PSCAD and provides simulation results, and Section 6 concludes the whole paper.

Rotor side of DFIG is connected to grid through a converter, and stator side is directly connected to grid as shown in

During normal operation, DFIG is controlled by rotor converter for excitation. When power grid faults, voltage of DFIG terminal suddenly drops, and a large transient voltage and current will be induced in its rotor winding. Then, crowbar protection is put into rotor winding side to suppress transient current and protect converter from damage. At this time, three-phase short-circuit current can be expressed as [

where _{c} is initial phase angle of short-circuit current after crowbar protection; _{1} is synchronous speed; _{r} is rotor speed; _{sc} and _{rc} are stator and rotor time decay constants considering crowbar protection action; respectively; _{c}, _{c}, and _{c} are coefficients of each component for short-circuit current considering crowbar protection, which are related to motor parameters and voltage drop of motor terminal as shown in

In

where _{cos} represents cosine coefficient of fundamental current after DFT; _{sin} represents sine coefficient of fundamental current after DFT. According to cosine and sine coefficients of fundamental wave obtained in

where |

Short-circuit current signal in

where

where _{cos1} and _{sin1} represent cosine coefficient and sine coefficients of fundamental frequency phasor for short-circuit current after Fourier transform. |_{c}| and ∠|_{c}| represent amplitude and angle of fundamental frequency component after short-circuit current is extracted by DFT. After extraction of short-circuit current by discrete Fourier transform, there is an error amount Δ_{c} with obtained fundamental frequency component _{c}. It shows that amplitude and phase angle of short-circuit current cannot be accurately extracted by Fourier transform, due to rotation speed frequency.

Direction of a fault is determined by angle relationship between current and voltage by directional protection based on angle comparison between voltage and current. The angle between voltage and current is [

A forward fault occurs, its protection criterion is

A reverse fault occurs, its protection criterion is

where _{A} represents angle between voltage and current, and arg represents angle of phasor

After occurrence of a three-phase fault, short-circuit current provided by wind farm is no longer power frequency component. According to analysis in the first section, the crowbar protection contains attenuating rotation speed frequency component, which leads to the error Δ_{c} when power frequency component current is extracted by DFT.

where _{sc}_{c}, _{c}Δ_{c}. Δ_{A} represents angle error between voltage and current. It can be seen from _{A} obtained based on angle comparison by Fourier transform is not accurate, and there is an error angle. The error may cause maloperation and refusal of protection.

The above analysis shows that short-circuit current caused by DFIG is very different from short-circuit current provided by traditional motor, which will cause directional protection based on angle comparison by Fourier transform to operate incorrectly. Therefore, time-domain protection based on model matching is proposed. In this section, Single-phase line is used as an example to analyze fault model characteristics of internal and external faults.

A fault occurs at

In _{f} is transition resistance. _{M} and _{N} are measured voltage, _{M} and _{N} are measured current at protection installation. _{M1} and _{N1} are current flowing through resistance and inductance parameters of the transmission line respectively.

According to

A fault occurs at

In _{M} and _{M} is resistance and inductance from fault to wind power side, respectively; _{N} and _{N} are unit resistance and unit inductance from fault to system side, respectively; _{M} and _{N} is capacitance to ground from fault to wind power and conventional power, respectively.

The parameters of resistance and inductance at both ends are different under a fault which does not occur at the midpoint of transmission line, as

So current flowing through parameters of resistance and inductance does not conform to characteristics of equal magnitude and opposite direction, which is _{M1}+_{N1} ≠ 0. Therefore, _{N} in

Although _{N} calculated by

In

Hausdorff distance is a kind of graph similarity algorithm, which mainly investigates difference between the overall characteristics of two images [

It is assumed that there are two finite point sets _{1}, …, _{n}} and _{1}, …, _{n}}. In _{i} in _{j}, which meets

where ||•|| represents Euclidean distance between two points.

For all points in

The one-way Hausdorff distance from

The bidirectional Hausdorff distance between

where

when a fault occurs, current _{N} calculated by _{NS} measured by protection installation are calculated by

where _{N}, _{NS}) is defined as mismatch between calculated current _{N} and measured current _{NS}, the smaller _{N}, _{NS}), the higher similarity between _{N} and _{NS}. And _{N}, _{NS}) is compared with the set threshold, the protection method criteria is

Theoretically, the similarity of _{N} and _{NS} is quite high under an external fault, _{N}, _{NS}) tends to 0, and _{N}, _{NS}) is larger under an internal fault. It is appropriate to set threshold to 0.2, considering the effectiveness of protection action.

For three-phase lines, voltage and current measured by measuring terminal are substituted into the Karenbauer transform, which is applied for phase mode transform to obtain its corresponding zero mode component and aerial mode component.

where _{MA}, _{MB}, and _{MC} are three-phase voltages measured at terminal-M; _{M0} is zero-mode voltage; _{Mα} and _{Mβ} are three aerial-mode voltages, respectively. Similarly, the phase-to-mode conversion is performed on three-phase current at terminal-M, and phase-to-mode conversion is performed on three-phase voltage and current at terminal-N to obtain corresponding aerial-mode components.

