Current transformer distortion current reconstruction method based on U-I trajectory curve

Abstract

The invention discloses a current transformer distortion current reconstruction method based on a U-I trajectory curve, and the method comprises the following steps: carrying out the synchronous sampling of a voltage value and a current value at a measurement point, and carrying out the per-unit processing; constructing a coordinate system taking the current value after per unit processing as a horizontal axis and the voltage value as a longitudinal axis in the two-dimensional coordinate, and drawing a U-I track curve; analyzing U-I track curve characteristics of the current transformer in a normal operation state, a transient state and a steady state; linear transmission sections of transient saturation and steady saturation are identified; and taking sampling points in the linear transmission section as input values, restoring a U-I trajectory curve by using an ellipse fitting algorithm, extracting current values corresponding to abscissas on the restored U-I trajectory curve, and arranging the current values according to a time sequence to realize current reconstruction. According to the method, the reconstruction of the CT secondary distortion current is realized through a least square ellipse fitting method by utilizing the similarity between a U-I trajectory curve and an elliptic curve during normal linear transmission. The problem that the differential protection adaptability is reduced or even fails due to distortion current is effectively prevented, and the protection stability is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of relay protection in power systems, and particularly to a method for reconstructing distorted current of a current transformer based on a U-I trajectory curve. Background Art

[0002] A current transformer (CT) is the most important measuring component in a power system, directly affecting the accuracy of subsequent differential protection. To date, electronic transformers have not been widely applied in the power system engineering field in an all-round manner, and ferromagnetic transformers are still the mainstream current measuring components. Limited by the non-linear excitation characteristics of the iron core component, in the case of an interphase fault in the line causing a strong fault current, the secondary circuit of the current transformer (CT) often saturates, resulting in distortion of the secondary current, which will directly lead to missed judgments and misjudgments of differential protection, causing serious consequences such as fault amplification. Therefore, accurately identifying the saturation phenomenon of the current transformer (CT) and promptly reconstructing the distorted current is of utmost importance for ensuring the correct operation of differential protection and the stability of system operation.

[0003] Currently, for the problem of current transformer (CT) saturation, it mainly relies on capturing correct waveform information in a linear transfer region before saturation. As recorded in Document [1]: Liu Yiqing, Wu Kai, Xu Mingyang, etc. Improved Scheme of Zero-Sequence Direction Element Based on Accurate Identification of CT Saturation [J]. Power System Technology, 2021, 45(10): 4161-4174. This method does not consider the steady-state saturation condition and the solution method for reconstructing distorted current. Another method, based on identifying saturation, uses the linear transfer current at the initial stage of the fault as the input and reconstructs the distorted current using the Taylor series expansion method, as recorded in Document [2]: Wang Feng, Zhu Jia, Jiao Shaolin, etc. Flux Density Feature Analysis and CT Saturation Region Identification and Reconstruction Technology [J]. Electric Power, 2023, 56(10): 179-185. However, the prediction effect of this method for severe saturation is not ideal, and it highly depends on the data window length, still falling short of the requirements for the rapidity and accuracy of distorted current reconstruction. Summary of the Invention

[0004] To solve the risk of failure of differential protection caused by distortion of the secondary current after CT saturation, the present invention provides a method for reconstructing distorted current of a current transformer based on a U-I trajectory curve, aiming to reconstruct the secondary distorted current under different degrees of saturation of the CT caused by large fault currents. Based on the coupling relationship between voltage and current, this method constructs a U-I trajectory curve on a two-dimensional plane, and uses the similarity between the U-I trajectory curve and the elliptic curve during normal linear transfer. Through the method of least squares ellipse fitting, the reconstruction of the secondary distorted current of the CT is realized. It effectively prevents the problem that the distorted current reduces the adaptability of differential protection or even causes it to fail, and effectively improves the protection stability.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for reconstructing distorted current of a current transformer based on a U-I trajectory curve, comprising the following steps:

[0007] Step 1: Synchronously sample the voltage and current values at the measuring point and perform per-unit processing;

[0008] Step 2: In a two-dimensional coordinate plane, construct a coordinate system with the per-unit processed current value as the horizontal axis and the voltage value as the vertical axis, and draw a U-I trajectory curve;

[0009] Step 3: Analyze the characteristics of the U-I trajectory curve under the normal operation state, transient state, and steady state of the current transformer;

[0010] Step 4: Identify the linear transfer sections under transient saturation and steady-state saturation;

[0011] Step 5: Use the sampling points in the linear transfer section as input values, use the ellipse fitting algorithm to restore the U-I trajectory curve, extract the current values corresponding to the abscissa on the restored U-I trajectory curve, and arrange them in time series to achieve current reconstruction.

