Single - ended Time - domain Distance Protection Method for the Transmission Line of Doubly - Fed Wind Farm Based on Arc Fault Model

Abstract

The present invention relates to a single - ended time - domain distance protection method for the outgoing line of a doubly - fed wind farm based on an arc fault model, belonging to the technical field of power system relay protection. First, the transient voltage and transient current on the wind farm side are collected. By using the fault boundary equation obtained from establishing the arc fault model and the fault voltage equation obtained from the line fault model, a time - domain distance equation containing three unknowns, namely the fault distance, resistance, and arc voltage, is formed and transformed into a matrix form. Then, the fault distance is solved according to the least - squares algorithm. If the fault distance is greater than or equal to 0 and less than or equal to the full length of the line, it is determined as an in - zone fault and the protection operates; otherwise, it is determined as an out - of - zone fault and the protection does not operate. The present invention avoids the incorrect operation of traditional distance protection caused by errors in extracting power frequency quantities due to the frequency deviation characteristics of the wind farm, and does not require the input of the impedance parameters of the opposite - end system, and can accurately and sensitively identify the in - zone and out - of - zone faults of the line under various fault conditions.

Description

Technical Field

[0001] The present invention relates to a single - ended time - domain distance protection method for the outgoing line of a doubly - fed wind farm based on an arc fault model, belonging to the technical field of relay protection in power systems. Background Technique

[0002] After a fault occurs in the outgoing line of a wind farm, if the configured protection can act quickly and accurately, it can prevent the expansion of the fault range and cause more serious impacts, and improve the reliability of the operation of the power system. Due to the significant differences in the short - circuit characteristics between a doubly - fed wind farm and a traditional synchronous generator, when a fault occurs on the line, the fault current on the wind farm side will have a frequency shift. Traditional protection will be affected by the frequency - deviation characteristics, resulting in errors when extracting power - frequency quantities, which may cause the protection to fail to act accurately and cannot meet the requirement of rapidity. The protection based on traditional power - frequency quantities will be challenged. Summary of the Invention

[0003] The purpose of the present invention is to provide a single - ended time - domain distance protection method for the outgoing line of a doubly - fed wind farm based on an arc fault model, aiming to solve the technical problem that the traditional distance protection fails to act correctly due to errors in extracting power - frequency quantities caused by the frequency - shift characteristics of the wind farm.

[0004] To achieve the above - mentioned purpose, the technical solution of the present invention is: a single - ended time - domain distance protection method for the outgoing line of a doubly - fed wind farm based on an arc fault model, and the specific steps are as follows:

[0005] Step1: Collect the transient voltage and transient current on the wind farm side;

[0006] Step2: Establish an arc fault model to obtain a fault boundary equation;

[0007] Step3: Establish a fault voltage equation through a line fault model;

[0008] Step4: Establish a time - domain distance equation containing three unknowns: fault distance, resistance, and arc voltage;

[0009] Step5: Convert the time - domain distance equation into a matrix form;

[0010] Step6: Solve the fault distance according to the least - squares algorithm;

[0011] Step7: If the fault distance is greater than or equal to 0 and less than or equal to the full length of the line, it is determined as an in - zone fault, and the protection acts; otherwise, it is determined as an out - of - zone fault, and the protection does not act.

[0012] The specific content of Step2 is as follows:

[0013] For the faulty arc current, the nonlinear behavior of the arc has little impact on it. Therefore, the arc is represented by the piecewise arc voltage-current characteristic. According to the arc characteristics, the fault boundary can be listed as follows:

[0014] (1)

[0015] where u f (t) represents the fault voltage, u arc (t) represents the arc voltage, R arc represents the arc resistance, i arc (t) represents the arc current, where:

[0016] (2)

[0017] (3)

[0018] where i f (t) represents the fault current, i 0 (t) represents the zero-sequence current. In the high-voltage transmission system, the reactance of the line and the system is much larger than the resistance. The currents i f1 and i f2 flowing through the equivalent resistances on both sides of the fault point have similar phases, that is, K≈i f2 / i f1 , K is a constant, U arc represents the amplitude of the arc voltage. Assuming that the transient current at the measurement end is in the same phase as the fault current, where sgn(·) represents the sign function:

[0019] (4)

[0020] From the above formulas, the fault voltage can be obtained as:

[0021] (5).

