Error determination method and device for distribution network current transformer
By identifying excitation impedance and secondary leakage impedance using low-frequency signals, and combining the equivalent circuit model and Kalman filtering algorithm, online error detection and compensation of current transformers were achieved, improving metering accuracy and anti-interference capability, and solving the problem of insufficient accuracy of traditional models.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- STATE GRID CHONGQING ELECTRIC POWER COMPANY MARKETING SERVICE CENTER
- Filing Date
- 2026-03-05
- Publication Date
- 2026-04-28
AI Technical Summary
In existing technologies, offline verification of current transformers requires equipment shutdown, which cannot reflect dynamic operating errors. Furthermore, the accuracy of traditional linear evaluation models is insufficient, resulting in inadequate power grid monitoring accuracy and power supply reliability.
By identifying the excitation impedance and secondary leakage impedance through the total energy of the low-frequency signal, and combining the equivalent circuit model and Kalman filter algorithm, the relationship between the turns ratio error and the phase difference is corrected to achieve online error detection and compensation.
It improves the metering accuracy of current transformers in complex distribution network environments, solves the problems of insufficient static stability and anti-interference, and achieves high-precision error compensation.
Smart Images
Figure CN121934009A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of smart grids, and in particular to a method and apparatus for determining the error of a distribution network current transformer. Background Technology
[0002] In power distribution networks, current transformers are core devices for current measurement, relay protection, and energy metering. Their operational errors directly determine the accuracy of power grid monitoring and the reliability of power supply. With the development of distribution networks towards intelligence and distribution, and the increasing prevalence of scenarios such as renewable energy grid integration and flexible load fluctuations, current transformers are often operating under non-rated conditions. In related technologies, offline verification of current transformers requires equipment shutdown, affecting power supply continuity and failing to reflect dynamic operational errors. Other methods rely heavily on high-precision sensing hardware, which is costly and susceptible to electromagnetic interference in the field. Furthermore, the diverse models of current transformers and the complex installation environments lead to the coupling of error-influencing factors, rendering traditional linear evaluation models insufficiently accurate. Summary of the Invention
[0003] The purpose of this invention is to provide a method and apparatus for determining the error of a distribution network current transformer. By using the total energy of the low-frequency signal, key parameters such as excitation impedance and secondary leakage impedance can be identified more accurately, truly reflecting the electromagnetic behavior of the transformer under actual operating conditions. This effectively compensates for measurement errors such as ratio difference and phase difference, improves the metering accuracy of the current transformer in complex distribution network environments, and solves the problems of insufficient static stability and anti-interference.
[0004] To solve the above-mentioned technical problems, the present invention provides a method for determining the error of a distribution network current transformer, comprising:
[0005] The relationship between the ratio error and the phase difference of the current transformer is determined based on the connection relationship of the internal components of the current transformer. The ratio error represents the deviation between the actual ratio and the rated ratio of the current transformer, and the phase difference represents the phase deviation between the primary current and the secondary current under ideal conditions of the current transformer.
[0006] Based on the total energy of the current transformer under low-frequency signal injection, the relationship between the transformation ratio error and the relationship between the phase difference are corrected.
[0007] Based on the corrected formulas for the ratio error and the phase difference, the ratio error and phase difference of the current transformer are obtained.
[0008] On the other hand, the relationship between the transformation ratio error and the phase difference of the current transformer is determined based on the connection relationship of the internal components of the current transformer, including:
[0009] An equivalent circuit model of the current transformer is established based on the physical parameters of the primary side, secondary side, and core circuit of the current transformer.
[0010] Based on the equivalent circuit model, and combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the formulas for the ratio error and phase difference of the current transformer are determined.
[0011] On the other hand, an equivalent circuit model of the current transformer is established based on the physical parameters of the primary side, secondary side, and core circuit of the current transformer, including:
[0012] Based on the primary current on the primary side of the current transformer Number of turns in primary winding and primary leakage resistance Secondary current on the secondary side Number of turns in the secondary winding Secondary leakage reactance Secondary leakage resistance Load impedance and secondary leakage impedance Excitation current of the iron core circuit and excitation impedance Establish an equivalent circuit model for the current transformer;
[0013] The expression for the load impedance is as follows: , The resistance of the load. Let be the reactance of the load, and the expression for the secondary leakage impedance is: .
