A voltage transformer error evaluation method based on multi-constraint optimization

Abstract

The application discloses a voltage transformer error evaluation method based on multi-constraint optimization and belongs to the technical field of online monitoring of electric power measurement, and comprises the following steps: collecting fundamental wave effective value measurement data and fundamental wave phase measurement data of at least two voltage transformers of the same voltage level and in parallel connection in the same phase, and constructing effective value vectors and phase vectors; constructing a multi-constraint-single-target optimization calculation model according to the effective value vectors and the phase vectors, introducing a primary side voltage consistency constraint, an error deviation degree constraint, a three-phase voltage unbalance degree constraint and a group state constraint, and taking the minimum relative difference between a voltage transformer measurement true value and an estimated value as an optimization target; solving the multi-constraint-single-target optimization calculation model by using an adaptive hybrid gradient evolution algorithm to obtain an optimal primary side voltage; and calculating a voltage transformer ratio error and a phase error. By constructing the multi-constraint-single-target optimization model and combining the adaptive hybrid gradient evolution algorithm, the application improves the accuracy of error evaluation and the abnormal detection capability.

Description

Technical Field

[0001] This invention belongs to the field of online power metering and monitoring technology, specifically relating to a voltage transformer error assessment method based on multi-constraint optimization. Background Technology

[0002] Voltage transformers, as a crucial component of electricity metering devices, directly impact the fairness and impartiality of electricity trade settlements due to their accuracy and reliability. Capacitive voltage transformers offer significant advantages in insulation performance and are widely used in substations and power plants with voltage levels of 110kV and above. However, existing research indicates that the variability of capacitor and reactor parameters leads to lower stability for capacitive voltage transformers compared to electromagnetic voltage transformers. Furthermore, preventative testing of capacitive voltage transformers in power systems may damage the electromagnetic components, and operational vibrations can cause displacement of the core gap in the compensating reactor, resulting in transformer deviations. If voltage transformers fail to meet the requirements for accurate, stable, and reliable electricity metering, significant metering risks exist, affecting the fairness and impartiality of electricity metering.

[0003] In practice, several problems exist in the operation and maintenance management of voltage transformers: First, due to the high difficulty and safety risks of voltage transformer calibration methods, coupled with frequent personnel changes in local maintenance teams, testing capabilities are insufficient to meet dynamic maintenance needs, leading to the inability to conduct timely periodic calibrations and posing a risk of exceeding tolerances. Second, due to the difficulty in coordinating power outage plans, the method of periodic power outage offline testing can only guarantee error assessment for voltage transformers in a small number of important substations, failing to cover the error assessment of voltage transformers across the entire network, resulting in a large number of in-operation voltage transformers exceeding their calibration period and with unknown errors. Third, fault repair is not timely; traditional manual on-site testing and paper-based data recording are inefficient and cannot effectively address the root causes of problems. Current big data dynamic monitoring and analysis cannot accurately and timely analyze and judge the metering performance status of operating voltage transformers, and cannot quickly and efficiently detect and eliminate equipment defects; fourth, the current method of periodic power outage testing has the problems of large workload and huge investment of manpower and material resources, which leads to the waste of operation and maintenance costs for the verification of more than 90% of the normally operating transformers, while increasing the risks of on-site operations, and failing to detect transformers with out-of-tolerance in a timely manner, resulting in poor timeliness of verification work, affecting the fairness of settlement, and causing difficulties in electricity recovery; fifth, the traditional metering performance testing of transformers is carried out in the offline state during power outages, and with the continuous improvement of power supply reliability requirements, the time window for metering performance testing of transformers is difficult to guarantee.