[0022] The specific content of Step3 is as follows:

[0023] The transient voltage measured at the measurement end of the wind farm is:

[0024] (6)

[0025] where R 1 , L 1 are the positive-sequence resistance and positive-sequence inductance per unit length of the line, x f represents the distance between the fault location and the measurement end of the wind farm, i N is the transient current measured on the wind farm side, and u f is the fault voltage;

[0026] The transient voltage of phase A measured at the measurement end of the wind farm is:

[0027] (7)

[0028] (8)

[0029] In the formula, K R and K L are the zero-sequence compensation coefficients of the resistance and inductance components respectively, R 1 and R 0 are the positive-sequence resistance and zero-sequence resistance per unit length of the transmission line respectively, L 1 and L 0 are the positive-sequence inductance and zero-sequence inductance per unit length of the transmission line respectively, i A is the transient current of phase A measured at the measurement end of the wind farm, i 0 is the zero-sequence current measured at the measurement end of the wind farm. Let δ be the difference of i(t) at n, i(t) represents the current varying with time, and n represents the number of sampling points, then the discrete form of the transient voltage of phase A is obtained as:

[0030] (9)

[0031] In the above formula,

[0032] (10)

[0033] i A (n) represents the discrete form of the transient current of phase A measured at the measurement end of the wind farm, i 0 (n) represents the discrete form of the zero-sequence current measured at the measurement end of the wind farm, u fA (n) represents the discrete form of the fault voltage of phase A, k R and k L are the zero-sequence compensation coefficients of the resistance and inductance components in the discrete form.

[0034] Specifically, Step4 is as follows:

[0035] Let R ′ =(K + 1)R arc , and we get:

[0036] (11)

[0037] In the formula, U arc (n) represents the discrete form of the arc voltage.

[0038] Specifically, Step5 is as follows:

[0039] Transform the time-domain distance equation into matrix form:

[0040] (12)

[0041] In the formula, U A represents the matrix form of the transient voltage of phase A at the measurement end of the wind farm side, A represents the calculation matrix, and T represents the transpose of the matrix.

[0042] Specifically, Step6 is as follows:

[0043] Solve the fault distance x according to the least squares algorithm f , and the following can be obtained:

[0044] (13)

[0045] Where:

[0046] (14)

[0047] (15)

[0048] In the formula, u A (n + 1), u A (n + 2), …, u A (n + m) represent the (n + 1)th, (n + 2)th, …, (n + m)th sampling points of the transient voltage of phase A at the measurement end of the wind farm side; i 0 (n + 1), i 0 (n + 2), …, i 0 (n + m) represent the (n + 1)th, (n + 2)th, …, (n + m)th sampling points of the zero-sequence current at the measurement end of the wind farm side, and i A (n + 1), i A (n + 2), …, i A (n + m) represent the (n + 1)th, (n + 2)th, …, (n + m)th sampling points of the transient current of phase A at the measurement end of the wind farm side.

[0049] The principle of the present invention is as follows: Starting from the perspective of the time-domain distance algorithm, combined with the characteristics of arc faults in high-voltage transmission lines, an arc fault model is established, the boundary equation required for single-ended measurement protection is constructed, and then a solution equation containing the fault distance is established in combination with the line fault model. Furthermore, the fault distance is calculated according to the least squares algorithm. When a fault occurs within the zone, the obtained fault distance will be between 0 and the full length of the line, and the protection will act. When a fault occurs outside the zone, the obtained fault distance will be less than 0 or greater than the full length of the line, and the protection will not act. Thus, the single-ended time-domain distance protection for the outgoing line of the doubly-fed wind farm is realized.