[0014] On the other hand, based on the equivalent circuit model, and combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the formulas for the ratio error and phase difference of the current transformer are determined, including:
[0015] The expression for the magnetomotive force balance relationship of the current transformer is: ;
[0016] in, For the rated ratio, ;
[0017] The expression for the voltage-current relationship in the excitation circuit is as follows: ;
[0018] The formulas for determining the ratio error and phase difference of the current transformer are determined by combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, including:
[0019] Based on the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the relationship between the primary current and the secondary current is determined. The expression for the relationship between the primary current and the secondary current is as follows:
[0020] ;
[0021] Based on the relationship between the primary current and the secondary current, determine the formulas for the ratio error and phase difference of the current transformer;
[0022] The relationship between the ratio error and the formula is:
[0023] ;
[0024] The relationship of the phase difference is:
[0025] ;
[0026] in, For the ratio error, For phase difference, The magnitude of the excitation current. This is the phase difference between the excitation current and the secondary voltage. The relevant phase angle of the secondary side, This represents the amplitude of the secondary current.
[0027] On the other hand, based on the total energy of the current transformer under the injected low-frequency signal, the relationships for the transformation ratio error and the phase difference are corrected, including:
[0028] A low-frequency current signal of a preset frequency is injected into the current transformer, and the total energy is determined, which includes active power and reactive power.
[0029] The excitation impedance of the core circuit and the secondary leakage impedance of the secondary side of the current transformer are corrected according to the active power and the reactive power under low frequency signals.
[0030] The relationship between the turns ratio error and the phase difference is corrected based on the corrected excitation impedance and the corrected secondary leakage impedance.
[0031] On the other hand, determining the total energy, which includes active power and reactive power, includes:
[0032] The expression for the active power is:
[0033] ;
[0034] The expression for the reactive power is:
[0035] ;
[0036] in, Active power Let be the amplitude of the voltage of the nth harmonic. Let be the amplitude of the current of the nth harmonic. Let be the phase difference between the voltage and current of the nth harmonic. This refers to reactive power.
[0037] On the other hand, the correction of the excitation impedance of the core circuit and the secondary leakage impedance of the current transformer under low-frequency signals based on the active power and the reactive power includes:
[0038] Based on the active power and the reactive power, the excitation impedance of the core circuit of the current transformer under low-frequency signal is corrected, and the corrected excitation impedance is:
[0039] , , ;
[0040] Based on the active power and the reactive power, the secondary leakage impedance of the current transformer under low-frequency signal conditions is corrected, and the corrected secondary leakage impedance is:
[0041] , , ;
[0042] in, This is the corrected excitation impedance. The corrected excitation resistor. The corrected magnetizing reactance. This is the corrected secondary leakage impedance. This is the corrected secondary leakage resistance. This is the corrected secondary leakage reactance. The magnitude of the excitation current. This refers to the amplitude of the secondary current;
[0043] The corrected excitation current is determined based on the corrected excitation impedance and the corrected secondary leakage impedance. The expression for the corrected excitation current is as follows:
[0044] ;
[0045] in, This is the corrected excitation current;
[0046] The relationship between the turns ratio error and the phase difference is corrected based on the corrected excitation impedance and the corrected secondary leakage impedance, including:
[0047] The formulas for the ratio error and phase difference of the current transformer are determined based on the corrected excitation current.
[0048] The corrected formula for the ratio error is:
[0049] ;
[0050] The corrected relationship for the phase difference is as follows:
[0051] ;
[0052] in, This is the corrected ratio error. This is the corrected phase difference.
[0053] On the other hand, based on the corrected formula for the ratio error and the formula for the phase difference, the ratio error and phase difference of the current transformer are obtained, including:
[0054] The corrected ratio error and phase difference of the current transformer are used to construct a state vector, and the actual measured error observations are used to construct an observation vector.
[0055] Based on historical offline calibration data, the prior distribution of phase difference is obtained, and the range of values of the phase difference is used as a regularization constraint to constrain the observation vector.
[0056] Based on the state vector and the observation vector with regularization constraints, Kalman filtering iteration is performed to obtain the optimal ratio error and phase difference.