[0012] In the said Step 1, synchronously collect the current quantity and voltage quantity data information on the primary side of the current transformer, and at the same time define a coordinate system in the rectangular coordinate space with the voltage quantity sampling sequence as the horizontal axis and the current quantity sampling sequence as the vertical axis, and perform per-unit processing on the voltage and current sequences;

[0013] Taking the voltage value U base and the current value I base during the steady-state operation of the system as the base values, perform normalization processing on the original sampling values u(t) and i(t) to ensure the analysis of the U-I trajectory curve on a unified scale;

[0014]

[0015] In formula (1), u pu and i pu are the coordinate values after normalization processing respectively.

[0016] In the said Step 2, on the two-dimensional coordinate plane, with the per-unit processed current value as the abscissa and the voltage value as the ordinate, draw a U-I trajectory curve based on the cycle duration of 0.02s corresponding to the standard power frequency of 50Hz.

[0017] In the said Step 3,

[0018] 3.1: Under power frequency, the voltage and current waveforms remain as standard sine curves and do not exceed the rated values. At this time, the characteristic of the measured point U-I trajectory curve is an ellipse centered at the origin of coordinates, which is obtained by multiplying the position corresponding to the standard ellipse equation by a rotation factor α. Specifically as follows:

[0019] The mathematical expression of the standard ellipse equation is: In the form of a graph in the coordinate system, it is a regular ellipse with the center at the origin of coordinates, the major axis along the x-axis with a length of a, and the minor axis along the y-axis with a length of b. Under normal operating conditions, due to a certain phase difference between the voltage and the current, the U-I trajectory curve rotates a certain angle compared to the standard form, as Figure 8 shown:

[0020] The mathematical expression form of the standard ellipse equation rotated by the θ angle is:

[0021]

[0022] The equation form obtained after arrangement is:

[0023]

[0024] The corresponding form is:

[0025] Ax 2 +Bxy+Cy 2 =1

[0026] Compared with the general equation form Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0, where D, E, F are 0 and the right side of the equal sign is 1.

[0027] In the U-I trajectory curve, the U-I ellipse curve corresponding to the normal operating condition can be characterized as being represented by multiplying the standard ellipse equation form by a rotation factor α. In actual situations, α is related to the power factor angle θ, and the rotation factor is represented in matrix form as:

[0028]

[0029] 3.2: During the transient saturation process of the current transformer, the distortion characteristics of the U-I trajectory curve show a dynamic evolution law:

[0030] When slightly saturated in the initial stage, the aperiodic component causes local magnetic flux deviation in the iron core, resulting in a slight distortion of the overall U-I trajectory curve showing an elliptical contour. The curve still maintains the closed characteristic, but the edge smoothness significantly decreases. There are tiny burr disturbances similar to the elliptical edge in the peak and valley regions, and at the same time, the trajectory shrinks towards the origin along the axis direction. At this time, the hysteresis effect of the iron core only affects the local transfer characteristics, the symmetry of the trajectory is not completely destroyed, and the curvature change still shows a continuous gradual change law; when severely saturated, the magnetic permeability of the iron core is severely limited, and the U-I trajectory curve undergoes a structural distortion. The transfer failure of more than half a cycle causes the trajectory to collapse into an acute peak-like structure. The curvature gradient in the peak / valley region increases sharply, forming an obvious kink-like mutation. The trajectory on the non-collapsed side has an abnormal bulge due to the instantaneous recovery of magnetic flux, and the overall shape shows a fractured asymmetric characteristic;

[0031] 3.3: During the steady-state saturation evolution process of the current transformer, the morphological distortion of the U-I trajectory curve shows a progressive characteristic: in the slight saturation stage, the U-I trajectory curve maintains the closed characteristic, and there is a horizontal compression deformation as a whole. The curvature radii in the peak / valley regions of the positive and negative half-cycles increase significantly, forming a "flattened" distortion similar to a trapezoidal structure, and the trajectory arc near the zero-crossing point still maintains a continuous and smooth transition; when reaching the medium and severe saturation stages, the hysteresis nonlinear effect of the iron core causes a mutation of the trajectory, and an acute turning distortion occurs in the peak / valley regions. The curve shows a multi-sided zigzag characteristic, and the sharpness of its kink is strongly nonlinearly correlated with the transfer error; in the severe saturation stage, the proportion of the linear transfer section of the trajectory is less than 30%, forming a distortion similar to a Z-shaped structure, and the kink distortion area has completely deviated from the elliptical motion law.