[0050] The beneficial effects of the present invention are:

[0051] (1) Compared with traditional power frequency protection, the present invention overcomes the adverse effects of the frequency deviation characteristics of a doubly-fed wind farm on protection;

[0052] (2) The present invention is less affected by the fault location and transition resistance;

[0053] (3) The data window length of the present invention is only 5 ms, which can quickly identify internal and external faults and improve the sensitivity of the outgoing line protection of the wind farm. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is the topological diagram of the simulation model of the present invention;

[0055] Figure 2 is the arc fault model established by the present invention;

[0056] Figure 3 is the schematic diagram of the line fault model of the present invention;

[0057] Figure 4 is the specific step flow chart of the embodiment of the present invention;

[0058] Figure 5 is the solution curve graph when a phase A ground short circuit fault occurs 35 km away from the wind farm in Embodiment 1 of the present invention;

[0059] Figure 6 is the solution curve graph when an external fault occurs in Embodiment 1 of the present invention;

[0060] Figure 7 is the fault distance curve graph when an AB phase ground short circuit fault occurs 30 km away from the wind farm and the transition resistance is 100 Ω in Embodiment 2 of the present invention;

[0061] Figure 8 is the fault distance curve graph when a three-phase short circuit fault occurs 30 km away from the wind farm and the transition resistance is 100 Ω in Embodiment 2 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] The present invention will be further described below in conjunction with the drawings and specific embodiments.

[0063] Embodiment 1: The simulation model of the large-scale wind farm grid-connected system is as Figure 1 shown. The total installed capacity of the wind farm is 300 MW. The low voltage ride-through mode of the wind turbines is divided into turning on the crowbar and continuous excitation by the frequency converter. The total length of the outgoing line is 65 km, and the voltage level is 220 kV. Set the fault to occur 35 km from the wind farm side of the line. The fault types are set as phase A ground short circuit fault and external fault respectively, and the transition resistance is set to 0.01 Ω for both. The sampling rate is 10 kHz. The arc fault model established by the present invention is as attachedFigure 2 As shown in Figure 3 is a schematic diagram of the line fault model of the present invention.

[0064] As Figure 4 shown, the specific steps are as follows:

[0065] Step1: Collect the transient voltage and transient current on the wind farm side;

[0066] Step2: Establish an arc fault model to obtain a fault boundary equation;

[0067] Specifically, the arc is represented by the segmented arc voltage-current characteristic. According to the arc characteristic, the fault boundary can be listed as follows:

[0068] (1)

[0069] In the formula, u f (t) represents the fault voltage, u arc (t) represents the arc voltage, R arc represents the arc resistance, i arc (t) represents the arc current, where:

[0070] (2)

[0071] (3)

[0072] In the formula, i f (t) represents the fault current, i 0 (t) represents the zero-sequence current, K≈i f2 / i f1 , K is a constant, i f1 and i f2 are the currents flowing through the equivalent resistances on both sides of the fault point, U arc represents the arc voltage amplitude. Assuming that the transient current at the measurement end is in phase with the fault current, where, sgn(·) represents the sign function:

[0073] (4)

[0074] From the above formulas, the fault voltage can be obtained as:

[0075] (5).

[0076] Step3: Establish a fault voltage equation through the line fault model;

[0077] Specifically, the transient voltage u N measured at the wind farm measurement end is:

[0078] (6)

[0079] Among them, R 1 , L 1 are the positive-sequence resistance and positive-sequence inductance per unit length of the line, x f represents the distance between the fault location and the measurement end of the wind farm, i N is the transient current measured on the wind farm side, and u f is the fault voltage;

[0080] The transient voltage of phase A measured at the measurement end of the wind farm is:

[0081] (7)

[0082] (8)

[0083] In the formula, K R , K L are the zero-sequence compensation coefficients of the resistance and inductance components respectively, R 1 , R 0 are the positive-sequence resistance and zero-sequence resistance per unit length of the transmission line respectively, L 1 , L 0 are the positive-sequence inductance and zero-sequence inductance per unit length of the transmission line respectively, i A is the transient current of phase A measured at the measurement end of the wind farm, i 0 is the zero-sequence current measured at the measurement end of the wind farm. Let δ be the difference of i(t) at n, i(t) represents the current varying with time, and n represents the number of sampling points, then the discrete form of the transient voltage of phase A is:

[0084] (9)

[0085] In the above formula,

[0086] (10)

[0087] i A (n) represents the discrete form of the transient current of phase A measured at the measurement end of the wind farm, i 0 (n) represents the discrete form of the zero-sequence current measured at the measurement end of the wind farm, u fA (n) represents the discrete form of the fault voltage of phase A, k R , k L are the zero-sequence compensation coefficients of the resistance and inductance components in the discrete form.