In _{M}, _{N}, _{M}, and _{N} is voltage and current measured at protection installation, respectively. Internal resistance of system power supply is 2 Ω; positive sequence impedance of the transmission lines is (0.034 + j0.415) Ω/km; positive sequence and zero-sequence capacitance is 0.0086 μF/km and 0.0061 μF/km respectively. Zero-sequence impedance is (0.253 + j0.873) Ω/km; length of the transmission lines is 60 km. The rated capacity of main transformer is 150 MVA; the rated voltage is 38.5 kV/110 kV; and voltage percentage is _{k}% = 10.5. The rated capacity of box transformer for DFIG is 2.5 MVA; rated voltage is 0.69 kV/38.5 kV. The voltage percentage is _{k}% = 6.5. The rated capacity of a single DFIG is 2 MW; rated voltage is 0.69 kV; stator impedance is (0.006813 + j0.1528) pu; rotor impedance is (0.007642 + j0.1359) pu; excitation reactance is 4.0152 pu; and moment of inertia is 3.5 s. The transformer is considered as ideal in the proposed method. Fault location is _{1}, _{2}, and _{3} respectably. _{1} is located outside wind power; _{2} is located at transmission line; _{3} is located outside conventional power.

A three-phase short-circuit fault occurs in the transmission lines considering crowbar protection, the operating characteristics of components based on positive sequence direction are shown in

Operating conditions | Fault location | Fault type | Activated | Deactivated | Action rejected | False activated |
---|---|---|---|---|---|---|

Sub-synchronous | External fault | AG | √ | |||

AB | √ | |||||

BCG | √ | |||||

ABC | √ | |||||

Synchronous speed | AG | √ | ||||

AB | √ | |||||

BCG | √ | |||||

ABC | √ | |||||

Super-synchronous | AG | √ | ||||

AB | √ | |||||

BCG | √ | |||||

ABC | √ | |||||

Sub-synchronous | Internal fault | AG | √ | |||

AB | √ | |||||

BCG | √ | |||||

ABC | √ | |||||

Synchronous speed | AG | √ | ||||

AB | √ | |||||

BCG | √ | |||||

ABC | √ | |||||

Super-synchronous | AG | √ | ||||

AB | √ | |||||

BCG | √ | |||||

ABC | √ |

The fundamental frequency component of short-circuit current cannot be accurately extracted by Fourier transform due to rotation speed frequency component, which is short-circuit current provided by DFIG considering crowbar protection. Angle measured by protection installation is inaccurate, which results in refusal and maloperation of protection action.

A single-phase ground fault occurs at _{3} and _{5} in _{N} and _{NS} is shown in _{N} represents calculated current, and _{NS} represents measured current, as does the meaning of _{N} and _{NS} that appear in the simulation below.

In _{N} and _{NS} is quite high. When an internal fault occurs, the similarity of _{N} and _{NS} is quite low. _{N}, _{NS}) under an external fault is 0.0089, which is close to 0. _{N}, _{NS}) under an internal fault is 0.7648, which is greater than set value. Therefore, the calculated current can be matched with measured current, and internal and external faults can be identified according to similarity. A longer sampling time window will be required at the higher sampling frequency by this method. The proposed method only needs to extract the first few sampling points of the fault signal, so the sampling frequency is lower. And a sampling device with the stronger processing capabilities will be required at the higher sampling frequency. The sampling frequency of actual sampling device on site is usually within 20 kHz. Therefore, the sampling frequency of the method proposed in this article is suitable for field operation.

A fault occurs at locations _{1}, _{2}, and _{3} in _{4} represents fault location at wind power outlet; _{5} represents fault location at conventional power outlet, and 15 km, 45 km distances from terminal-M (respectively recorded as _{6}, _{7}). The relationship between _{N} and _{NS} is shown in _{N}, _{NS}) at different fault location and fault type are shown in

Fault location | Fault type | _{N}, _{NS}) |
Activated | Deactivated |
---|---|---|---|---|

_{1} |
AG | 0.0201 | √ | |

AB | 0.0805 | √ | ||

ABG | 0.0753 | √ | ||

ABC | 0.0812 | √ | ||

_{2} |
AG | 0.7648 | √ | |

AB | 2.7499 | √ | ||

ABG | 2.7485 | √ | ||

ABC | 2.7408 | √ | ||

_{3} |
AG | 0.0089 | √ | |

AB | 0.0768 | √ | ||

ABG | 0.0549 | √ | ||

ABC | 0.0761 | √ | ||

_{4} |
AG | 0.6809 | √ | |

AB | 1.8355 | √ | ||

ABG | 1.8402 | √ | ||

ABC | 1.8413 | √ | ||

_{5} |
AG | 1.4333 | √ | |

AB | 5.6052 | √ | ||

ABG | 5.6098 | √ | ||

ABC | 5.6019 | √ | ||

_{6} |
AG | 0.6808 | √ | |

AB | 1.7739 | √ | ||

ABG | 1.7810 | √ | ||

ABC | 1.7780 | √ | ||

_{7} |
AG | 0.9324 | √ | |

AB | 3.7978 | √ | ||

ABG | 3.7973 | √ | ||

ABC | 3.8137 | √ |

In _{N}, _{NS}) all less than 0.2 under an external fault, and the similarity of calculated current and measured current is quite high. _{N}, _{NS}) all greater than 0.2 under an internal fault, and the similarity of calculated current and measured current is quite low. Therefore, this method is less affected by fault types and fault locations.