[0004] Chinese invention patent application CN116679254A discloses a method for calculating the initial error of a voltage transformer. This method eliminates the need for power-off calibration of the initial error. It establishes in-phase and multi-phase constraint models for both the primary and secondary sides of the voltage transformer to obtain the initial error expression. A genetic algorithm is then used for optimization to calculate the initial error value for each channel of the voltage transformer, thus achieving the calculation of the initial error for each channel. However, this method is based on the conversion relationship between the primary and secondary voltages, which depends on the accurate acquisition of the primary voltage. Furthermore, the model is only based on in-phase and multi-phase constraints, making it insufficiently adaptable to complex operating conditions. Summary of the Invention

[0005] To address the problems in the prior art, this invention proposes a voltage transformer error assessment method based on multi-constraint optimization. By constructing a multi-constraint single-objective optimization model and combining it with an adaptive hybrid gradient evolution algorithm, the accuracy of error assessment and anomaly detection capability are improved.

[0006] The technical solution of the present invention is as follows: This invention proposes a voltage transformer error evaluation method based on multi-constraint optimization, comprising the following steps: Collect fundamental effective value measurement data and fundamental phase measurement data from at least two voltage transformers of the same voltage level and connected in parallel in the same phase, and construct effective value vector and phase vector; A multi-constraint-single-objective optimization calculation model is constructed based on the effective value vector and the phase vector. The multi-constraints include constraints for limiting the consistency of primary voltage, the degree of error deviation, the three-phase voltage imbalance, and the state of the voltage transformer group. The multi-constraint-single-objective optimization calculation model takes minimizing the relative difference between the true and estimated values ​​of voltage transformer measurements as the optimization objective. An adaptive hybrid gradient evolution algorithm is used to solve the multi-constraint-single-objective optimization calculation model to obtain the optimal primary side voltage; Calculate the amplitude and phase of the optimal primary voltage, calculate the voltage transformer ratio error based on the amplitude of the optimal primary voltage, and calculate the voltage transformer phase error based on the phase of the optimal primary voltage.

[0007] Furthermore, the constraints imposed by the multi-constraint-single-objective optimization calculation model on the consistency of the primary-side voltage are specifically as follows: Within the same time slice, the relative difference between the primary side voltages of each voltage transformer does not exceed a first preset threshold.

[0008] Furthermore, the constraints on the degree of error deviation in the multi-constraint-single-objective optimization calculation model are specifically as follows: The ratio error and phase error of each voltage transformer deviate from the average error of the corresponding operating voltage transformer by no more than the second preset threshold.

[0009] Furthermore, based on the voltage amplitude and average value of different phases of the same voltage transformer in the same time slice, and the deviation of each phase voltage amplitude from the average value is determined, the maximum value of the deviation is selected and normalized to calculate the three-phase voltage imbalance. The fluctuation range of the three-phase voltage imbalance within the preset time window does not exceed the third preset threshold.

[0010] Furthermore, an abnormal state index is constructed based on the ratio error and phase error of each voltage transformer. The abnormal state index represents the probability level of the voltage transformer being in a normal state, and the average value of the abnormal state index is constrained within a fourth preset threshold range.

[0011] Furthermore, the adaptive hybrid gradient evolution algorithm uses gradient-sensitive sampling to generate an initial population and selects the optimal solution. It then obtains the gradient solution through projection gradient descent iteration, introduces the Lévy flight mutation solution into the projection gradient descent, compares the optimal solution, the gradient solution, and the Lévy flight mutation solution with the function value of the optimization objective function, and takes the solution with the smallest function value as the optimal primary side voltage.

[0012] Furthermore, the initial population is generated using gradient-sensitive sampling, specifically: Based on the gradient information of the constraint function of the multi-constraint single-objective optimization calculation model, the value range of the primary voltage is weighted and sampled, and the gradient is normalized by the activation function to obtain the initial population.

[0013] Furthermore, the Lévy flight mutation solution is generated by perturbing the difference between the current optimal solution and the current gradient solution using Lévy flight random numbers, and the search step size is adjusted by a scaling factor.

[0014] In a second aspect, the present invention provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement any of the methods described above.

