Capacitive voltage transformer excitation characteristic test method based on model predictive control

Abstract

The application provides a model predictive control-based capacitor voltage transformer excitation characteristic test method, which constructs a model predictive optimal controller, adopts a model predictive control technology to optimize a voltage scanning strategy, can reduce the number and time of point-by-point scanning under the premise of ensuring test accuracy, and improves test efficiency. By calculating an optimal control strategy in real time, overvoltage application to equipment in the test process is reduced, the risk of capacitor voltage transformer overheating is reduced, equipment damage is avoided, and long-term healthy operation of the equipment is ensured. And the position of the inflection point is judged by the distortion coefficient, the demarcation point of the nonlinear region and the linear region of the capacitor voltage transformer can be accurately determined, the accurate excitation characteristic curve can be drawn through the least data points, and a large amount of time and resources in the traditional detection method are saved. It is suitable for detection and health assessment of capacitor voltage transformers.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of capacitor voltage transformer excitation characteristic testing, and in particular to a capacitor voltage transformer excitation characteristic testing method based on model predictive control. BACKGROUND

[0002] As an important measurement and protection device in the power system, capacitor voltage transformers (CVTs) are widely used in high-voltage power transmission and distribution. Their main function is to convert high voltage into standard low voltage signals for power system measurement, protection, and automation control. In the design and application of capacitor voltage transformers, excitation characteristic testing is one of the key steps to evaluate their performance and health status.

[0003] Currently, the excitation characteristic detection of capacitor voltage transformers usually relies on the point-by-point scanning method, which tests at a series of voltage points and records the current response of the transformer. Although this detection method can fully reflect the excitation characteristics of the transformer, it has the problems of low efficiency, complex operation, and large consumption of manpower and resources. Especially when conducting long-term detection, the windings of the transformer may be damaged due to overheating, which affects its health status and use precision, causing certain risks. SUMMARY

[0004] In actual production and maintenance, fast and efficient excitation characteristic detection is crucial to ensure the stable operation of power equipment. Therefore, how to improve the detection efficiency, reduce human intervention in the detection process, and effectively avoid damage to the transformer has become a challenge that needs to be solved in current technology.

[0005] To solve the above problems, the present application proposes a capacitor voltage transformer excitation characteristic testing method based on model predictive control. This method introduces model predictive control technology to optimize the voltage scanning strategy in the detection process, reducing the number and time of point-by-point scanning, thereby improving the detection efficiency and reducing the risk of overheating of the transformer. Model predictive control can ensure detection accuracy by calculating the optimal control strategy in real time, quickly and efficiently performing excitation characteristic testing.

[0006] In addition, the present application also considers the influence of voltage changes on the health status of the transformer during the detection process, optimizes the step size and frequency of voltage changes, avoids excessive thermal load on the equipment, and improves the test speed and accuracy, providing reliable technical support for intelligent operation and maintenance and equipment management of the power system.

[0007] Through the above-mentioned technical means, the present invention provides an efficient, accurate and low-risk method for detecting the excitation characteristics of capacitive voltage transformers, which has significant technical advantages and greatly improves work efficiency and reduces maintenance costs in routine testing of capacitive voltage transformers.

[0008] This invention provides a method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control. This invention can accurately and quickly locate the inflection point of the excitation curve, complete the detection of excitation characteristics, and thus assess whether the transformer is operating normally in the linear region and whether it requires repair or replacement.

[0009] Generally, the excitation characteristic curve of a capacitive voltage transformer is a smooth curve, and its general expression can be given by a function. U = f ( I ),in U The vertical axis of the curve represents the excitation voltage. I The excitation current is the variable on the horizontal axis of the curve. f () is a complex function. Let's define it as follows: t For natural numbers, t To detect the sequence number, X t ( U t , I t (This is used to plot the excitation characteristic curve) U = f ( I The detection data points. When t When =0, U 0= I 0=0, X 0( U 0, I 0) is zero, and zero must exist; when t When >0, U t Indicates the first t The excitation voltage detected in this test. I t For the first t The excitation current detected next time, X t ( U t , I t ) is the first t Data points for secondary excitation detection. Let... N This refers to the number of excitation tests performed on the capacitive voltage transformer. N Secondary excitation detection, plus zero point detection N +1 point is used to plot the excitation characteristic curve.