[0057] On the other hand, based on historical offline calibration data, the prior distribution of the phase difference is obtained, and the range of values of the phase difference is used as a regularization constraint to constrain the observation vector, including:
[0058] The prior distribution of the historical offline calibration data is determined, and the prior distribution is as follows:
[0059] ;
[0060] in, For the prior distribution, This is the average phase difference from historical offline calibration data. The variance of the phase difference in historical offline calibration data;
[0061] The regularized phase difference is determined as follows:
[0062] ;
[0063] in, The phase difference after regularization. Phase difference;
[0064] By introducing a regularization matrix into the observation vector, we obtain an observation vector with regularization constraints.
[0065] The observation vector is:
[0066] ;
[0067] The observation vector with regularization constraints is:
[0068] ;
[0069] in, For the observation vector, For regularization matrix, , For regularized noise, , For the observation matrix, Let k be the state vector at the k-th time step. Let be the observation vector at the k-th time step. This represents the standard deviation of the phase difference in historical offline calibration data.
[0070] To address the aforementioned technical problems, the present invention also provides an error determination device for distribution network current transformers, comprising:
[0071] Memory, used to store computer programs;
[0072] A processor is used to implement the steps of the above-described method for determining the error of a distribution network current transformer when executing the computer program.
[0073] This application provides a method and apparatus for determining the error of a distribution network current transformer, relating to the field of smart grids. The method includes: determining the relationship between the current transformer's ratio error and phase difference based on the connection relationships of its internal components; correcting the relationship between the ratio error and phase difference based on the total energy of the current transformer under injected low-frequency signals; and obtaining the ratio error and phase difference of the current transformer based on the corrected relationship between the ratio error and phase difference. At low frequencies, the losses and hysteresis characteristics of the current transformer core exhibit different patterns than at power frequency. By using the total energy of the low-frequency signal, key parameters such as excitation impedance and secondary leakage impedance can be more accurately identified, truly reflecting the electromagnetic behavior of the transformer under actual operating conditions. This effectively compensates for measurement errors such as ratio difference and phase difference, improves the metering accuracy of the current transformer in complex distribution network environments, and solves the problems of insufficient static stability and anti-interference capability. Attached Figure Description
[0074] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the prior art and embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0075] Figure 1 A flowchart of a method for determining the error of a distribution network current transformer provided by the present invention;
[0076] Figure 2 This is a schematic diagram of the error determination device for a distribution network current transformer provided by the present invention. Detailed Implementation
[0077] The core of this invention is to provide a method and device for determining the error of a distribution network current transformer. By using the total energy of the low-frequency signal, key parameters such as excitation impedance and secondary leakage impedance can be identified more accurately, truly reflecting the electromagnetic behavior of the transformer under actual operating conditions. This effectively compensates for measurement errors such as ratio difference and phase difference, improves the metering accuracy of the current transformer in complex distribution network environments, and solves the problems of insufficient static stability and anti-interference.
[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0079] Figure 1 A flowchart of a method for determining the error of a distribution network current transformer provided by the present invention is provided. The method for determining the error of a distribution network current transformer includes:
[0080] S11: Determine the relationship between the ratio error and the phase difference of the current transformer based on the connection relationship of the internal components of the current transformer. The ratio error characterizes the deviation between the actual ratio and the rated ratio of the current transformer, and the phase difference characterizes the phase deviation between the primary current and the secondary current under ideal conditions.
[0081] Based on the actual wiring and topology of current transformers, a fundamental theoretical mathematical model of the turns ratio error and phase difference is established, clarifying the relationship between the error and the electrical parameters of the transformer. The cyber-physical relationships of the current transformer include the equivalent circuit model, circuit laws, material properties, load characteristics, turns ratio law, and error propagation. It should be noted that the equivalent circuit of the current transformer is a simplified model that neglects core losses.
[0082] Constructing an equivalent model based on hardware connections is related to the actual topology, which facilitates subsequent error correction and solution, while also avoiding model bias caused by unfounded empirical formulas.
[0083] S12: Based on the total energy of the current transformer under low-frequency signal injection, correct the relationship between the turns ratio error and the phase difference;
[0084] At low frequencies, the losses and hysteresis characteristics of current transformer cores exhibit different patterns compared to those at power frequencies. By analyzing the total energy (active power and reactive power) of low-frequency signals, key parameters such as excitation impedance and secondary leakage impedance can be identified more accurately. A more accurate parameter model can more realistically reflect the electromagnetic behavior of the transformer under actual operating conditions, thereby effectively compensating for measurement errors such as ratio error and phase angle error, and improving model accuracy. Therefore, the total energy of low-frequency signals is used for correction.