[0088] Step4: Establish a time-domain distance equation containing three unknowns: fault distance, resistance, and arc voltage;

[0089] Specifically, let R ′ =(K + 1)R arc , and we get:

[0090] (11)

[0091] where U arc (n) represents the discrete form of the arc voltage.

[0092] Step5: Convert the time-domain distance equation into matrix form;

[0093] (12)

[0094] where U A represents the matrix form of the phase-A transient voltage at the measurement terminal on the wind farm side, A represents the calculation matrix, and T represents the transpose of the matrix.

[0095] Step6: Solve for the fault distance according to the least squares algorithm;

[0096] (13)

[0097] where:

[0098] (14)

[0099] (15)

[0100] where u A (n + 1), u A (n + 2), …, u A (n + m) represent the (n + 1)-th, (n + 2)-th, …, (n + m)-th sampling points of the phase-A transient voltage at the measurement terminal on the wind farm side; i 0 (n + 1), i 0 (n + 2), …, i 0 (n + m) represent the (n + 1)-th, (n + 2)-th, …, (n + m)-th sampling points of the zero-sequence current at the measurement terminal on the wind farm side, and i A (n + 1), i A (n + 2), …, i A (n + m) represent the (n + 1)-th, (n + 2)-th, …, (n + m)-th sampling points of the phase-A transient current at the measurement terminal on the wind farm side.

[0101] Step7: If the fault distance x f is greater than or equal to 0 and less than or equal to the line full length l, it is determined as an in-zone fault and the protection operates; otherwise, it is determined as an out-of-zone fault and the protection does not operate. The criterion is:

[0102] (16)

[0103] As Figure 5 is the solution curve graph under the condition of phase A grounding short - circuit fault occurring 35 km away from the wind farm; Figure 6 is the solution curve graph under the condition of external fault occurring. The fault distance x obtained by solving under the condition of phase A grounding short - circuit fault f is 34.71 km, which is greater than 0 and less than the full - length of the line 65 km. It can be determined as an internal fault, and the protection operates. The fault distance x obtained by solving under the condition of external fault f is 76.13 km, which is greater than the full - length of the line 65 km. It is determined as an external fault, and the protection does not operate.

[0104] Embodiment 2: The simulation model of a large - scale wind farm grid - connection system is as Figure 1 shown. The total installed capacity of the wind farm is 300 MW. The low - voltage ride - through methods of wind turbines are divided into putting into crowbar and continuous excitation by the frequency converter. The full - length of the outgoing line is 65 km, and the voltage level is 220 kV. Set the fault to occur 30 km away from the wind - farm side of the line. The fault types are set as AB two - phase grounding short - circuit fault and three - phase short - circuit fault respectively, and the transition resistance is set as 200 Ω, and the sampling rate is 10 kHz.

[0105] The specific implementation steps are as follows:

[0106] Step1: Collect the transient voltage and transient current on the wind - farm side;

[0107] Step2: Establish an arc - fault model to obtain the fault boundary equation;

[0108] Specifically, the arc is represented by the piece - wise arc voltage - current characteristic. According to the arc characteristic, the fault boundary can be listed as follows:

[0109] (1)

[0110] In the formula, u f (t) represents the fault voltage, u arc (t) represents the arc voltage, R arc represents the arc resistance, i arc (t) represents the arc current, where:

[0111] (2)

[0112] (3)

[0113] In the formula, i f (t) represents the fault current, i 0 (t) represents the zero - sequence current, K≈i f2 / i f1 , K is a constant, if1 and i f2 are the currents flowing through the equivalent resistances on both sides of the fault point, and U arc represents the amplitude of the arc voltage. Assuming that the transient current at the measurement end is in phase with the fault current, where sgn(·) represents the sign function:

[0114] (4)

[0115] From the above formula, the fault voltage can be obtained as:

[0116] 。(5)

[0117] Step3: Establish a fault voltage equation through the line fault model;

[0118] Specifically, the transient voltage u N measured at the measurement end of the wind farm is:

[0119] (6)

