Method for detecting inter-turn faults in three-phase power transformers based on equivalent magnetic circuit

Abstract

The application belongs to the field of power system fault diagnosis, and provides a three-phase power transformer inter-turn fault detection method based on equivalent magnetic circuit to solve the technical problem that it is difficult to identify inter-turn fault through each phase working voltage. The equivalent magnetic circuit under normal operation state is established according to the structural characteristics of the three-phase power transformer, and is simplified. Any phase in the equivalent magnetic circuit under normal operation state after simplification is selected as a fault phase, and the equivalent magnetic circuit under inter-turn fault state is established. The equivalent magnetic circuit under inter-turn fault state is analyzed, and the following conclusion is derived: only when inter-turn fault occurs, N f I f ≠ 0, wherein N f represents the number of turns shortened on the primary or secondary winding due to inter-turn fault, i.e. fault turn number; I f represents the induced current on the fault turn number, i.e. fault current; whether inter-turn fault occurs is judged according to N f I f . The application has economy, and can stably detect low-level inter-turn fault during system transient and external fault because the phase voltage is decoupled.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of local power system fault diagnosis, in particular to a three-phase power transformer inter-turn fault detection method based on equivalent magnetic circuit. BACKGROUND

[0002] With the rapid development of the country, the continuous development of social and economic level and the continuous enrichment of people's material life, the demand for electricity is growing. The power transformer is one of the core components of the entire power system, and is also one of the most critical and most expensive equipment in the power system industry. The role of power transformer is multifaceted, not only can it raise the voltage to send electricity to the power consumption area, but also can reduce the voltage to the use voltage of each level to meet the needs of power consumption. With the continuous improvement of people's living standards, the fault detection technology of power transformer is crucial to ensure the safe and stable operation of the power system.

[0003] The existing engineering actual cases show that the main challenge faced by the existing transformer protection system in detecting inter-turn faults is that when inter-turn faults occur, the voltage of each phase changes little, so it is difficult to identify inter-turn faults through the voltage of each phase. A more reliable and accurate method is needed to detect these faults. SUMMARY

[0004] The purpose of the present application is to solve the problems existing in the prior art, to provide a three-phase power transformer inter-turn fault detection method based on equivalent magnetic circuit, to solve the technical problem that it is difficult to identify inter-turn faults through the voltage of each phase.

[0005] The present application is realized by the following technical scheme: a three-phase power transformer inter-turn fault detection method based on equivalent magnetic circuit, comprising the following steps:

[0006] Establish the equivalent magnetic circuit under normal operating state according to the structural characteristics of three-phase power transformer, and simplify it;

[0007] Select any one phase of the simplified equivalent magnetic circuit under normal operating state as the fault phase, and establish the equivalent magnetic circuit under inter-turn fault state;

[0008] Analyze the equivalent magnetic circuit under inter-turn fault state and derive the following conclusions: only when inter-turn fault occurs, N f I f ≠ 0, wherein N f represents the number of turns shortened on the primary or secondary winding due to inter-turn fault, i.e. fault turns; I f represents the induced current on the fault turns, i.e. fault current;

[0009] According to N f I f , judge whether inter-turn fault occurs.

[0010] Further, the N f I f As the inter-turn fault indicator FDI, when FDI≥Δ, it is determined that an inter-turn fault occurs, Δ is an inter-turn fault threshold, and Δ≠0.

[0011] Further, the fault indicator FDI is calculated according to the following formula:

[0012]

[0013] Wherein, I f represents a fault current, θ f represents a phase angle of the fault current.

[0014] Further, the inter-turn fault threshold is determined according to the rated current of the power transformer.

[0015] Further, 2-6% of the rated current of the power transformer is taken as the inter-turn fault threshold.

[0016] Further, 4% of the rated current of the power transformer is taken as the inter-turn fault threshold.

[0017] Further, an unknown vector matrix X is constructed to solve the parameters used to calculate the fault indicator FDI, and the unknown vector matrix X is as follows:

[0018]

[0019] Wherein, θ a , θ b , θ f , N f I f are all unknown parameters; represents the magnetic flux of phase a, and phase a is an assumed fault phase, represents the magnetic flux of phase b, and phase b is an arbitrarily selected non-fault phase, θ a represents the phase angle of phase a, θ b represents the phase angle of phase b, θ f represents a phase angle of the fault current, N f I f represents the product of the fault turn number and the fault current size.