[0015] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the methods described above.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention constructs a multi-constraint single-objective optimization model based on measurement data from multiple voltage transformers of the same voltage level and connected in parallel in the same phase. It enables online evaluation of voltage transformer errors without the need to obtain the actual primary voltage, reducing reliance on power outage detection and improving the safety and feasibility of the evaluation. By introducing primary voltage consistency constraints, error distribution constraints, three-phase voltage imbalance constraints, and group statistical constraints, the metering characteristics of voltage transformers are modeled from multiple dimensions, which improves the accuracy of error assessment and the adaptability to complex operating conditions. By constructing a comprehensive status index for voltage transformers, a quantitative assessment of the transformer's operating status can be achieved, and abnormal equipment can be effectively screened, reducing operation and maintenance costs. Attached Figure Description

[0017] Figure 1 This is a flowchart of a voltage transformer error evaluation method based on multi-constraint optimization; Figure 2 This is a performance comparison chart of the adaptive hybrid gradient evolution algorithm with NSGA-III and MOEA / D. Detailed Implementation

[0018] 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 a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0019] Example 1 This embodiment provides a voltage transformer error assessment method based on multi-constraint optimization, such as... Figure 1 As shown, it includes the following steps: S100: Collect fundamental RMS and fundamental phase measurement data from several voltage transformers of the same voltage level and connected in parallel in phase, forming a vector... and Expressed as a formula: ; ; in, For the first Taiwan voltage transformer; A This represents the total number of voltage transformers. For the first A time slice; B This represents the total number of time slices. For the first Taiwan voltage transformer in time slice The fundamental effective value measurement results; For the first Taiwan voltage transformer in time slice The fundamental phase measurement results.

[0020] S200. Based on the collected fundamental RMS and fundamental phase measurement data of several voltage transformers, a multi-constraint-single-objective optimization calculation model is constructed, which specifically includes the following steps: S201. Construct constraints, including: The first constraint is that, for all monitored voltage transformers, the primary voltage of their measured objects should theoretically be completely identical, and the actual relative difference should not exceed the preset allowable range. The formula for calculating the ratio error of the voltage transformer is as follows: ; in, For the first The operating ratio error of the voltage transformer; For the first Taiwan voltage transformer in time slice The magnitude of the primary side voltage; The formula for calculating phase error is: ; in, For the first The operating phase error of the voltage transformer; For the first Taiwan voltage transformer in time slice The primary voltage phase; Primary voltage The calculation formula is: ; Where e is the natural constant; j is the imaginary unit; The primary voltage constraint is satisfied as follows: ; Where Limit1 is the first preset threshold; The second constraint is that the deviations of the ratio error and phase error from the corresponding mean error of the operating transformer fluctuate within a preset range, and the ratio error follows a normal distribution. , This represents the mean of the ratio error. Let be the standard deviation of the ratio error, and be the probability density function of the ratio error. Expressed as a formula: ; The phase error follows a mixed distribution of uniform and normal distributions, and the probability density function of the phase error is... Expressed as a formula: ; in, For indicator functions; The mixing coefficient; This represents the mean of the phase error; denoted as the standard deviation of the phase error; a is the minimum value of the uniform distribution; b is the maximum value of the uniform distribution. Deviation of ratio error Expressed as a formula: ; in, This represents the average ratio error of the current transformers in operation. Deviation of phase error Expressed as a formula: ; in, This represents the average phase error of the current transformer in operation. The constraint on error deviation is satisfied as follows: ; Limit2 is the second preset threshold. The third constraint is that the fluctuation of the three-phase unbalance of the voltage transformer within a preset time window meets a preset threshold condition. Due to factors such as primary load changes and active regulation of the grid voltage, the three-phase voltage amplitudes of the same group of capacitive voltage transformers are asymmetrical. The theoretical value of the three-phase voltage unbalance, VUF, which characterizes the correlation of the three-phase voltages on the primary side, is... P Expressed as a formula: ; in, For the first Taiwan voltage transformer in time slice Measurement results of phase A voltage amplitude; For the first Taiwan voltage transformer in time slice Measurement results of phase B voltage amplitude; For the first Taiwan voltage transformer in time slice Measurement results of the voltage amplitude of phase C; for , and The average value; max indicates taking the maximum value; From the formula for calculating the error of a current transformer, it can be seen that... , , It is directly related to the secondary side data and the transformer error. When the metering performance of the voltage transformer changes, the three-phase imbalance of the primary side voltage will change. Under normal operating conditions, since the three-phase voltage imbalance of the primary side fluctuates relatively little within the preset time window, the three-phase voltage imbalance constraint is satisfied as follows: ; Limit3 is the third preset threshold. The fourth constraint is that since the majority of voltage transformers in the voltage transformer group are in normal condition and the minority are in abnormal condition, the statistical value of the normal condition of the transformer group is within the preset threshold range. The probability that the ratio error is normal can be expressed by the formula: ; in, This represents the minimum value of the ratio error; This represents the maximum value of the ratio error; The probability that the phase error is normal can be expressed by the formula: ; in, This represents the minimum value of the phase error; This represents the maximum value of the phase error; Voltage transformer abnormal status indicators Expressed as a formula: ; in, This is the ratio error weighting coefficient; This refers to the phase error weighting coefficient; I For indicator functions; The voltage transformer abnormal state index constraints are satisfied as follows: ; in, This represents the average value of the abnormal state indicators of the voltage transformer; Limit 41 Limit is the minimum value of the fourth preset range; 42 The maximum value within the fourth preset range; S202. Set the optimization objective, which is to minimize the relative difference between the measured true value and the estimated value for all monitored voltage transformers. The optimization objective is expressed as: .