[0010] The excitation characteristic detection of the capacitive voltage transformer can be a problem of optimizing finding the inflection point, that is, finding the inflection point using the least detection points. The inflection point is the demarcation point between the linear and the sub-linear regions of the excitation characteristic curve, and is set as X G ( U G , I G ), U G is the excitation voltage for detecting the inflection point, I G is the excitation current for detecting the inflection point, and G is the detection sequence number corresponding to the inflection point. The present application uses the distortion coefficient to determine the inflection point, and is set as δ is the distortion coefficient, and is set as X a ( U a , I a ), X b ( U b , I b ) are any two excitation detection points, that is, X a , X b ∈ X t , and a>0, b>0. Meanwhile, it is set that I a > I b , then the expression of δ is:

[0011]

[0012] When δ ≤1, X a ( U a , I a ), X b ( U b , I b ) are in the linear region of the excitation characteristic curve, and when δ >1, the X a ( U a , I a) is in the nonlinear region. According to the tolerance of the degree of nonlinearity, i.e. the degree of distortion, the distortion coefficient can be set δ to be a certain value greater than 1, usually δ = 5, i.e. when δ = 5, X G ( U G , I G )= X a ( U a , I a )。

[0013] The general expression of the excitation curve U = f ( I ) can be used to draw the excitation characteristic curve of the capacitive voltage transformer through at least 4 points, including the inevitable zero point X 0( U 0, I 0), the inflection point X G ( U G , I G ). That is, when N ≥ 3, G≤ N , the sequence X 0( U 0, I 0)、 X 1( U 1, I 1)、……、 X t ( U t , I t )、……、 X N ( U N , I N ) is used to draw the excitation characteristic curve of the capacitive voltage transformer through the general expression of the excitation curve U = f ( I ).

[0014] The present application comprises the following steps:

[0015] S1: constructing a model predictive optimal controller;

[0016] S2: setting initial parameters;

[0017] S3: Obtain and record the initial excitation detection point, and number the detection point;

[0018] S4: Current prediction control;

[0019] S5: Obtain the response excitation current, and calculate the distortion coefficient between the detection points;

[0020] S6: Determine whether an inflection point occurs, if yes, execute S8, if not, execute S7;

[0021] S7: Distortion coefficient prediction control;

[0022] S8: Find and determine the inflection point;

[0023] S9: Check whether the number of detection points is greater than or equal to a preset value; if yes, execute S11; if not, execute S10;

[0024] S10: Supplement low-voltage linear region detection points;

[0025] S11: Stop applying excitation voltage to the capacitive voltage transformer; let the output excitation voltage be 0;

[0026] S12: Fit and construct the excitation characteristic curve vector expression;

[0027] S13: Draw the excitation characteristic curve, mark the inflection point, and complete the excitation characteristic detection.

[0028] Specifically:

[0029] S1: Construct a model prediction optimal controller; construct a model prediction optimal controller: where k is the current time, k+1 is the next control time, is the next time control amount output by the controller, y k is the current time system response, y ref,k+1 is the next time system target response, and MPC() is the model prediction controller;

[0030] S2: Set the distortion coefficient of the excitation characteristic of the capacitive voltage transformer δ ; set the initial excitation voltage to U 1; output U 1 to the capacitive voltage transformer, and the capacitive voltage transformer responds with the initial excitation current I 1;

[0031] S3: Obtain and record the initial excitation detection point, and number the detection point; obtain the response excitation current I 1, and record the excitation voltageU 1 with response field current I 1 is X 1( U 1, I 1), t is detection sequence number, at this time t =1;

[0032] S4: current prediction control; current response field current I k and next target field current are input to model prediction optimization controller MPC(), and next field detection field voltage U k+1 , i.e. ; field voltage U k+1 is output to capacitive voltage transformer, and capacitive voltage transformer responds to field current I k+1 ;