[0032] In step 4, according to the electrical and magnetic transfer characteristics of the primary and secondary sides of the current transformer, for transient saturation, there is an interval in the initial stage of the cycle to restore linear transfer, and for steady-state saturation, there are two intervals after passing through zero to exit saturation within the cycle. In the case of the deepest saturation, there is at least a 2 - 3s linear transfer section. Due to the dynamic attenuation characteristic of the aperiodic component, transient saturation forms a short linear transfer window in the initial stage after the fault starts, which is manifested as a smooth section in the current waveform that is not distorted; while steady-state saturation is affected by the periodic demagnetization effect, and symmetrically distributed linear intervals are generated near the current zero-crossing point, and the duration of its continuous time is inversely related to the remanence intensity of the iron core. In specific implementation, an adaptive sliding window algorithm is used to detect the peak and valley extreme points of the current waveform, and combined with the power frequency periodic verification and saturation type characteristics, the linear transfer section can be accurately extracted in a noisy environment. During this process, the linear transfer section of transient saturation is concentrated in the front section of the cycle, showing unidirectional integrity; while the linear transfer sections of steady-state saturation are distributed at the starting positions of the positive and negative half-cycles, reflecting the symmetric recovery characteristic.

[0033] In step 4, the sampling points within the linear transfer section are extracted as follows:

[0034] During the fault transient period, due to the influence of the decaying DC component and harmonic components, the system frequency is no longer 50 Hz power frequency, and the waveform on the primary side is no longer a standard sinusoidal cycle wave. The corresponding cycle duration may change, thus affecting to a certain extent the identification of the linear transformation section length. However, according to the nature of the cycle, there must be a peak value and a valley value within a complete cycle. The difference between the corresponding moments of the two is half of the cycle duration. Therefore, an adaptive sliding window algorithm is used to detect the peak and valley values of the current within the cycle. Among them, the conditions for detecting two points are as follows:

[0035] Peak: Valley:

[0036] After detecting the corresponding moments, twice the difference between the two is the corresponding complete cycle duration, that is:

[0037] T rl = 2|t pk - t lw |

[0038] Among them, T rl is the actual cycle duration, and t pk , t lw are the corresponding moments of the detected peak and valley values respectively.

[0039] According to the electromagnetic transformation characteristics of the CT, after a fault occurs, the CT will not saturate immediately, but there is still a linear transformation region. The secondary current within this linear transformation region can accurately represent the actual situation of the primary current. As Figure 9 shown, the left side is the transient saturation situation of the CT, and the right side is the steady-state saturation situation. According to the literature, there is only one linear transformation region with transient saturation within one cycle, and the steady-state saturation shows a linear transformation section corresponding to zero-crossing and exiting saturation. As Figure 9 marked, the sampled points taken within the linear transformation section can all be used as the input data for the ellipse fitting algorithm.

[0040] In step 5 described above, the form of the ellipse equation is as follows:

[0041] Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 (3);

[0042] In equation (3), A, B, C, D, E, and F are 6 parameters that determine a unique ellipse equation. Through the ellipse equation, relevant characteristic parameters can be obtained:

[0043]

[0044] In Equation (4), θ is the rotation angle of the ellipse relative to the standard ellipse equation form; a and b are the major and minor axes of the ellipse, respectively. This also means that at least 6 sampling points are required to determine a unique ellipse equation. Based on the sampling points extracted from the linear transfer region, the objective function and constraints are obtained, and solving the objective function and constraints can obtain the fitted ellipse.

[0045] In step 5, the voltage data obtained by the potential transformer PT at the measuring point is known, that is, the ordinate of the fitted U-I trajectory curve is known. The current data corresponding to the abscissa on the U-I trajectory curve is extracted and arranged in time series to obtain the accurate secondary side current of the CT after reconstruction. Specifically as follows:

[0046] For Equation (5), it is essentially a constraint solving problem. The ellipse equation establishment process can be added in front of it to make the solution result more perfect and intuitive, as follows:

[0047] Six sampling points are selected on the U-I trajectory curve segment corresponding to the previously selected linear transfer section, which just correspond to the six parameters required to solve the ellipse equation. The abscissas of these sampling points are current values, and the ordinates are voltage values, and the ellipse equation is represented in the form of vector multiplication.

[0048] According to the foregoing, the form of the general ellipse equation is known as Equation (3): Ax 2 +Bxy+Cy 2 +Dx+Ey+F = 0, f(Φ,Q i ′) is defined as the form of the multiplication of the vector matrix Φ and the vector matrix Q i ′, and the multiplication result corresponds to the general ellipse equation of Equation (3); the specific parameters of the two matrices are given by the other two equations in the curly brackets. The six parameters A to F in the vector matrix Φ are the values for determining a unique ellipse, which are obtained according to mathematical definitions and do not need to be specifically explained. x i and y i That is, they represent the abscissa and ordinate of the sampling points in the plane coordinate system. In the present invention, they are: the current quantity I is the abscissa, and the voltage quantity U is the ordinate.