[0085] The compensation method addresses the impact of magnetic circuit characteristics and energy loss on the error of current transformers under low-frequency operating conditions, eliminating the error deviation between the traditional ideal model and the actual low-frequency operating characteristics.
[0086] S13: Based on the corrected formulas for the ratio error and the phase difference, the ratio error and phase difference of the current transformer are obtained.
[0087] Based on the corrected model, the error value is calculated stably and accurately by filtering to suppress interference such as measurement noise and electromagnetic interference.
[0088] Specifically, the recursive optimal estimation characteristic of Kalman filtering can be used to dynamically solve the corrected error model, suppressing computational fluctuations caused by measurement noise, electromagnetic interference, and model uncertainties, and achieving high-precision dynamic estimation of the ratio error and phase difference. Kalman filtering is a recursive optimal filter, requiring no storage of large amounts of historical data, with low computational load and strong real-time performance. It can meet the online and real-time error detection requirements of current transformers, dynamically suppressing random noise and system interference, significantly improving the stability and accuracy of error solutions, and adapting to the dynamic operating conditions of current transformers. This results in continuous and accurate estimation of the ratio error and phase difference, with the error results more closely reflecting the actual operating conditions.
[0089] This application provides a method for determining the error of a distribution network current transformer, relating to the field of smart grids. The method includes: determining the relationship between the current transformer's ratio error and phase difference based on the connection relationships of its internal components; correcting the relationship between the ratio error and phase difference based on the total energy of the current transformer under injected low-frequency signals; and obtaining the ratio error and phase difference of the current transformer based on the corrected relationship between the ratio error and phase difference. At low frequencies, the losses and hysteresis characteristics of the current transformer core exhibit different patterns than at power frequency. By using the total energy of the low-frequency signal, key parameters such as excitation impedance and secondary leakage impedance can be more accurately identified, truly reflecting the electromagnetic behavior of the transformer under actual operating conditions. This effectively compensates for measurement errors such as ratio difference and phase difference, improves the metering accuracy of the current transformer in complex distribution network environments, and solves the problems of insufficient static stability and anti-interference capability.
[0090] Based on the above embodiments:
[0091] In some embodiments, determining the relationship between the current transformer's ratio error and phase difference based on the connection relationship of its internal components includes:
[0092] An equivalent circuit model of the current transformer is established based on the physical parameters of the primary side, secondary side, and core circuit of the current transformer.
[0093] Based on the equivalent circuit model, the formulas for the ratio error and phase difference of the current transformer are determined by combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit.
[0094] The information physical relationships of a current transformer include the equivalent circuit model, circuit laws, material properties, load characteristics, turns ratio law, and error propagation.
[0095] First, establish the equivalent circuit of the current transformer. Then, using the magnetomotive force balance combined with the voltage-current relationship of the excitation circuit, finally derive the error relationship by solving the equations simultaneously.
[0096] The equivalent circuit of the current transformer is a simplified model that ignores core losses.
[0097] In some embodiments, an equivalent circuit model of the current transformer is established based on the physical parameters of the primary side, secondary side, and core circuit of the current transformer, including:
[0098] Based on the primary current on the primary side of the current transformer Number of turns in primary winding and primary leakage resistance Secondary current on the secondary side Number of turns in the secondary winding Secondary leakage reactance Secondary leakage resistance Load impedance and secondary leakage impedance Excitation current of the iron core circuit and excitation impedance Establish an equivalent circuit model for the current transformer;
[0099] The expression for the load impedance is as follows: , The resistance of the load. Let be the load reactance, and the expression for the secondary leakage impedance is: .
[0100] According to Kirchhoff's laws, the voltage equation for the secondary circuit is: .
[0101] in, Represents the secondary voltage phasor. This represents the secondary current vector.
[0102] The voltage in the excitation circuit is balanced by the induced electromotive force on the secondary side, i.e. ,and .