[0033] S5: obtain response field current, calculate distortion coefficient between detection points; obtain response field current I k+1 , detection sequence number t = t +1, record field voltage U k+1 and response field current I k+1 is X t ( U t , I t ); calculate X t ( U t , I t ) and distortion coefficient sequence X 1( U 1, I 1), …, X t-1 ( U t-1 , I t-1 ) of δ 1, … δ t-1 , i.e. calculate X t ( U t , I t) the distortion coefficient between all previous detection points;

[0034] S6: Determine if there is an inflection point X G U G I G ) that is, determine if the distortion coefficient set in S3 δ exists in the distortion coefficient sequence δ 1、…… δ t-1 , that is, if it does not exist, execute S7, if it exists, execute S8;

[0035] S7: Distortion coefficient predictive control; set δ k as the distortion coefficient at the current time, and the target distortion coefficient set in S3 δ , input to the model predictive optimal controller MPC(), and obtain the field voltage of the next field detection U k+1 , that is U k+1 =MPC( δ k , δ ) ; the field voltage U k+1 is output to the capacitive voltage transformer, and the capacitive voltage transformer responds to the field current I k+1 ;

[0036] S8: Find and determine the inflection point X G U G , I G ) ; query the distortion coefficient sequence δ 1、…… δ t-1 corresponding to the two detection points of the distortion coefficient equal to the distortion coefficient set in S3 δ , determine and record the inflection point from the two detection points X G U G , I G ;

[0037] S9: Check if the number of detection points is greater than or equal to 3; if t<3, execute S10; if t≥3, execute S11;

[0038] S10: Supplement low-voltage linear region detection points; detection sequence number t =​​​​t +1, 0 U t U 1, the excitation voltage U t to the capacitive voltage transformer, the capacitive voltage transformer in response to the output excitation current I t , record X t U t , I t );

[0039] S11: stop applying excitation voltage to the capacitive voltage transformer; make the output excitation voltage 0.

[0040] S12: fitting to build excitation characteristic curve vector expression; build the general expression of excitation characteristic curve U = f ( I ), and all detection points X 1( U 1, I 1)、 X 2( U 2, I 2)、……、 X t ( U t , I t ) into the general expression of excitation characteristic curve U = f ( I ), fitting to determine the vector expression corresponding to the measured capacitive voltage transformer excitation characteristic curve U = f o ( I );

[0041] S13: draw excitation characteristic curve, mark the inflection point, complete the excitation characteristic detection; using the vector expression corresponding to the measured capacitive voltage transformer excitation characteristic curve U = f o ( I ) in the display device to draw the excitation characteristic curve, and mark the inflection point in the curve X G ( U G , I G ), complete the capacitive voltage transformer excitation characteristic detection.

[0042] ​​Optionally, S1: constructing a model predictive optimal controller; constructing a model predictive optimal controller: where k is the current time, k+1 is the next control time, is the control variable at the next time of the controller output, y k is the system response variable at the current time, y ref,k+1 is the target response of the system at the next time, and MPC() is a model predictive controller, including:

[0043] S1a: constructing a capacitive voltage transformer system model:

[0044] First, a dynamic model of the system is constructed, and a discrete-time state space model is usually used to describe the dynamic behavior of the system. The state space model of the system is as follows:

[0045]

[0046] where k represents the current time, z k represents the state variable of the system at the current time, v k represents the control variable, A k is the state transition coefficient, B k is the control variable response coefficient.

[0047] The output model of the system is given by the following equation:

[0048]

[0049] where, y k represents the output variable of the system, C k is the output coefficient, D k is the control input influence coefficient

[0050] S1b: constructing a capacitive voltage transformer prediction model:

[0051] At each time k, according to the current state and control input, the state space model of the system constructed in S11 and the output model of the system are used to predict the system state and output at the future M time. The prediction formula is:

[0052]

[0053] S1c: defining an excitation detection optimal control cost function:

[0054] A cost function is defined, which aims to minimize the weighted sum of output error and control input cost. The prediction model built in S12 is used to predict the output of the system at future time M y k+1 , y k+2 , …, y k+M M y ref,k+1 , y ref,k+2 , …, y ref,k+M M v k , v k+1 , …, v k+M-1

[0055]

[0056] y ref,k+j is the reference output, Q is the cost coefficient of output error, and R is the cost of output error and control input.