[0021] S300: An adaptive hybrid gradient evolution algorithm is used to solve the multi-constraint single-objective optimization calculation model. The upper bound of the primary voltage is set based on the voltage transformer measurement values. and lower bound of values ; Gradient-sensitive sampling is used to generate the initial population. : ; Where softmax(·) is the activation function; Δg is the nominal voltage; Δg is the gradient of the multi-constraint function. Perform projective gradient descent on the Pareto front solution: ; in, For the first The first-side voltage value of the next iteration; For the first The first-side voltage value of the next iteration; Ω represents the learning rate; Proj represents the projection operator; and Ω represents the feasible region. For the first One constraint function; Dynamic weights; For the first A constraint function in gradient at; To address local optima and accelerate global optimization, the Lévy flight strategy is employed to overcome the locality of the gradient method, expressed as: ; The solution after mutation; This is the scaling factor; For Levi's flight, random numbers were generated; The shape parameter of the Lévy distribution; This is the vector of the optimal solution found during the current population search process; like The calculation result substituted into the optimization objective is less than Substituting the calculation results into the optimization objective, then... Updated to ; like The calculation result substituted into the optimization objective is less than Substituting the calculation results into the optimization objective, then... Updated to ; like and The results substituted into the optimization objective are all greater than The calculation results substituted into the optimization objective are then used. .

[0022] S400. According to Euler's formula, the optimal primary voltage amplitude can be calculated through modulus and argument operations. and optimal primary side voltage phase ; The transformer error is calculated based on the optimal solution, and the ratio error is expressed by the formula: ; Phase error is expressed by the formula: ; Performance comparison of the adaptive hybrid gradient evolution algorithm with NSGA-III and MOEA / D: Figure 2 As shown, the adaptive hybrid gradient evolution algorithm has the lowest inverse generation distance (IGD) value and the best convergence and distribution.

[0023] To verify the performance of the algorithm of this invention, an online monitoring device for the metering performance of voltage transformers was deployed at a substation in a certain area. Online metering performance monitoring was conducted on 12 voltage transformers in four groups on the 220kV I bus, 220kV II bus, 110kV IV bus, and 110kV V bus. In conjunction with a power outage plan, power outage monitoring was also conducted on 6 voltage transformers on the 220kV #1 bus and 220kV #2 bus. The monitoring results are shown in Table 1.

[0024] As can be seen from Table 1, the absolute value of the deviation between the evaluation ratio error and the actual error of the present invention is within 0.06%. Among the 6 current transformers, 4 current transformers have out-of-tolerance detection error status, and 2 current transformers are normal, which is consistent with the online monitoring results.