[0020] Further, according to the measurement samples at different times, the least error plane method is used to solve the unknown vector matrix X:

[0021] X=(A T A) -1 A T B

[0022] Wherein, A represents the known coefficient matrix, B represents the measurement sample matrix changing with time;

[0023]

[0024]

[0025] Wherein, R a , R b , R c respectively represent the cross-section reluctance of a, b, c three-phase; i pa , i pb , i pc respectively represent the primary current of a, b, c three-phase; i sa , i sb , i sc respectively represent the secondary current of a, b, c three-phase; the primary winding turns of a, b, c three-phase are all N p ; the secondary winding turns of a, b, c three-phase are all N s ; ω represents the angular frequency;

[0026] j is the sampling number, n is the total number of measurement samples, l is the number of measurement samples in the moving data window, Δt is the time difference of two consecutive measurement samples, t l =-(n-l)Δt, t j =-(n-j)Δt, t n =0.

[0027] Further, the simplified method of equivalent magnetic circuit under normal operation state is: ignoring the parallel reluctance, ignoring the path reluctance between the top and bottom of the transformer core.

[0028] Further, according to the equivalent magnetic circuit under inter-turn fault state, the following equation is derived in time domain:

[0029]

[0030]

[0031]

[0032] Wherein, a phase is the assumed fault phase, N pa is the primary winding turns after fault occurs, N p ' a =N pa -N f ; i pa , i pb , i pc respectively represent the primary current of a, b, c three-phase; i sa , i sbi sc These represent the primary currents of phases a, b, and c, respectively. N represents magnetic flux. pa and N sa R represents the number of turns in the primary winding and the number of turns in the secondary winding of phase a; a R b R c These represent the cross-sectional magnetic reluctance of phases a, b, and c, respectively.

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] 1. This invention, through analysis of the equivalent magnetic circuit under inter-turn fault conditions, derives the product N of the number of faulty turns and the magnitude of the fault current. f I f When the value is not equal to 0, an inter-turn fault can be uniquely determined, ensuring the reliability of the judgment.

[0035] 2. To improve accuracy in practical applications, N is adopted. f I f FDI is used as an inter-turn fault indicator, and an inter-turn fault threshold Δ is set. The fault threshold Δ improves the anti-interference capability and eliminates false judgments caused by certain interference conditions, such as small current interference causing N f I f It is not equal to 0. In addition, the fault threshold Δ can be set according to the transformer model and nominal parameters, and has good individual adaptability.

[0036] 3. This invention constructs an unknown vector matrix X to solve for parameters used in calculating the Fault Index (FDI). The minimum error square method is used to solve for the unknown vector matrix X. By solving for N in the unknown vector matrix X... f I f cosθ f With N f I f sinθ f The element can be used to calculate N using the formula for the fault index FDI. f I f Compared to solving N separately f I f Calculating the product again greatly reduces the difficulty of solving the problem.

[0037] 4. This invention does not require the installation of any sensors or new equipment. The only data that needs to be measured from the operating transformer is the primary and secondary currents, which can be easily obtained from the current transformers (CTs) already installed on the transformer.

[0038] 5. This invention is economical, and because it decouples the phase voltage, it can reliably detect low-level inter-turn faults during system transients and external faults. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 Average path of the magnetic flux in a typical three-phase power transformer;

[0040] Figure 2 Equivalent magnetic circuit in normal operating condition;

[0041] Figure 3 Simplified equivalent magnetic circuit in normal operating condition;

[0042] Figure 4 Equivalent magnetic circuit in inter-turn fault condition;

[0043] Figure 5 Flowchart of the calculation process of the inter-turn fault index FDI. DETAILED DESCRIPTION

[0044] The application will be described in further detail below with reference to the accompanying drawings.