A fault occurs at _{2} and _{3}; fault type is A-phase ground fault; transition resistance is set to 20 Ω, 50 Ω, 80 Ω, and 120 Ω, respectively. The curves of waveform for _{N} and _{NS} under different transition resistances are shown in _{N}, _{NS}) is shown in _{1}(_{N}, _{NS}) and _{2}(_{N}, _{NS}) represents the value of a fault location is _{2} and _{3} respectably.

Transition resistance/Ω | 20 | 50 | 80 | 120 |
---|---|---|---|---|

_{1}(_{N}, _{NS}) |
0.6173 | 0.5413 | 0.4409 | 0.3121 |

_{2}(_{N}, _{NS}) |
0.0104 | 0.0116 | 0.0085 | 0.0105 |

In _{N}, _{NS}) is greater than 0.2 under an internal fault, and _{N}, _{NS}) is less than 0.2 under an external fault, which can be correctly distinguish internal and external faults. In this protection method, the waveform characteristics of calculated current depend on waveform characteristics of voltage and current measured on both sides. It does not directly depend on magnitude of short-circuit current, so _{N}, _{NS}) can also meet requirements of criterion under different transition resistances.

Power systems are susceptible to electromagnetic interference, and there must be some noise in their signals. A fault occurs at _{1}, _{2}, and _{3}, respectively; transition resistance is set to 20 Ω and 100 Ω, respectively. Therefore, _{N}, _{NS}) of Gaussian white noise under signal-to-noise ratio (SNR) of 10 dB, 15 dB, and 20 dB and under various short-circuit fault types are shown in

Fault location | Fault type | Transition resistance (Ω) | SNR/dB | _{N}, _{NS}) |
---|---|---|---|---|

_{1} |
AG | 20 | 10 | 0.0185 |

100 | 15 | 0.0068 | ||

AB | 20 | 20 | 0.0651 | |

100 | 10 | 0.0264 | ||

ABC | 20 | 15 | 0.0596 | |

100 | 20 | 0.0312 | ||

_{2} |
AG | 20 | 10 | 0.6413 |

20 | 0.5137 | |||

100 | 10 | 0.4381 | ||

20 | 0.4035 | |||

AB | 20 | 10 | 2.5362 | |

20 | 2.3872 | |||

100 | 10 | 2.0132 | ||

20 | 1.8013 | |||

ABC | 20 | 10 | 2.5286 | |

20 | 2.4126 | |||

100 | 10 | 1.9231 | ||

20 | 1.8057 | |||

_{3} |
AG | 20 | 10 | 0.0051 |

100 | 15 | 0.0452 | ||

AB | 20 | 20 | 0.0597 | |

100 | 10 | 0.0247 | ||

ABC | 20 | 15 | 0.0532 | |

100 | 20 | 0.0221 |

In _{N}, _{NS}) is still greater than set value under an internal fault, _{N}, _{NS}) is less than set value under external faults and the effect of noise on the proposed method is little.

Characteristics of short-circuit current provided by DFIG considering crowbar protection is analysed. According to expressions of amplitude and angle for fundamental frequency current obtained by Fourier transform, furthermore, action characteristics of traditional directional protection based on angle comparison of voltage and current and time-domain protection based on model matching are analysed, and the following conclusions are obtained:

Derivation and simulation analysis show that measurement angle based on Fourier transform is affected by rotation speed frequency component, which causes traditional directional protections using angle comparison between voltage and current to operate incorrectly. However, the time-domain protection based on model matching is not affected by rotation speed frequency component.

Hausdorff distance can be used to match the waveforms through analysis, thereby can be formed a criterion for correctly identifying internal and external faults. The algorithm does not require length of time window, can be carried out in a shorter window.

The proposed method has a high accuracy and efficiency in fault identification, which is not affected by fault locations, fault types, and noise. Accuracy of the protection action is about 20% higher than accuracy of the traditional directional protection under high-impedance faults. Theoretically, it is not affected by the frequency deviation of current on wind power system, high-order harmonics, and impedance variations.

Future studies will be focused on the following two aspects:

The measured data will be used to verify feasibility of the proposed method;

The proposed method will be tested in RTDS.

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (51977102 and 51807084).

where _{s} is terminal voltage of DFIG after a fault; _{s} is stator resistance; _{rc} is rotor equivalent resistance considering crowbar protection. _{s} and _{r} are stator and rotor inductance of DFIG respectively. _{s} = _{m} + _{σs}, _{r} = _{m} + _{σr}. _{σs} and _{σr} are leakage inductance of stator and rotor respectively, and _{m} is mutual inductance of stator and rotor windings. _{1} _{−} _{r})/_{1};