[0025] Example 2 This embodiment proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the method described in one embodiment of the present invention.

[0026] Example 3 This embodiment proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method described in one embodiment of the present invention.

[0027] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structure made using the contents of the present invention specification and drawings, or directly or indirectly applied to other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for voltage transformer error evaluation based on multi-constraint optimization, characterized in that, Includes the following steps: Collect fundamental effective value measurement data and fundamental phase measurement data from at least two voltage transformers of the same voltage level and connected in parallel in the same phase, and construct effective value vector and phase vector; A multi-constraint-single-objective optimization calculation model is constructed based on the effective value vector and the phase vector. The multi-constraints include constraints for limiting the consistency of primary voltage, the degree of error deviation, the three-phase voltage imbalance, and the state of the voltage transformer group. The multi-constraint-single-objective optimization calculation model takes minimizing the relative difference between the true and estimated values ​​of voltage transformer measurements as the optimization objective. An adaptive hybrid gradient evolution algorithm is used to solve the multi-constraint-single-objective optimization calculation model to obtain the optimal primary side voltage; Calculate the amplitude and phase of the optimal primary voltage, calculate the voltage transformer ratio error based on the amplitude of the optimal primary voltage, and calculate the voltage transformer phase error based on the phase of the optimal primary voltage.

2. The method for voltage transformer error evaluation based on multi-constraint optimization according to claim 1, characterized in that, The constraints imposed on primary-side voltage consistency by the multi-constraint-single-objective optimization calculation model are as follows: Within the same time slice, the relative difference between the primary side voltages of each voltage transformer does not exceed a first preset threshold.

3. The method for voltage transformer error evaluation based on multi-constraint optimization according to claim 1, characterized in that, The constraints on the degree of error deviation in the multi-constraint-single-objective optimization calculation model are as follows: The ratio error and phase error of each voltage transformer deviate from the average error of the corresponding operating voltage transformer by no more than the second preset threshold.

4. The method for voltage transformer error evaluation based on multi-constraint optimization according to claim 1, characterized in that, Based on the voltage amplitude and average value of different phases of the same voltage transformer in the same time slice, and the deviation of each phase voltage amplitude from the average value is determined, the maximum value of the deviation is selected and normalized, and the three-phase voltage imbalance is calculated. The fluctuation range of the three-phase voltage imbalance within the preset time window does not exceed the third preset threshold.

5. The method for voltage transformer error evaluation based on multi-constraint optimization according to claim 1, characterized in that, An abnormal state index is constructed based on the ratio error and phase error of each voltage transformer. The abnormal state index represents the probability level of the voltage transformer being in a normal state, and the average value of the abnormal state index is constrained within a fourth preset threshold range.

6. The method for voltage transformer error evaluation based on multi-constraint optimization according to claim 1, characterized in that, The adaptive hybrid gradient evolution algorithm uses gradient-sensitive sampling to generate an initial population and selects the optimal solution. It then obtains the gradient solution through projection gradient descent iteration, introduces the Lévy flight mutation solution into the projection gradient descent, compares the optimal solution, the gradient solution, and the Lévy flight mutation solution with the function value of the optimization objective function, and takes the solution with the smallest function value as the optimal primary side voltage.

7. The method for voltage transformer error evaluation based on multi-constraint optimization according to claim 6, characterized in that, The initial population was generated using gradient-sensitive sampling, specifically: Based on the gradient information of the constraint function of the multi-constraint single-objective optimization calculation model, the value range of the primary voltage is weighted and sampled, and the gradient is normalized by the activation function to obtain the initial population.

8. The method for voltage transformer error evaluation based on multi-constraint optimization according to claim 6, characterized in that, The Lévy flight mutation solution is generated by perturbing the difference between the current optimal solution and the current gradient solution using Lévy flight random numbers, and the search step size is adjusted by a scaling factor.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 8.

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