[0057] S1d: Solve the optimization problem:

[0058] At each time step, find the minimum solution of the cost function defined in S13 J

[0059]

[0060] v min is the minimum boundary of the control variable value, v max is the maximum boundary of the control variable value, and the boundary value is determined according to the safety rules of the test site. J

[0061] S1e: After optimization, take the first control input from the optimal control input sequence , and apply it to the system. Then , the model predictive controller MPC() is built.

[0062] ​​​​​​​​​​​Optionally, S2: set the distortion coefficient of the excitation characteristic of the capacitive voltage transformer δ ; set the initial excitation voltage as U 1 U 1 ; output the initial excitation voltage I 1 to the capacitive voltage transformer, and the capacitive voltage transformer responds to output the initial excitation current

[0063] S21: set the measured capacitive voltage transformer capacity as W, the protection multiple as P, the rated secondary current as I E , and the damage tolerance coefficient of the measured capacitive voltage transformer as T, then the initial excitation voltage U 1 can be determined by the following expression:

[0064]

[0065] wherein the value range of the damage tolerance coefficient T is [0, 1], and generally 0.75 is taken.

[0066] S22: set the distortion coefficient δ as a certain value greater than 1 as the inflection point distortion coefficient, generally δ = 5.

[0067] Optionally, S4: current prediction control; input the current response excitation current I k and the next target excitation current to the model prediction optimal controller MPC(), and obtain the excitation voltage of the next excitation detection U k+1 , i.e. ; output the excitation voltage U k+1 to the capacitive voltage transformer, and the capacitive voltage transformer responds to output the excitation current I k+1 , including:

[0068] The target excitation current is determined by the following expression:

[0069]

[0070] wherein the distortion coefficient δ has been determined in S3, I k is the current excitation current, δ s is the distortion coefficient scaling coefficient, generally δ s = 10.

[0071] Optionally, S5: Obtain the response excitation current, calculate the distortion coefficient between the detection points; Obtain the response excitation current I k+1 , detection sequence number t = t +1, record the excitation voltage U k+1 and the response excitation current I k+1 is X t ( U t , I t );Calculate X t ( U t , I t ) and X 1( U 1, I 1)、……、 X t-1 ( U t-1 , I t-1 ) distortion coefficient sequence δ 1、…… δ t-1 , that is, calculate X t ( U t , I t ) and the distortion coefficient between all previous detection points, including:

[0072] Calculate X t ( U t , I t ) and X 1( U 1, I 1)、……、 X t-1 ( U t-1 , I t-1 ) distortion coefficient sequence δ 1、…… δ t-1 The formula is as follows:

[0073]

[0074] Where max( It , I jj ) denotes the maximum value of the field current of the detection point X t ( U t , I t ) denotes the minimum value of the field current of the detection point X jj ( U jj , I jj ) denotes the maximum value of the field voltage of the detection point I t , I jj ) denotes the minimum value of the field voltage of the detection point X t ( U t , I t ) denotes the maximum value of the field current of the detection point X jj ( U jj , I jj ) denotes the minimum value of the field current of the detection point U t , U jj ) denotes the maximum value of the field voltage of the detection point X t ( U t , I t ) denotes the minimum value of the field voltage of the detection point X jj ( U jj , I jj ) denotes the maximum value of the field current of the detection point U t , U jj ) denotes the minimum value of the field current of the detection point X t ( U t , I t ) denotes the maximum value of the field voltage of the detection point X jj ( U jj , I jj ) denotes the minimum value of the field voltage of the detection point

[0075] Optionally, S6: determining whether an inflection point occurs X G (U G , I G ); that is, if there is no inflection point, S7 is executed, and if there is an inflection point, S8 is executed, including: δ δ 1、… δ t-1 , that is, if there is no inflection point, S7 is executed, and if there is an inflection point, S8 is executed, including:

[0076] Let δ x be a point in the sequence of distortion coefficients δ 1、… δ t-1 that satisfies the following conditions:

[0077]

[0078] If the inflection point X G ( U G , I G ) exists in the sequence of detection points X 1( U 1, I 1), …, X t ( U t , I t ), that is:

[0079]

[0080] Optionally, S8: find and determine the inflection point X G ( U G , I G ); query the sequence of distortion coefficients δ 1、… δ t-1 corresponding to the distortion coefficient equal to the distortion coefficient δ set in S3, and determine and record the inflection point X G ( U G , I G ) from the two detection points, including:

[0081] Let δ x be a point in the sequence of distortion coefficients δ 1、…​δ t-1 A point satisfies the following condition:

[0082]

[0083] inflection point X G ( U G , I G ) exists in the distortion coefficient δ x The two corresponding detection points X t ( U t , I t ), X x ( U x , I x Then the inflection point X G ( U G , I G The definite expression for ) is:

[0084]

[0085] inflection point X G ( U G , I G ) represents the distortion coefficient. θ x The two corresponding detection points X t ( U t , I t ), X x ( U x , I x The point with a larger excitation current in the middle.

[0086] Optionally, S10: Supplement low-voltage linear region detection points; detection sequence number. t = t +1, let 0 < U t < U 1. Set the excitation voltage U tThe output is given to the capacitive voltage transformer, and the capacitive voltage transformer responds to the field current I t , record X t ( U t , I t ), comprising:

[0087] Supplement the excitation voltage of the low-voltage linear region detection point U t The value range of (0, U 1), in general U t = U 1 / 5.

[0088] Optionally, S12: fitting to construct the excitation characteristic curve vector expression; construct the general expression of the excitation characteristic curve U = f ( I ), and substitute all detection points X 1( U 1, I 1)、 X 2( U 2, I 2)、……、 X t ( U t , I t ) into the general expression of the excitation characteristic curve U = f ( I ), fitting to determine the vector expression corresponding to the measured capacitive voltage transformer excitation characteristic curve U = f o ( I ), comprising:

[0089] The general expression of the excitation characteristic curve U = f ( I ) can be represented by the following parameter equation:

[0090]

[0091] In the formula, Figure 1 ∈[0,1] is a parameter, representing a point on the curve; U i is the i th detection point X i ( Ui , I i ) of the voltage coordinate; I i is the first i detection point X i ( U i , I i ) of the current coordinate; (ti) is a binomial coefficient representing the contribution of each detection point to the curve.

[0092] Substitute all detection points X 1( U 1, I 1)、 X 2( U 2, I 2)、……、 X t ( U t , I t ) and zero point X 0( U 0, I 0) into the parametric equation, and the equation established is the vector expression corresponding to the measured capacitor voltage mutual inductor excitation characteristic curve U = f o ( I ).

[0093] Compared with the prior art, the present application has the following advantages:

[0094] 1. The present application optimizes the voltage scanning strategy using model predictive control technology, greatly reducing the number and time of point-by-point scanning, thereby improving detection efficiency. By reducing the number of test points, the detection process is faster and more accurate.

[0095] 2. Compared with the traditional point-by-point scanning method, the model predictive control method can effectively avoid overheating of the mutual inductor due to long-time detection, reducing the risk of equipment damage and improving safety during the testing process.

[0096] 3. This method can accurately find the inflection point of the excitation curve and use a small number of data points to draw an accurate excitation characteristic curve, ensuring high precision of the detection results.

[0097] 4. The use of model predictive control makes the detection process highly automated, reducing manual intervention and further improving the intelligent level of the detection process. BRIEF DESCRIPTION OF DRAWINGS

[0098] Figure 1This is a flowchart illustrating a method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control, provided in an embodiment of the present invention. Detailed Implementation

[0099] The present invention will be further described below with reference to the accompanying drawings, and the objectives and effects of the present invention will become more apparent. It is understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present invention are shown in the accompanying drawings, not the entire structure.