[0049] The ellipse equation is represented in the form of vector multiplication as follows:

[0050]

[0051] According to the least squares principle, six sampling points are selected in the linear transfer region to determine the objective function and constraints as shown in Equation (5):

[0052]

[0053] Solve the system of equations in Equation (5) to obtain six parameter values, that is, determine a fitted ellipse. Then, use the ellipse fitting result as the reconstructed U-I trajectory curve. The abscissa of each point on this curve is the current value, and the ordinate is the voltage value. Since the voltage curve is not distorted, that is, the voltage waveform measured by the PT is accurate, by comparing the voltage waveform with the fitted U-I trajectory curve, the current value at the corresponding moment can be obtained and rearranged in time series, that is, the reconstruction of the distorted current is realized. The schematic diagram is as shown in Figure 10 shown.

[0054] The method for reconstructing the distorted current of a current transformer based on the U-I trajectory curve in the present invention has the following technical effects:

[0055] 1) The method of the present invention can solve the reconstruction and reduction of the secondary current distortion under different types and degrees of saturation of the current transformer, effectively prevent the possible missed judgment and misjudgment of differential protection, and improve the system stability.

[0056] 2) The method of the present invention has a low requirement for the data window length and the calculation method is relatively simple.

[0057] 3) The method for reconstructing the distorted current proposed in the present invention is accurate and reliable, can effectively restore the waveform, and prevent the misoperation and refusal of differential protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The present invention will be further described below in conjunction with the drawings and examples;

[0059] Figure 1 is the U-I trajectory curve during normal operation.

[0060] Figure 2 is the U-I trajectory curve when the current transformer CT is in transient saturation.

[0061] Figure 3 is the U-I trajectory curve when the current transformer CT is in steady-state saturation.

[0062] Figure 4 is a typical situation of transient and steady-state ellipse fitting.

[0063] Figure 5 is the flow chart for realizing the reconstruction of the distorted current by the U-I trajectory curve.

[0064] Figure 6 is the topology of the 220 kV infinite system.

[0065] Fig. 7(a) shows the fitting and reconstruction effect of a typical current transformer CT in transient saturation;

[0066] Fig. 7(b) shows the fitting and reconstruction effect of a typical current transformer CT in steady-state saturation;

[0067] Figure 7(c) shows the fitting and reconstruction effect of the superimposed noise of the transient and steady-state saturation of a typical current transformer CT.

[0068] Figure 8 It is a schematic diagram that the U-I trajectory curve rotates a certain angle compared to the standard form.

[0069] Figure 9 It is a schematic diagram of the linear transmission section in the annotation under the transient saturation and steady-state saturation of CT.

[0070] Figure 10 It is a schematic diagram of realizing the reconstruction of distorted current by rearranging in time series.

[0071] Figure 11 It is a schematic diagram of the process that the distortion degree of the corresponding U-I trajectory curve continuously deepens due to the deepening of the transient saturation of CT.

[0072] Figure 12 It is a schematic diagram of the distortion situation of the U-I trajectory curve as the steady-state saturation degree of CT continuously deepens.

[0073] Figure 13 It is a schematic diagram of the linear transmission section existing in the most severe saturation situation. Specific implementation manner

[0074] A new method for reconstructing the distorted current of CT based on the U-I trajectory curve. At the measurement point, the voltage value obtained by the potential transformer PT and the current value measured by the current transformer CT are used to establish a coupling relationship and represent it in a two-dimensional plane, establish a U-I trajectory curve, and use the similarity between the U-I trajectory curve and the elliptic curve as the basis for fitting to realize the reconstruction of the distorted current on the secondary side after the saturation of the current transformer CT. Specifically, it includes the following:

[0075] (1): At the measurement point, a current transformer CT and a potential transformer PT are often installed simultaneously. Under the influence of the fault current, the potential transformer PT has a prominent saturation problem, but the potential transformer PT does not have a saturation problem. Therefore, the voltage quantity provided by the potential transformer PT is used to assist in constructing the curve. The secondary voltage u(t) of the potential transformer PT and the secondary current i(t) of the current transformer CT are synchronously sampled using a high-precision synchronous clock.

[0076] The IRIG-B timing module is used to synchronously collect the current quantity and voltage quantity data information on the primary side of the current transformer CT, and the sampling rate is required to meet the complete capture of the harmonic of the power frequency signal (4 kHz). At the same time, a coordinate system is defined in the rectangular coordinate space with the voltage quantity sampling sequence as the horizontal axis and the current quantity sampling sequence as the vertical axis. As Figure 4 shown.

[0077] Without eliminating the dimension difference, it is required to perform per-unit processing on the voltage and current sequences. Using the voltage value U during the steady-state operation of the systembase With the current value I base as the base value, the original sampled values u(t) and i(t) are normalized to ensure that the trajectory curve is analyzed under a unified scale:

[0078]

[0079] In the formula, u pu and i pu are the coordinate values after normalization respectively.