[0045] I) Establishing the equivalent magnetic circuit in inter-turn fault condition and performing theoretical derivation

[0046] Figure 1 Average path of the magnetic flux in a typical three-phase power transformer (dashed line), including its core, windings, etc. For power transformers, in normal operating condition, the magnetic flux is mainly concentrated in the core and the leakage flux is mainly concentrated in the air and oil. The leakage flux is much smaller than the flux in the core, so the leakage flux is neglected in the equivalent magnetic circuit. Figure 2 Equivalent magnetic circuit showing the magnetic field in a lumped reluctance circuit is depicted. In the circuit phase a, N pa and N sa are the number of turns of the primary and secondary windings, respectively. i pa and i sa are the currents flowing through the primary and secondary windings, respectively. R La and R Ya represent the reluctance of the limbs and the yoke, respectively. R ma represents the reluctance of the path between the top and bottom of the transformer core, which is related to the core flux that passes through the parallel air and oil tank. R lpa and R lsa represent the leakage reluctance of the primary and secondary windings, respectively. For other phases, the same symbols are used, but the subscripts end with b and c.

[0047] The equivalent circuit of Figure 2 can be simplified using the following assumptions: 1) Since the leakage reluctance spreads through the air, they have higher values compared to the reluctance that spreads through the iron, i.e. the reluctance of the limbs and the yoke, R L and R Y . Therefore, these parallel reluctances are neglected in the simplified equivalent circuit.

[0048] R lpa = R lsa = ∞, Rlpb =R lsb =∞, R lpc =R lsc =∞ (1)

[0049] 2) For the same reason, the path magnetic resistance between the top and bottom of the transformer core can also be ignored.

[0050] R ma =∞, R mb =∞, R mc =∞ (2)

[0051] Simplified equivalent circuit such as Figure 3 As shown, in this circuit, R a =R La +R Ya R b =R Lb ,

[0052] R c =R Lc +R Yc During normal operation of a transformer, the absolute permeability (μ) of the core can be considered constant within its linear region. Therefore, each reluctance in the equivalent circuit can be calculated using the well-known formula R = L / μS, where L and S are the average length and net cross-sectional area of ​​the cross section.

[0053] Figure 3 This is a simplified equivalent circuit of the transformer under normal operating conditions. Now, assume an inter-turn fault occurs in the primary or secondary winding of phase a. This fault condition is similar to that of an autotransformer with a shortened secondary winding, due to the shortened number of turns (N). f The number of turns in the shortened winding is much lower than the normal number of turns remaining in the primary winding, therefore the induced current (I) in the shortened winding is much lower. f The induced current is very high, and it will generate a reverse magnetomotive force to counteract the magnetomotive force generated by the normal winding.

[0054] The main challenge faced by transformer protection systems in detecting inter-turn faults is the difficulty in responding to low-level faults caused by a small number of shortened turns. When a few turns of the transformer winding are shortened, the operating voltage of each phase does not change significantly, and the operating point of the transformer is not substantially altered. Figure 3 Existing reluctance in the simplified circuit can also be used in transformers with inter-turn faults.

[0055] Therefore, the simplified equivalent magnetic circuit of the transformer during inter-turn faults can be considered as follows: Figure 4 Existing literature has also used similar equivalent circuits to verify the analyses performed. and Let be the magnetic flux of each phase.

[0056] useFigure 4 The equivalent magnetic circuit is derived in the time domain as follows:

[0057]

[0058]

[0059]

[0060] Among them, N' pa The number of primary winding turns after the fault occurs is equal to N. pa -N f The above equation applies to Figure 4 The simplified equivalent circuit of the faulty transformer is shown. When the transformer is operating normally, the following conditions are satisfied in (3) and (4):

[0061] N' pa =N pa N f I f =0 (6)

[0062] N f I f The only case where the term is not zero is when an inter-turn fault occurs. In the early stages of a fault event, the number of faulty turns is small, and N' can be considered negligible. pa ≈N pa Now consider that the number of turns per phase on both the primary and secondary sides is equal, i.e., N. pa =N pb =N pc =N p And N sa =N sb =N sc =N s Considering formula (5), equations (3)-(4) can be expressed in the following form:

[0063]

[0064]

[0065] The left-hand side of the above time-domain equation can be extended using the following equation:

[0066]

[0067]

[0068]

[0069] ii) Solving the unknown vector matrix X using the minimum error square method

[0070] Substitute (9)-(11) into (7)-(8), equations (12)-(13) are obtained. In these obtained equations, there are six unknown parameters, i.e. θ a 、θ b 、θ f 、N f I f This makes the system underdetermined, in order to solve the unknown parameters, more equations are needed, different time samples can be used to bring into (12) and (13).