[0100] This embodiment uses the excitation characteristic detection of a certain capacitive voltage transformer as an example to describe the present invention in detail. Figure 1 This is a schematic flowchart of a method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control, provided in an embodiment of the present invention. δ As shown, the method includes 13 steps: S1: Constructing a model to predict the optimal controller; S2: Setting the excitation characteristic distortion coefficient of the capacitive voltage transformer. δ Set the initial excitation voltage to U 1; S3: Acquire and record the initial excitation detection point, and number the detection point; S4: Current prediction control; S5: Acquire the response excitation current and calculate the distortion coefficient between detection points; S6: Determine whether an inflection point has occurred. X G ( U G , I G S7: Distortion coefficient prediction control; S8: Find and determine the inflection point X G ( U G , I G S9: Check that the number of detection points is greater than or equal to 3; S10: Supplement the detection points in the low voltage linear region; S11: Stop applying excitation voltage to the capacitive voltage transformer; S12: Fit and construct the vector expression of the excitation characteristic curve; S13: Plot the excitation characteristic curve, mark the inflection point, and complete the excitation characteristic detection.

[0101] First, execute S1: Construct a model prediction optimization controller; Construct a model prediction optimization controller: Where k is the current time and k+1 is the next control time. The control quantity output by the controller at the next moment. y k This represents the system response at the current moment. y ref,k+1 For the system's target response at the next time step, MPC() is the model predictive controller, which includes:

[0102] Construct a model of a capacitive voltage transformer system:

[0103] To construct a dynamic model of a system, a discrete-time state-space model is typically used to describe the system's dynamic behavior. Let the system's state-space model be as follows:

[0104]

[0105] Where k represents the current time, z k This represents the system's state variables at the current moment. v k Indicates the control quantity. A k These are the state transition coefficients. B k The response coefficient is the control quantity.

[0106] The system's output model is given by the following equation:

[0107]

[0108] in, y k This represents the system's output. C k For output coefficients, D k To control the input influence coefficient

[0109] Constructing a predictive model for capacitive voltage transformers:

[0110] At each time k, based on the current state and control input, the future is predicted using the system's state-space model and output model constructed in S11. M The system state and output at time t. The prediction formula is:

[0111]

[0112] Define the excitation detection optimal control cost function:

[0113] Define a cost function that aims to minimize the weighted sum of output error and control input costs. Use the prediction model built in S12 to predict the future. M Output at time 1 y k+1 , y k+2 ... y k+M , and the future M The target output at each moment y ref,k+1 ,y ref,k+2 ,..., y ref,k+M , calculate the cost function after applying M control variables v k , v k+1 ,..., v k+M-1 The cost function after

[0114]

[0115] where, y ref,k+j is the reference output, Q is the cost coefficient of the control output error, and R is the cost of the control output error and the control input.

[0116] Solve the optimization problem:

[0117] At each time step, find the minimum solution of the cost function defined in S13 J Optimize the problem to obtain the optimal control input sequence:

[0118]

[0119] where v min is the minimum boundary value of the control variable, v max is the maximum boundary value of the control variable, and the boundary value is determined according to the safety rules of the test site. Solve the cost function J to obtain the optimal control sequence obtained by solving the minimum solution optimization problem.

[0120] After optimization, take the first control input from the optimal control input sequence , output the control variable, and apply it to the system. Then , the model predictive controller MPC() is constructed.

[0121] After executing S1, execute S2: set the excitation characteristic distortion coefficient of the capacitive voltage transformer δ ; set the initial excitation voltage to U 1; output U 1 to the capacitive voltage transformer, and the capacitive voltage transformer responds with an initial excitation current I 1, including:

[0122] Let the measured capacitive voltage transformer capacity be W, the protection multiple be P, and the rated secondary current be IE, and the damage tolerance coefficient of the measured capacitive voltage transformer is T, then the initial excitation voltage U 1 can be determined by the following expression:

[0123]

[0124] where the damage tolerance coefficient T is in the range of [0, 1], and is generally taken as 0.75. The distortion coefficient δ is a certain value greater than 1, which is the inflection point distortion coefficient, and is generally δ = 5.