[0120] where R 1 and L 1 are the positive sequence resistance and positive sequence inductance per unit length of the line, x f represents the distance between the fault location and the measurement end of the wind farm, i N is the transient current measured on the wind farm side, and u f is the fault voltage;

[0121] The transient voltage of phase A measured at the measurement end of the wind farm is:

[0122] (7)

[0123] (8)

[0124] In the formula, K R and K L are the zero-sequence compensation coefficients of the resistance and inductance components respectively, R 1 and R 0 are the positive sequence resistance and zero-sequence resistance per unit length of the transmission line respectively, L 1 and L 0 are the positive sequence inductance and zero-sequence inductance per unit length of the transmission line respectively, i A is the transient current of phase A measured at the measurement end of the wind farm, i 0 is the zero-sequence current measured at the measurement end of the wind farm. Let δ be the difference of i(t) at n, i(t) represents the current changing with time, and n represents the number of sampling points, then the discrete form of the transient voltage of phase A is:

[0125] (9)

[0126] In the above formula,

[0127] (10)

[0128] i A (n) represents the discrete form of the transient current of phase A measured at the measurement end of the wind farm, and i 0 (n) represents the discrete form of the zero-sequence current measured at the measurement end of the wind farm, and u fA (n) represents the discrete form of the fault voltage of phase A, and k R 、k L are the zero-sequence compensation coefficients of the resistance and inductance components in the discrete form.

[0129] Step4: Establish a time-domain distance equation containing three unknowns: fault distance, resistance, and arc voltage;

[0130] Specifically, let R ′ =(K + 1)R arc , and we get:

[0131] (11)

[0132] In the formula, U arc (n) represents the discrete form of the arc voltage.

[0133] Step5: Transform the time-domain distance equation into matrix form;

[0134] (12)

[0135] In the formula, U A represents the matrix form of the transient voltage of phase A at the measurement end on the wind farm side, A represents the calculation matrix, and T represents the transpose of the matrix.

[0136] Step6: Solve the fault distance according to the least squares algorithm;

[0137] (13)

[0138] Among them:

[0139] (14)

[0140] (15)

[0141] In the formula, u A (n + 1), u A (n + 2), …, u A(n + m) represents the (n + 1)-th, (n + 2)-th, …, (n + m)-th sampling points of the transient voltage of phase A at the measurement terminal on the wind farm side; i 0 (n + 1), i 0 (n + 2), …, i 0 (n + m) represents the (n + 1)-th, (n + 2)-th, …, (n + m)-th sampling points of the zero-sequence current at the measurement terminal on the wind farm side, i A (n + 1), i A (n + 2), …, i A (n + m) represents the (n + 1)-th, (n + 2)-th, …, (n + m)-th sampling points of the transient current of phase A at the measurement terminal on the wind farm side.

[0142] Step7: If the fault distance x f is greater than or equal to 0 and less than or equal to the line full length l, it is determined as an in-zone fault and the protection operates; otherwise, it is determined as an out-of-zone fault and the protection does not operate. The criterion is:

[0143] (16)

[0144] As Figure 7 shown in the figure is the fault distance curve when an AB-phase ground short circuit fault occurs 30 km away from the wind farm with a transition resistance of 100 Ω, Figure 8 and it is the fault distance curve when a three-phase short circuit fault occurs 30 km away from the wind farm with a transition resistance of 100 Ω. The fault distance x f solved for the AB-phase ground short circuit fault is 29.03 km, which is greater than 0 and less than the line full length of 65 km, and it can be determined as an in-zone fault and the protection operates. The fault distance x f solved for the three-phase short circuit fault is 29.01 km, which is greater than 0 and less than the line full length of 65 km, and it can be determined as an in-zone fault and the protection operates.

[0145] Therefore, the method can accurately operate under various fault types and when the fault passes through a high transition resistance of 200 Ω.

[0146] The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those of ordinary skill in the art, various changes can be made without departing from the gist of the present invention.

Claims

1. A single-ended time domain distance protection method for a double-fed wind farm transmission line based on an arc fault model, characterized in that: The method comprises: Step 1: Collect transient voltage and transient current on the wind farm side; Step 2: Establish an arc fault model and obtain the fault boundary equation; Step 3: Establish the fault voltage equation through the line fault model; Step 4: Establish a time domain distance equation containing three unknowns: fault distance, resistance and arc voltage; Step 5: Convert the time domain distance equation into a matrix form; Step 6: Solve the fault distance according to the least squares algorithm; Step 7: If the fault distance is greater than or equal to 0 and less than or equal to the total length of the line, it is determined to be an internal fault and the protection is activated. Otherwise, it is determined to be an external fault and the protection is not activated.