[0080] (2): On the two-dimensional coordinate plane, with the processed current value as the abscissa and the processed voltage value as the ordinate, a U-I trajectory curve is drawn based on the cycle duration of 0.02s corresponding to the standard power frequency of 50Hz. As Figure 4 shown, in the coordinate system established with the current quantity as the abscissa and the voltage quantity as the ordinate, when generating the U-I trajectory, taking 20ms corresponding to the power frequency as a cycle duration, the voltage and current sampling points within this duration are taken together to draw the U-I trajectory.

[0081] Under power frequency, the waveforms of voltage and current quantities remain as standard sine curves and do not exceed the rated values. At this time, the characteristics of the measured point U-I trajectory curve are manifested as an ellipse centered at the coordinate origin, rotating a certain angle around the center on the basis of the standard ellipse curve.

[0082] This ellipse is obtained by multiplying the position corresponding to the standard ellipse equation by a rotation factor α, and α is determined by the power factor angle θ:

[0083]

[0084] The trajectory strictly satisfies the linear transfer equation of voltage and current, and remains stable in shape without distortion or collapse characteristics when the system impedance is constant. When the system operates in a steady state, the U-I trajectory curve is smooth and closed, without local collapse or distortion caused by signal distortion, the curve curvature changes uniformly, without sudden changes and step points.

[0085] (3): During the transient saturation process of the current transformer CT, the distortion characteristics of the U-I trajectory curve show a dynamic evolution law:

[0086] In the initial stage of slight saturation, the non-periodic component causes local magnetic flux deviation in the iron core, resulting in a slight distortion of the overall U-I trajectory curve in the shape of an ellipse. The curve still maintains the closed characteristic, but the edge smoothness significantly decreases, and there are small burr disturbances similar to the ellipse edge in the peak and trough regions. At the same time, the trajectory shrinks towards the origin along the axis direction. At this time, the hysteresis effect of the iron core only affects the local transfer characteristics, and the trajectory symmetry is not completely destroyed, and the curvature change still shows a continuous gradual change law;

[0087] When severely saturated, the magnetic permeability of the iron core is severely limited, and the U-I trajectory curve undergoes structural distortion. The transmission failure exceeding half a cycle causes the trajectory to collapse into an acute peak-like structure, with a sharp increase in the curvature gradient in the peak / trough region, forming an obvious kink-type mutation. The trajectory on the non-collapsed side exhibits abnormal bulges due to the instantaneous recovery of magnetic flux, and the overall shape shows a fractured and asymmetric characteristic.

[0088] The morphological differences between the two saturation modes are as Figure 2 shown in the comparison, which intuitively reflects the dynamic evolution law of the non-linear transmission mechanism of the iron core and provides a quantifiable visual criterion for grading the severity of transient saturation.

[0089] Describing the changes in the U-I trajectory curve of the CT under different degrees of transient saturation, the change in the internal magnetic flux cannot be intuitively characterized by a graph, but as an internal cause, it affects the manifestation form of the U-I curve. As Figure 11 shown, it can more intuitively show the process of the distortion degree of the corresponding U-I trajectory curve increasing with the deepening of CT transient saturation.

[0090] (IV): During the steady-state saturation evolution process of the current transformer CT, the morphological distortion of the U-I trajectory curve also shows a progressive characteristic:

[0091] In the mild saturation stage, although the trajectory maintains a closed characteristic, the overall undergoes a horizontal compression deformation, and the curvature radius of the peak / trough region in the positive and negative half-cycles increases significantly, forming a "flattened" distortion similar to a trapezoidal structure, while the trajectory arc near the zero-crossing point still maintains a continuous and smooth transition. When reaching the medium and severe saturation conditions, the hysteresis non-linear effect of the iron core causes a mutation in the trajectory, and acute turning distortions occur in the peak / trough region, and the curve shows a multi-sided kinked characteristic, and the sharpness of its kink is strongly non-linearly correlated with the transmission error.

[0092] Especially in the severe saturation stage, the proportion of the linear transmission section of the trajectory is less than 30%, forming an obvious distortion similar to a Z-shaped structure, and the kink distortion area has completely deviated from the elliptical motion law.

[0093] The U-I trajectory curves corresponding to the typical slight steady-state saturation and severe saturation of the current transformer CT are as Figure 3 shown. Describing the changes in the U-I trajectory curve of the CT under different degrees of steady-state saturation, as Figure 12 shown, it reflects the distortion of the U-I trajectory curve as the steady-state saturation degree of the CT continuously deepens.