[0103] In some embodiments, based on the equivalent circuit model, and combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the formulas for the ratio error and phase difference of the current transformer are determined, including:
[0104] The expression for the magnetomotive force balance relationship of a current transformer is: ;
[0105] in, For the rated ratio, ;
[0106] The expression for the voltage-current relationship in the excitation circuit is: ;
[0107] Based on the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the formulas for the ratio error and phase difference of the current transformer are determined, including:
[0108] The relationship between the primary and secondary currents is determined based on the magnetomotive force balance relationship and the voltage-current relationship in the excitation circuit. The expression for the relationship between the primary and secondary currents is as follows:
[0109] ;
[0110] The relationship between the primary current and the secondary current is used to determine the formulas for the current transformer's ratio error and phase difference.
[0111] The relationship between the ratio error and the formula is:
[0112] ;
[0113] The relationship for phase difference is:
[0114] ;
[0115] in, For the ratio error, For phase difference, The magnitude of the excitation current. This is the phase difference between the excitation current and the secondary voltage. The relevant phase angle of the secondary side, This represents the amplitude of the secondary current.
[0116] The magnetomotive force balance equation for a current transformer using magnetomotive force balance is: , transform into Let the rated ratio ,but .
[0117] Based on the voltage-current relationship of the excitation circuit, the excitation impedance The secondary side induced dynamic force The relationship with secondary side voltage and leakage reactance voltage drop is as follows: ,Will Substitute, and we get .
[0118] Will Combining the two expressions, we get... .
[0119] The relationship between the primary current and the secondary current is obtained by reorganization. .
[0120] The transformation ratio error of a current transformer is the deviation between the actual transformation ratio and the rated transformation ratio, defined as follows: ,Will Substituting the values (using amplitude analysis under sinusoidal steady state) and combining the phase relationship of the excitation current with the phase difference of the secondary voltage, we finally obtain... .
[0121] The phase difference is the difference between the primary current and the ideal secondary current ( The phase deviation, in degrees. This is determined using complex phase operations and radian-degree conversion factors. The derivation yields .
[0122] Combining the transformation ratio error and phase difference, the operating error state equation of the current transformer is:
[0123] .
[0124] in, This reflects the combined influence of excitation impedance, load, secondary leakage impedance, and turns ratio on the error.
[0125] In some embodiments, the relationships between the turns ratio error and the phase difference are corrected based on the total energy of the current transformer under the injected low-frequency signal, including:
[0126] A low-frequency current signal of a preset frequency is injected into the current transformer, and the total energy is determined, which includes active power and reactive power.
[0127] The excitation impedance of the core circuit and the secondary leakage impedance of the secondary side of the current transformer are corrected based on the active power and reactive power under low frequency signals.
[0128] The formulas for the turns ratio error and the phase difference are corrected based on the corrected excitation impedance and the corrected secondary leakage impedance.
[0129] Under low-frequency signals, the core loss and hysteresis characteristics of current transformers will exhibit different patterns. Therefore, the excitation impedance and secondary leakage impedance can be corrected by the total energy (active power and reactive power) of the low-frequency signal.
[0130] At low frequencies, the losses and hysteresis characteristics of the current transformer core exhibit different patterns than at power frequency. By using the total energy (active power and reactive power) of the low-frequency signal, key parameters such as excitation impedance and secondary leakage impedance can be identified more accurately. A more accurate parameter model can more realistically reflect the electromagnetic behavior of the transformer under actual operating conditions, thereby effectively compensating for measurement errors such as ratio difference and phase difference, and improving model accuracy.
[0131] In some embodiments, determining the total energy, which includes active power and reactive power, includes:
[0132] The expression for active power is:
[0133] ;
[0134] The expression for reactive power is:
[0135] ;
[0136] in, Active power Let be the amplitude of the voltage of the nth harmonic. Let be the amplitude of the current of the nth harmonic. Let be the phase difference between the voltage and current of the nth harmonic. This refers to reactive power.
[0137] A low-frequency current signal of a specific frequency is injected into the current transformer, and its active power and reactive power are calculated. The active power P reflects the core loss, and the reactive power reflects the magnetic flux storage energy.