2. The single-ended time domain distance protection method for a double-fed wind farm transmission line based on an arc fault model according to claim 1 is characterized in that: The Step 2 is specifically as follows: The arc is represented by the segmented arc voltage-current characteristics. According to the arc characteristics, the fault boundaries are listed as follows: （1）； In the formula, u f (t) represents the fault voltage, u arc (t) represents the arc voltage, R arc represents the arc resistance, i arc (t) represents the arc current, where: （2）； （3）； In the formula, i f (t) represents the fault current, i0(t) represents the zero-sequence current, K≈i f2 / i f1 , K is a constant, i f1 and i f2 is the current flowing through the equivalent resistance on both sides of the fault point, U arc represents the arc voltage amplitude, assuming that the transient current at the measuring end is in phase with the fault current, where sgn(·) represents the sign function: （4）； From the above formula, the fault voltage can be obtained as: （5）。 3. The single-ended time domain distance protection method for a double-fed wind farm transmission line based on an arc fault model according to claim 2 is characterized in that: The Step 3 is specifically as follows: Transient voltage measured at the wind farm measurement end for: （6）； Among them, R1 and L1 are the positive sequence resistance and positive sequence inductance per unit length of the line, and x f Indicates the distance between the fault location and the wind farm measurement end, i N is the transient current measured at the wind farm side, u f is the fault voltage; The transient voltage of phase A measured at the wind farm measurement end for: （7）； （8）； In the formula, K R , K L are the zero-sequence compensation coefficients of the resistance and inductance components, respectively. R1 and R0 are the positive-sequence resistance and zero-sequence resistance per unit length of the transmission line, respectively. L1 and L0 are the positive-sequence inductance and zero-sequence inductance per unit length of the transmission line, respectively. i A is the transient current of phase A measured by the wind farm measurement end, i0 is the zero-sequence current measured by the wind farm measurement end, let δ be the difference of i(t) at point n, i(t) represents the current changing with time, n represents the number of sampling points, then the discrete form of the transient voltage of phase A is obtained for: （9）； In the above formula, （10）； i A (n) represents the discrete form of the A-phase transient current measured at the wind farm measurement end, i0(n) represents the discrete form of the zero-sequence current measured at the wind farm measurement end, u fA (n) represents the discrete form of the fault voltage of phase A, k R , k L is the zero-sequence compensation coefficient of the resistance and inductance components in discrete form.

4. The single-ended time domain distance protection method for a double-fed wind farm transmission line based on an arc fault model according to claim 3 is characterized in that: The Step 4 is specifically as follows: Let R ′ =(K+1)R arc ,get: （11）； Where U arc (n) represents the discrete form of arc voltage.

5. The single-ended time domain distance protection method for a double-fed wind farm transmission line based on an arc fault model according to claim 4 is characterized in that: The Step 5 is specifically as follows: Convert the time domain distance equation into matrix form: （12）； Where U A The matrix form represents the transient voltage of phase A at the measuring end of the wind farm side, where A represents the calculation matrix and T represents the transpose of the matrix.

6. The single-ended time domain distance protection method for a double-fed wind farm transmission line based on an arc fault model according to claim 5 is characterized in that: The Step 6 is specifically as follows: Solve the fault distance x according to the least squares algorithm f , we can get: （13）； in: （14）； （15）； In the formula, u A (n+1),u A (n+2),…,u A (n+m) represents the n+1th, n+2th, ..., n+mth sampling points of the A-phase transient voltage at the measuring end on the wind farm side; i0(n+1), i0(n+2), …, i0 (n+m) represent the n+1, n+2, …, n+mth sampling points of the zero-sequence current at the wind farm side measurement end, i A (n+1), i A (n+2),…,i A (n+m) represents the n+1th, n+2th, …, n+mth sampling points of the A-phase transient current at the measuring end on the wind farm side.

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