[0094] (5): Under the condition of CT saturation of current transformers, based on the non-linear characteristics of the dynamic hysteresis loop of the iron core, its transmission characteristics show significant time-varying characteristics. Theoretical analysis and experimental verification show that within the power frequency cycle of any saturation degree, there is a linear transmission section, and its duration is affected by the comprehensive action of the demagnetization characteristics of the iron core material and the non-periodic component of the fault current. Specifically, when the fault current passes through zero, the magnetic flux density of the iron core returns to the linear working area due to the reverse excitation effect. Even under the most severe saturation conditions, a linear transmission window lasting about 3-4 ms can still be formed.

[0095] Within this interval, the secondary current and the primary current satisfy the linear transmission equation; the secondary current of the current transformer CT can correctly reflect the primary fault current situation. Therefore, the coordinate points within this section are taken as the input quantities for ellipse fitting. In the design of the input quantities of the ellipse fitting algorithm, based on the mathematical completeness requirement of the least square method, only 6 or more effective data points within each power frequency cycle are required to solve the ellipse parameters.

[0096] In the most severe saturation case, there is at least still a linear transmission section of about 3-4 ms, as Figure 13 shown. Within the linear transmission area, the linear transmission equation of the secondary current and the primary current is:

[0097]

[0098] where, is the transformation ratio. If the influence of the residual magnetic flux B r of the iron core and the magnetic permeability μ is considered, the transmission equation can be extended to:

[0099]

[0100] The specific algorithm of ellipse fitting is as shown in Equation (5), which has been described based on the above formulas.

[0101] For ensuring data availability under the most severe working conditions, for transient saturation requirements, data points are evenly collected within the initial phase interval of the cycle, covering the linear transmission section where the magnetic flux of the iron core is not saturated; for steady-state saturation requirements, symmetric sampling is performed at the start of the positive and negative half-cycles after the current passes through zero, making full use of the high-precision transmission characteristics during the demagnetization recovery period of the iron core.

[0102] (6): Generally speaking, the form of the ellipse equation is as follows:

[0103] Ax 2 +Bxy+Cy 2 +Dx+Ey+F = 0 (3);

[0104] In the formula, A, B, C, D, E, and F are 6 parameters that determine a unique ellipse equation. Relevant characteristic parameters can be obtained through the ellipse equation:

[0105]

[0106] In the formula, θ is the rotation angle of the ellipse relative to the standard ellipse equation form; a and b are the major and minor axes of the ellipse respectively. This also means that at least 6 sampling points are required to determine a unique ellipse equation. According to the sampling points extracted in the linear transfer region, the objective function and constraints are obtained as shown in Equation (5):

[0107]

[0108] This process ensures the existence and stability of the solution through the ellipse parameter uniqueness theorem, and solves Equation (2); thus, the fitted ellipse can be obtained.

[0109] Given the voltage data obtained by the potential transformer PT at the measured point, that is, the ordinate of the fitted U-I trajectory curve is known, and the corresponding abscissa current data on the curve is extracted and arranged in time series, then the accurate secondary current of the reconstructed CT can be obtained. The complete steps for using the U-I trajectory curve to identify the saturation of the current transformer CT and reconstruct the distorted current are as Figure 5 shown.

[0110] (VII): Simulation verification:

[0111] Build a 220 kV line model on the PSCAD platform, and the topology is as Figure 6 shown. The three-terminal infinite power supply supplies power to the load center through a double-circuit line, and the line lengths are 30 km, 40 km, and 50 km respectively. The specific parameter settings are shown in Table 1.

[0112] Table 1 Specific simulation parameters

[0113]

[0114]

[0115] The measurement point is set at the outlet of the line where the load is located, including a current transformer CT and a potential transformer PT respectively used to measure the current and voltage. For the convenience of result expression, the transformation ratios are all taken as 1000:1, and the results of phase A are used for all simulations. The simulation verification is carried out according to the following three major types of examples:

[0116] Example 1. Set the CT to have a transient saturation phenomenon, and a typical fitting and reconstruction effect is shown in Figure 7(a). Example 2. Set the CT to have a steady-state saturation phenomenon. A typical fitting and reconstruction effect is shown in Figure 7(b). Example 3. Under the conditions of the above-mentioned transient and steady-state saturation of the CT, superimpose 25 dB of noise interference, and a typical fitting and reconstruction effect is shown in Figure 7(c).

[0117] Meanwhile, each set of example cases was subdivided, and each type of working condition was repeated 10 times. The root mean square error mean (RMSE) was used to measure the error between the reconstructed waveform and the actual waveform. The results are shown in Table 2.

[0118] Table 2 Identification results under different closing angles

[0119]

[0120] The accuracy of the distorted current reconstruction method is proved. Through simulation verification in multiple scenarios, the applicability of the method in a new energy high-penetration power grid is systematically proved, providing an engineering solution for the treatment of current transformer CT saturation.