[0138] In some embodiments, the correction of the excitation impedance of the core circuit and the secondary leakage impedance of the current transformer under low-frequency signals based on active power and reactive power includes:
[0139] The excitation impedance of the current transformer core circuit under low-frequency signals is corrected based on the active and reactive power. The corrected excitation impedance is:
[0140] , , ;
[0141] The secondary leakage impedance of the current transformer under low-frequency signals is corrected based on the active and reactive power values. The corrected secondary leakage impedance is:
[0142] , , ;
[0143] in, This is the corrected excitation impedance. The corrected excitation resistor. The corrected magnetizing reactance. This is the corrected secondary leakage impedance. This is the corrected secondary leakage resistance. This is the corrected secondary leakage reactance. The magnitude of the excitation current. This refers to the amplitude of the secondary current;
[0144] The corrected excitation current is determined based on the corrected excitation impedance and the corrected secondary leakage impedance. The expression for the corrected excitation current is as follows:
[0145] ;
[0146] in, This is the corrected excitation current;
[0147] The relationships between the turns ratio error and the phase difference are corrected based on the corrected excitation impedance and the corrected secondary leakage impedance, including:
[0148] The formulas for the ratio error and phase difference of the current transformer are determined based on the corrected excitation current.
[0149] The corrected formula for the ratio error is:
[0150] ;
[0151] The corrected phase difference relationship is as follows:
[0152] ;
[0153] in, This is the corrected ratio error. This is the corrected phase difference.
[0154] Magnetizing impedance Related to active and reactive power, and combined with the power relationship at low frequencies, corrections are made. real part and the virtual part Secondary leakage impedance Related to active and reactive power, and combined with the power relationship at low frequencies, corrections are made. real part and the virtual part .
[0155] Substituting the corrected excitation impedance and secondary leakage impedance into the operating error state equation yields the parameter-corrected operating error state equation.
[0156] In some embodiments, the ratio error and phase difference of the current transformer are obtained based on the corrected formulas for the ratio error and phase difference, including:
[0157] The corrected ratio error and phase difference of the current transformer are used to construct a state vector, and the actual measured error observations are used to construct an observation vector.
[0158] Based on historical offline calibration data, the prior distribution of phase difference is obtained, and the range of phase difference values is used as a regularization constraint to constrain the observation vector.
[0159] Based on the state vector and the observation vector with regularization constraints, Kalman filtering iteration is performed to obtain the optimal ratio error and phase difference.
[0160] The Kalman filter algorithm is used to solve the corrected operating error state equation of the current transformer to obtain the optimal error of the current transformer. The specific process is as follows:
[0161] Define a state vector and an observation space. The state space vector x includes the ratio error. and phase difference This indicates the corrected ratio angle difference. Constructing the observation vector z .
[0162] The dynamic change of the current transformer error can be regarded as a slow time-varying phenomenon; therefore, the state equation is:
[0163] .
[0164] Where k represents the time step, Let A represent the state vector at the k-th time step, and let A be the identity matrix. This is process noise.
[0165] Deriving the observation relationship from the error formula , Let be the observation vector at the k-th time step.
[0166] , H represents the observation noise, and H is the observation matrix.
[0167] To avoid the Kalman filter falling into erroneous convergence due to abnormal measurements, this invention obtains the prior distribution of phase difference based on a large amount of offline calibration data, and uses the reasonable range of phase difference as a constraint condition.
[0168] In some embodiments, based on historical offline calibration data, a priori distribution of the phase difference is obtained, and the range of phase difference values is used as a regularization constraint to constrain the observation vector, including:
[0169] The prior distribution of historical offline calibration data is determined as follows:
[0170] ;
[0171] in, For the prior distribution, This is the average phase difference from historical offline calibration data. The variance of the phase difference in historical offline calibration data;
[0172] The regularized phase difference is determined as follows:
[0173] ;
[0174] in, The phase difference after regularization. Phase difference;
[0175] By introducing a regularization matrix into the observation vector, we obtain an observation vector with regularization constraints.
[0176] The observation vector is:
[0177] ;
[0178] The observation vector with regularization constraints is:
[0179] ;
[0180] in, For the observation vector, For regularization matrix, , For regularized noise, , For the observation matrix, Let k be the state vector at the k-th time step. Let be the observation vector at the k-th time step. This represents the standard deviation of the phase difference in historical offline calibration data.
[0181] Kalman filtering is , Let k be the prior state estimate at time k. This is the posterior state estimate at time k-1.
[0182] The prediction error covariance is .
[0183] in, Let be the prior error covariance at time k. Let D be the posterior error covariance at time k-1, and D be the process noise covariance. The statistical characteristics are determined.
[0184] Calculate Kalman gain ;
[0185] in, Let G be the Kalman gain, and G be the observation noise covariance. The statistical characteristics determine this.