[0125] After S2 is executed, S3 is executed: the initial excitation detection point is obtained and recorded, and the detection point is numbered; the response excitation current I 1 is obtained, and the excitation voltage U 1 and the response excitation current I 1 are recorded X 1( U 1, I 1), t is the detection sequence number, and at this time t = 1;

[0126] After S3 is executed, S4 is executed: current prediction control; the current response excitation current I k and the next target excitation current are input to the model prediction optimization controller MPC(), and the excitation voltage U k+1 of the next excitation detection is obtained, that is ; the excitation voltage U k+1 is output to the capacitive voltage transformer, and the capacitive voltage transformer responds to the excitation current I k+1 , including:

[0127] The target excitation current is determined by the following expression:

[0128]

[0129] where the distortion coefficient δ has been determined in S3, I k is the current excitation current, δ s is the distortion coefficient scaling coefficient, and is generally δ s = 10.

[0130] After S4 is executed, S5 is executed: the response excitation current is obtained, and the distortion coefficient between the detection points is calculated; the response excitation currentI k+1 , the detection sequence number t = t +1, record the excitation voltage U k+1 and the response excitation current I k+1 is X t ( U t , I t );calculate X t ( U t , I t ) and X 1( U 1, I 1)、……、 X t-1 ( U t-1 , I t-1 ) distortion coefficient sequence δ 1、…… δ t-1 , that is, calculate X t ( U t , I t ) and the distortion coefficient between all previous detection points, including:

[0131] calculate X t ( U t , I t ) and X 1( U 1, I 1)、……、 X t-1 ( U t-1 , I t-1 ) distortion coefficient sequence δ 1、…… δ t-1 The formula is as follows:

[0132]

[0133] Where max( I t , I jj ) represents takingX t ( U t , I t ) with other detection points X jj ( U jj , I jj ) the greater value of the field current, min( I t , I jj ) indicates taking X t ( U t , I t ) with other detection points X jj ( U jj , I jj ) the smaller value of the field current, max( U t , U jj ) indicates taking X t ( U t , I t ) with other detection points X jj ( U jj , I jj ) the greater value of the field voltage, min( U t , U jj ) indicates taking X t ( U t , I t ) with other detection points X jj ( U jj , I jj ) the smaller value of the field current.

[0134] After S5 is executed, S6 is executed: determining whether an inflection point occurs X G ( U G , IG That is, to determine the distortion coefficient set in S3. δ Does it exist in the distortion coefficient sequence? δ 1. ... δ t-1 That is, if it does not exist, execute S7; if it exists, execute S8, including:

[0135] set up δ x Distortion coefficient sequence δ 1. ... δ t-1 A point satisfies the following condition:

[0136]

[0137] inflection point X G ( U G , I G ) appears and exists in the detection point sequence. X 1( U 1, I 1) ... X t ( U t , I t In, that is:

[0138]

[0139] Assuming inflection point X G ( U G , I G If not found, execute S7: Distortion Coefficient Predictive Control; set δ k The distortion coefficients at the current moment and the target distortion coefficients set by S3. δ The input is fed into the model predictive optimization controller (MPC()) to obtain the excitation voltage for the next excitation detection. U k+1 ,Right now U k+1 =MPC( δ k , δ ); to excite voltage U k+1 The output is supplied to a capacitive voltage transformer, which then responds with an excitation current. I k+1 ;

[0140] S5: Obtain the response excitation current, calculate the distortion coefficient between the detection points; obtain the response excitation current I k+1 , detection sequence number t = t +1, record the excitation voltage U k+1 and the response excitation current I k+1 is X t ( U t , I t ); calculate X t ( U t , I t ) and the distortion coefficient sequence of X 1( U 1, I 1), …, X t-1 ( U t-1 , I t-1 ) δ 1, …… δ t-1 , that is, calculate X t ( U t , I t ) and the distortion coefficient between all previous detection points, including:

[0141] Calculate X t ( U t , I t ) and the distortion coefficient sequence of X 1( U 1, I 1), …, X t-1 ( U t-1 , I t-1 ) δ 1, …… δ t-1 The formula is as follows:

[0142]