[0071]

[0072]

[0073] If the number of equations and the number of observation values exceed the number of unknown variables, the system is overdetermined, and the unknown variables can be found through the estimation process. In this way, the following matrix is realized:

[0074] AX = B (14)

[0075] Where A represents the known coefficient matrix, which is given in (15); X represents the unknown vector matrix, and B represents the measurement sample matrix varying with time, and the detailed physical meaning of each measurement is as follows:

[0076]

[0077]

[0078]

[0079] Where, θ a 、θ b 、θ f 、N f I f are all unknown parameters; represents the magnetic flux of phase a, phase a is the assumed faulty phase, represents the magnetic flux of phase b, phase b is an arbitrarily selected non-faulty phase, θ a represents the phase angle of phase a, θ b represents the phase angle of phase b, θ f represents the phase angle of the fault current, N f I f represents the product of the fault turn number and the fault current size.

[0080] Where, R a , R b , R c respectively represent the cross-sectional magnetic resistance of a, b, and c three-phase; i pa , ipb i pc These represent the primary currents of phases a, b, and c, respectively; i sa i sb i sc These represent the secondary currents of phases a, b, and c, respectively; the number of turns in the primary windings of phases a, b, and c are all N. p The number of turns in the secondary windings of phases a, b, and c are all N. s ω represents angular frequency;

[0081] Where j is the number of samplings, n is the total number of measurement samples, l is the number of measurement samples within the moving data window, Δt is the time difference between two consecutive measurement samples, and t l =-(nl)Δt,t j =-(nj)Δt,t n =0.

[0082] The Least Squares (LES) algorithm is used to solve for the unknown vector:

[0083] X = (A T A) -1 A T B (18)

[0084] The LES algorithm is used to obtain the unknown vector matrix X, and N in the unknown vector matrix X is solved. f I f cosθ f With N f I f sinθ f The element can be used to calculate N using the formula for the fault index FDI. f I f Compared to solving N separately f I f Recalculating the product greatly reduces the difficulty of the solution. Where N... f I f It is the product of the number of faulty turns and the magnitude of the fault current.

[0085] III) Calculation of inter-turn fault indicators

[0086] Because this parameter is not zero when an inter-turn fault occurs, its value can serve as a very good indicator for determining inter-turn faults. Therefore, this paper defines it as the Inter-Turn Fault Index (FDI), and its calculation method is as follows:

[0087]

[0088] To make the calculation process of the inter-turn fault index (FDI) easier to understand, please refer to... Figure 5 The calculation process is shown below.

[0089] Four), determining inter-turn fault

[0090] In normal operation, external fault or operation under unbalanced conditions, FDI does not change much, but when a component fault occurs, its value will increase sharply. Therefore, when the following conditions are met, it can be determined that there is an inter-turn fault:

[0091] | FDI | ≥ Δ (20)

[0092] Where Δ is the inter-turn fault threshold, Δ ≠ 0, and 2-6% of the rated current of the power transformer is taken as the inter-turn fault threshold. Under load changes from the outside of the transformer and abnormal operating conditions, the FDI value will not change.

[0093] The implementation is not complex and does not require the installation of any sensors or new equipment. The only data required to be measured from the operating transformer is the primary and secondary currents, which can be easily obtained through the current transformers (CT) already installed on the transformer. In addition, in order to carry out the required calculations, some easily obtained transformer parameters should be determined, including the winding configuration vector group, the number of turns of the winding (N p and N s ) and the cross-sectional reluctance (R a , R b and R c ). In addition to the above parameters, the setting of the inter-turn fault threshold Δ for the proposed method should be adjusted by the user according to specific needs. In equation (20), it is important to adjust the FDI threshold. Similar to other current-based detection methods, the threshold Δ can generally be selected as a percentage of the rated current of the transformer, for example, it can be set to 4% of the rated current, and the difference in nominal parameters of the transformer will affect the specific setting.