[0186] Update state estimation ;
[0187] in, This is the posterior state estimate at time k, i.e., the optimal error estimate.
[0188] Update error covariance ;
[0189] Where I is the identity matrix, Let be the posterior error covariance at time k.
[0190] After iterative convergence, The elements in the equation are the optimal estimates of the ratio error f and the phase difference δ.
[0191] The iterative convergence conditions are as follows:
[0192] (1) The state transition matrix A of the state equation must be asymptotically stable, that is, the magnitude of all its eigenvalues is less than 1.
[0193] (2) Process noise The noise must be zero-mean, stationary white noise, and its covariance matrix D must be a positive semi-definite matrix; observation noise It must be zero-mean, stationary white noise, and its covariance matrix G must be a positive definite matrix;
[0194] (3) The observation matrix H must satisfy the system observability, that is, through the observation vector The state vector can be uniquely determined. For the error model in this paper, it is necessary to ensure that and They are not both zero at the same time.
[0195] When the above conditions are met, the error covariance of the Kalman filter... It will gradually converge to a constant matrix, and the state estimation It will also converge to the optimal estimate of the true error.
[0196] Figure 2 This is a schematic diagram of the structure of an error determination device for a distribution network current transformer provided by the present invention. The error determination device for the distribution network current transformer is characterized by comprising:
[0197] Memory 21 is used to store computer programs;
[0198] The processor 22 is used to execute computer programs to implement the steps of the error determination method for distribution network current transformers as described above.
[0199] Please refer to the above embodiments for a description of the error determination device for distribution network current transformers provided in this application, and it will not be repeated here.
[0200] It should also be noted that, in this specification, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0201] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.
[0202] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for determining the error of a distribution network current transformer, characterized in that, include: The relationship between the ratio error and the phase difference of the current transformer is determined based on the connection relationship of the internal components of the current transformer. The ratio error represents the deviation between the actual ratio and the rated ratio of the current transformer, and the phase difference represents the phase deviation between the primary current and the secondary current under ideal conditions of the current transformer. Based on the total energy of the current transformer under low-frequency signal injection, the relationship between the transformation ratio error and the relationship between the phase difference are corrected. Based on the corrected formulas for the ratio error and the phase difference, the ratio error and phase difference of the current transformer are obtained.
2. The error determination method for distribution network current transformers as described in claim 1, characterized in that, The relationships between the current transformer's transformation ratio error and phase difference are determined based on the connection relationships of the internal components of the current transformer, including: An equivalent circuit model of the current transformer is established based on the physical parameters of the primary side, secondary side, and core circuit of the current transformer. Based on the equivalent circuit model, and combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the formulas for the ratio error and phase difference of the current transformer are determined.
3. The error determination method for distribution network current transformers as described in claim 2, characterized in that, An equivalent circuit model of the current transformer is established based on the physical parameters of its primary side, secondary side, and core circuit, including: Based on the primary current on the primary side of the current transformer Number of turns in primary winding and primary leakage resistance Secondary current on the secondary side Number of turns in the secondary winding Secondary leakage reactance Secondary leakage resistance Load impedance and secondary leakage impedance Excitation current of the iron core circuit and excitation impedance Establish an equivalent circuit model for the current transformer; The expression for the load impedance is as follows: , The resistance of the load. Let be the reactance of the load, and the expression for the secondary leakage impedance is: .
4. The error determination method for distribution network current transformers as described in claim 3, characterized in that, Based on the equivalent circuit model, and combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the formulas for the ratio error and phase difference of the current transformer are determined, including: The expression for the magnetomotive force balance relationship of the current transformer is: ; in, For the rated ratio, ; The expression for the voltage-current relationship in the excitation circuit is as follows: ; The formulas for determining the ratio error and phase difference of the current transformer are determined by combining the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, including: Based on the magnetomotive force balance relationship and the voltage and current relationship of the excitation circuit, the relationship between the primary current and the secondary current is determined. The expression for the relationship between the primary current and the secondary current is as follows: ； Based on the relationship between the primary current and the secondary current, determine the formulas for the ratio error and phase difference of the current transformer; The relationship between the ratio error and the following formula is: ； The relationship of the phase difference is: ； in, For the ratio error, For phase difference, The magnitude of the excitation current. This is the phase difference between the excitation current and the secondary voltage. The relevant phase angle of the secondary side, This represents the amplitude of the secondary current.