[0121] Figure 7(a) 、 7(b) Figures 7(a), 7(b), and 7(c) are the reconstruction effects of CT transient saturation distorted current, CT steady-state saturation distorted current, and their intuitive fitting reconstruction effects under the condition of adding noise, respectively. The reconstruction effects should be presented together with the data in Table 2.

[0122] For Figure 7(a) shown, the fault occurs at 1.8 s. By using the distorted current reconstruction method of the present invention, the subsequent distorted part can be corrected to a continuous and smooth waveform curve by extracting the initial linear section (3 - 4 ms window). Combining with the RMSE data in Table 2, it can be seen that the method has a good reconstruction effect on the distorted current of CT transient saturation.

[0123] For Figure 7(b) shown, the reconstructed waveform is almost the same as the primary side original waveform, verifying that the method used in the present invention also has a good reconstruction effect on the steady-state saturated distorted current without decaying DC components.

[0124] For Figure 7(c) shown, under the condition of adding 25 dB noise interference to the original data, combining with the RMSE data in Table 2, it can be seen that the reconstruction accuracy of CT transient and steady-state saturated currents both decreases, but the overall error does not exceed 6%. It can be seen that the method used in the present invention has good noise resistance for the reconstruction of distorted current.

[0125] In addition, the relevant RMSE calculation formula:

[0126]

[0127] In the formula, R pre,i is the predicted value, R real,i is the measured value, and n is the number of samples.

Claims

1. A current transformer distorted current reconstruction method based on UI trajectory curve, characterized by The following steps are involved: Step 1: synchronously sample the voltage and current values ​​at the measuring point and perform standardization processing; Step 2: In a two-dimensional coordinate plane, construct a coordinate system with the normalized current value as the horizontal axis and the voltage value as the vertical axis, and draw the UI trajectory curve; Step 3: Analyze the UI trajectory curve characteristics of the current transformer in normal operation, transient and steady state; Step 4: Identify the linear transition section under transient saturation and steady-state saturation; Step 5: Use the sampling points in the linear transition section as input values ​​and use the ellipse fitting algorithm to restore the UI trajectory curve. The current value corresponding to the horizontal axis on the restored UI trajectory curve is extracted and arranged in time series to achieve current reconstruction.

2. The method for reconstructing the distorted current of a current transformer based on a UI trajectory curve according to claim 1, characterized in that: In the step 1, the current and voltage data information of the primary side of the current transformer are synchronously collected, and at the same time, a coordinate system with the voltage sampling sequence as the horizontal axis and the current sampling sequence as the vertical axis is defined in the rectangular coordinate space, and the voltage and current sequences are normalized.

3. The method for reconstructing the distorted current of a current transformer based on a UI trajectory curve according to claim 2, characterized in that: Voltage value U when the system is running in steady state base With current value I base As the base value, the original sampling values ​​u(t) and i(t) are normalized to ensure that the UI trajectory curve is analyzed at a unified scale; In formula (1), u pu and i pu are the normalized coordinate values.

4. The method for reconstructing the distorted current of a current transformer based on a UI trajectory curve according to claim 1, characterized in that: In the step 2, on a two-dimensional coordinate plane, the UI trajectory curve is drawn with the normalized current value as the horizontal coordinate and the voltage value as the vertical coordinate, and with the cycle length of 0.02s corresponding to the standard power frequency of 50Hz as the reference.

5. The method for reconstructing the distorted current of a current transformer based on a UI trajectory curve according to claim 1, characterized in that: In step 3, in the UI trajectory curve, the corresponding UI elliptical curve under normal operating conditions can be represented by a standard elliptical equation multiplied by a rotation factor α. In actual situations, α is related to the power factor angle θ, and the rotation factor is expressed in the form of a matrix:

6. The method for reconstructing the distorted current of a current transformer based on a UI trajectory curve according to claim 5, characterized in that: In step 3, during the transient saturation of the current transformer, the distortion characteristics of the UI trajectory curve show a dynamic evolution law: in the initial stage of slight saturation, the non-periodic component causes the local magnetic flux offset of the core, resulting in the overall slight distortion of the UI trajectory curve to an elliptical contour, the curve still maintains a closed characteristic, but the edge smoothness is significantly reduced, and tiny burr disturbances resembling the edge of an ellipse appear in the crest and trough regions, while the trajectory shrinks toward the origin along the axis direction; at this time, the hysteresis effect of the core only affects the local transmission characteristics, the trajectory symmetry is not completely destroyed, and the curvature change still shows a continuous gradual change law; in severe saturation, the magnetic conductivity of the core is severely limited, and the UI trajectory curve undergoes structural distortion. Transmission failure exceeding half a cycle causes the trajectory to collapse into a sharp-angled peak-like structure, the curvature gradient in the crest / trough region increases sharply, forming an obvious broken line mutation, and the non-collapsed side trajectory produces an abnormal bulge due to the instantaneous recovery of the magnetic flux, and the overall morphology presents a fractured asymmetric feature; During the steady-state saturation evolution of the current transformer, the morphological distortion of the UI trajectory curve presents a progressive characteristic: In the mild saturation stage, the UI trajectory curve maintains a closed characteristic, and the overall horizontal compression deformation occurs. The radius of curvature of the peak / valley area in the positive and negative half-cycles increases significantly, forming a "flattened" distortion similar to a trapezoidal structure, while the trajectory arc near the zero point still maintains a continuous and smooth transition; when it reaches the medium and severe saturation stage, the nonlinear effect of core hysteresis causes a sudden change in the trajectory, and the peak / valley area produces a sharp-angle turning distortion. The curve presents a polygonal broken line feature, and the sharpness of the angle shows a strong nonlinear correlation with the transmission error; In the severe saturation stage, the linear transmission section of the trajectory accounts for less than 30%, forming a distortion similar to a Z-shaped structure, and the angle distortion zone has completely deviated from the law of elliptical motion.

7. The method for reconstructing the distorted current of a current transformer based on a UI trajectory curve according to claim 1, characterized in that: In step 4, an adaptive sliding window algorithm is used to detect the peak and valley extreme points of the current waveform and extract the linear transmission section; the linear transmission section of transient saturation is concentrated in the front section of the cycle, showing unidirectional integrity; the linear transmission section of steady-state saturation is distributed at the starting position of the positive and negative half cycles, reflecting the symmetrical recovery characteristics.

8. The method for reconstructing the distorted current of a current transformer based on a UI trajectory curve according to claim 7, characterized in that: Extract the sampling points in the linear transition section as follows: Adaptive sliding window algorithm is used to detect the peak and valley values ​​of the current in the cycle, where the conditions for detecting two points are as follows: crest: and trough: and After the corresponding moment is detected, twice the difference between the two is the corresponding complete cycle duration, that is: T rl =2|t pk -t lw Among them, T rl is the actual cycle duration, t pk ,t lw are the corresponding moments of the detected peak and valley values ​​respectively; According to the electromagnetic transmission characteristics of CT, after a fault occurs, the CT will not be saturated immediately, but will include a linear transmission region. The secondary current in this linear transmission region can accurately represent the actual situation of the primary current.

9. The method for reconstructing distorted current of a current transformer based on a UI trajectory curve according to claim 1, characterized in that: In step 5, the ellipse equation is as follows: Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0(3); In formula (3), A, B, C, D, E, and F are six parameters that determine the unique ellipse equation. The relevant characteristic parameters can be obtained through the ellipse equation: In formula (4), θ is the rotation angle of the ellipse relative to the standard ellipse equation; a and b are the major and minor axes of the ellipse respectively; At least 6 sampling points can determine a unique ellipse equation; based on the extracted sampling points in the linear transition region, the objective function and constraints are obtained, and the fitting ellipse can be obtained by solving the objective function and the constraints.

10. The method for reconstructing distorted current of a current transformer based on a UI trajectory curve according to claim 9, characterized in that: In step 5, 6 sampling points are selected on the UI trajectory curve segment corresponding to the linear transmission segment, corresponding to the 6 parameters required to solve the elliptic equation; The horizontal coordinates of these sampling points are current values, and the vertical coordinates are voltage values. The elliptic equation is represented by vector multiplication; specifically, it includes: f(Φ,Q i ′) is defined as the vector matrix Φ and the vector matrix Q i ′ is a form of multiplication, and the multiplication result corresponds to the general elliptic equation of formula (3); The six parameters A to F in the vector matrix Φ are the values ​​that determine the unique ellipse; i With y i That is, the current I is the horizontal coordinate, and the voltage U is the vertical coordinate; The ellipse equation can be expressed in the form of vector multiplication as follows: According to the principle of least squares method, six sampling points in the linear transition region are selected to determine the objective function and constraints as shown in formula (5): Solving the equation group (5), we get 6 parameter values, that is, we determine a fitting ellipse. Then, we use the fitting result of this ellipse as the reconstructed UI trajectory curve. The horizontal coordinate of each point on the curve is the current value, and the vertical coordinate is the voltage value. Since the voltage curve is not distorted, that is, the voltage waveform measured by the PT is accurate, the current value at the corresponding moment can be obtained by comparing the voltage waveform with the fitting UI trajectory curve, and the reconstruction of the distorted current can be achieved by rearranging them in time series.

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