[0094] The technical solution described above is only one embodiment of the present application. For those skilled in the art, on the basis of the principles disclosed in the present application, various types of improvements or modifications can be easily made, and are not limited to the technical solutions described in the above specific embodiments of the present application. Therefore, the above description is only preferred, and is not limited in meaning.

Claims

1. A method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit, characterized in that: Based on the structural characteristics of a three-phase power transformer, an equivalent magnetic circuit under normal operating conditions is established and simplified. Select any one phase in the simplified equivalent magnetic circuit under normal operating conditions as the fault phase, and establish the equivalent magnetic circuit under inter-turn fault conditions. Analyzing the equivalent magnetic circuit under inter-turn fault conditions and deriving the following conclusion: Only when an inter-turn fault occurs, N f I f ≠0, where N f This indicates the number of turns shortened in the primary or secondary winding due to an inter-turn fault, i.e., the number of faulty turns; I f This represents the induced current on the faulty turns, i.e., the fault current. According to N f I f To determine whether an inter-turn fault has occurred; using N f I f As an inter-turn fault indicator, FDI is determined to be an inter-turn fault when |FDI|≥Δ, where Δ is the inter-turn fault threshold and Δ≠0.

2. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 1, characterized in that, Calculate the Failure Index (FDI) using the following formula: Among them, I f Represents the fault current, θ f The phase angle represents the fault current.

3. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 1, characterized in that, The inter-turn fault threshold is determined based on the rated current of the power transformer.

4. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 3, characterized in that, The threshold for inter-turn faults is set at 2-6% of the rated current of the power transformer.

5. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 4, characterized in that, The inter-turn fault threshold is set at 4% of the rated current of the power transformer.

6. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 2, characterized in that, An unknown vector matrix X is constructed to solve for the parameters used to calculate the Fault Indicator (FDI). The unknown vector matrix X is as follows: in, θ a θ b θ f N f I f All parameters are unknown; This represents the magnetic flux of phase a, where phase a is the assumed fault phase. θ represents the magnetic flux of phase b, where phase b is an arbitrarily chosen non-faulty phase. a θ represents the phase angle of phase a. b θ represents the phase angle of phase b. f The phase angle N represents the fault current. f I f This represents the product of the number of faulty turns and the magnitude of the fault current.

7. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 6, characterized in that, Based on measurement samples from different times, the unknown vector matrix X is solved using the minimum error square method: X=(A T A) -1 A T B Where A represents a known coefficient matrix, and B represents a measurement sample matrix that changes over time; Among them, R a R b R c These represent the cross-sectional magnetic reluctances of phases a, b, and c, respectively; i pa i pb i pc These represent the primary currents of phases a, b, and c, respectively; i sa i sb i sc These represent the secondary currents of phases a, b, and c, respectively; the number of turns in the primary windings of phases a, b, and c are all N. p The number of turns in the secondary windings of phases a, b, and c are all N. s ω represents angular frequency; Where j is the number of samplings, n is the total number of measurement samples, l is the number of measurement samples within the moving data window, Δt is the time difference between two consecutive measurement samples, and t l =-(nl)Δt,t j =-(nj)Δt,t n =0.

8. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 1, characterized in that, The simplified method for the equivalent magnetic circuit under normal operating conditions is to ignore the parallel magnetic reluctance and the path magnetic reluctance between the top and bottom of the transformer core.

9. The method for detecting inter-turn faults in a three-phase power transformer based on an equivalent magnetic circuit according to claim 1, characterized in that, Based on the equivalent magnetic circuit under inter-turn fault conditions, the following equation is derived in the time domain: Where phase a is the assumed fault phase, and N' pa N′ represents the number of primary winding turns after the fault occurs. pa =N pa -N f i pa i pb i pc These represent the primary currents of phases a, b, and c, respectively; i sa i sb i sc These represent the primary currents of phases a, b, and c, respectively. N represents magnetic flux. pa and N sa R represents the number of turns in the primary winding and the number of turns in the secondary winding of phase a; a R b R c These represent the cross-sectional magnetic reluctance of phases a, b, and c, respectively.

Images