5. The method for determining the error of a distribution network current transformer as described in claim 1, characterized in that, Based on the total energy of the current transformer under low-frequency signal injection, the relationships for the transformation ratio error and the phase difference are corrected, including: A low-frequency current signal of a preset frequency is injected into the current transformer, and the total energy is determined, which includes active power and reactive power. The excitation impedance of the core circuit and the secondary leakage impedance of the secondary side of the current transformer are corrected according to the active power and the reactive power under low frequency signals. The relationship between the turns ratio error and the phase difference is corrected based on the corrected excitation impedance and the corrected secondary leakage impedance.
6. The error determination method for distribution network current transformers as described in claim 5, characterized in that, Determine the total energy, which includes active power and reactive power, including: The expression for the active power is: ； The expression for the reactive power is: ； in, Active power Let be the amplitude of the voltage of the nth harmonic. Let be the amplitude of the current of the nth harmonic. Let be the phase difference between the voltage and current of the nth harmonic. This refers to reactive power.
7. The error determination method for distribution network current transformers as described in claim 5, characterized in that, The excitation impedance and secondary leakage impedance of the core circuit of the current transformer under low-frequency signals are corrected based on the active power and the reactive power, including: Based on the active power and the reactive power, the excitation impedance of the core circuit of the current transformer under low-frequency signal is corrected, and the corrected excitation impedance is: ， ， ； Based on the active power and the reactive power, the secondary leakage impedance of the current transformer under low-frequency signal conditions is corrected, and the corrected secondary leakage impedance is: ， ， ； in, This is the corrected excitation impedance. The corrected excitation resistor. The corrected magnetizing reactance. This is the corrected secondary leakage impedance. This is the corrected secondary leakage resistance. This is the corrected secondary leakage reactance. The magnitude of the excitation current. This represents the amplitude of the secondary current. The corrected excitation current is determined based on the corrected excitation impedance and the corrected secondary leakage impedance. The expression for the corrected excitation current is as follows: ； in, This is the corrected excitation current. The load impedance; The relationship between the turns ratio error and the phase difference is corrected based on the corrected excitation impedance and the corrected secondary leakage impedance, including: The formulas for the ratio error and phase difference of the current transformer are determined based on the corrected excitation current. The corrected formula for the ratio error is: ； The corrected relationship for the phase difference is as follows: ； in, This is the corrected ratio error. The corrected phase difference, This is the phase difference between the excitation current and the secondary voltage. The relevant phase angle of the secondary side, This represents the amplitude of the secondary current. This is the rated transformer ratio.
8. The method for determining the error of a distribution network current transformer as described in any one of claims 1 to 7, characterized in that, Based on the corrected formulas for the ratio error and the phase difference, the ratio error and phase difference of the current transformer are obtained, including: The corrected ratio error and phase difference of the current transformer are used to construct a state vector, and the actual measured error observations are used to construct an observation vector. Based on historical offline calibration data, the prior distribution of phase difference is obtained, and the range of values of the phase difference is used as a regularization constraint to constrain the observation vector. Based on the state vector and the observation vector with regularization constraints, Kalman filtering iteration is performed to obtain the optimal ratio error and phase difference.
9. The error determination method for distribution network current transformers as described in claim 8, characterized in that, Based on historical offline calibration data, the prior distribution of the phase difference is obtained. The range of values for the phase difference is used as a regularization constraint to constrain the observation vector, including: The prior distribution of the historical offline calibration data is determined, and the prior distribution is as follows: ； in, For the prior distribution, This is the average phase difference from historical offline calibration data. The variance of the phase difference in historical offline calibration data; The regularized phase difference is determined as follows: ； in, The phase difference after regularization. Phase difference; By introducing a regularization matrix into the observation vector, we obtain an observation vector with regularization constraints. The observation vector is: ； The observation vector with regularization constraints is: ； in, For the observation vector, For regularization matrix, , For regularized noise, , For the observation matrix, Let k be the state vector at the k-th time step. Let be the observation vector at the k-th time step. This represents the standard deviation of the phase difference in historical offline calibration data.
10. An error determination device for a distribution network current transformer, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the error determination method for a distribution network current transformer as described in any one of claims 1 to 9.