[0143] Where max(I t , I jj ) represents the value of the field current at the detection point X t ( U t , I t ) the value of the field current at the other detection points X jj ( U jj , I jj ) the value of the field current at the other detection points I t , I jj ) represents the value of the field current at the detection point X t ( U t , I t ) the value of the field current at the other detection points X jj ( U jj , I jj ) the value of the field current at the other detection points U t , U jj ) represents the value of the field current at the detection point X t ( U t , I t ) the value of the field current at the other detection points X jj ( U jj , I jj ) the value of the field voltage at the other detection points U t , U jj ) represents the value of the field voltage at the detection point X t ( U t , I t ) the value of the field voltage at the other detection points X jj ( U jj , I jj ) the value of the field current at the other detection points

[0144] After S5 has been executed, S6 is executed: determining whether a knee point has occurredX G ( U G , I G That is, to determine the distortion coefficient set in S3. δ Does it exist in the distortion coefficient sequence? δ 1. ... δ t-1 That is, if it does not exist, execute S7; if it exists, execute S8, including:

[0145] set up δ x Distortion coefficient sequence δ 1. ... δ t-1 A point satisfies the following condition:

[0146]

[0147] inflection point X G ( U G , I G ) appears and exists in the detection point sequence. X 1( U 1, I 1) ... X t ( U t , I t In, that is:

[0148]

[0149] Assuming an inflection point X G ( U G , I G If an inflection point appears, execute S8: Find and determine the inflection point. X G ( U G , I G ); Query the distortion coefficient sequence δ 1. ... δ t-1 The distortion coefficient set by S3 δ Two detection points with equal distortion coefficients are used to determine and record the inflection point. X G ( U G ,I G ), including:

[0150] Set δ x is a sequence of distortion coefficients δ 1、… δ t-1 is a certain point, which satisfies the following conditions:

[0151]

[0152] Then the inflection point X G ( U G , I G ) exists in the distortion coefficient δ x The corresponding two detection points X t ( U t , I t ) and X x ( U x , I x ), then the determination expression of the inflection point X G ( U G , I G ) is:

[0153]

[0154] That is, the inflection point X G ( U G , I G ) is the point with larger excitation current in the distortion coefficient θ x The corresponding two detection points X t ( U t , I t ) and X x ( U x , I x ).

[0155] After S8 is executed, S9 is executed: check if the number of detection points is greater than or equal to 3;

[0156] If the number of detection points is greater than 3, S11 is executed: stop applying the excitation voltage to the capacitive voltage transformer; let the output excitation voltage be 0.

[0157] After S11 is executed, S12 is executed: fit to construct the excitation characteristic curve vector expression; construct the general expression of the excitation characteristic curve U = f ( I ), and substitute all detection points X 1( U 1, I 1)、 X 2( U 2, I 2)、……、 X t ( U t , I t ) into the general expression of the excitation characteristic curve U = f ( I ), fit to determine the vector expression corresponding to the measured capacitive voltage transformer excitation characteristic curve U = f o ( I ), including:

[0158] The general expression of the excitation characteristic curve U = f ( I ) can be represented by the following parameter equation:

[0159]

[0160] In the formula, ​ ∈[0,1] is a parameter, representing a point on the curve; U i is the voltage coordinate of the i th detection point X i ( U i , I i ); I i is the voltage coordinate of the i th detection point X i ( U i , I i) in the current coordinate; (ti) is a binomial coefficient, representing the contribution of each detection point to the curve.

[0161] Substitute all detection points X 1( U 1, I 1)、 X 2( U 2, I 2)、……、 X t ( U t , I t ) and zero point X 0( U 0, I 0) into the parametric equation, the equation established is the vector expression corresponding to the measured excitation characteristic curve of the capacitive voltage transformer U = f o ( I ).

[0162] After S12 is executed, S13 is executed: draw the excitation characteristic curve, mark the inflection point, complete the excitation characteristic detection; use the vector expression corresponding to the measured excitation characteristic curve of the capacitive voltage transformer U = f o ( I ) to draw the excitation characteristic curve in the display device, and mark the inflection point in the curve X G ( U G , I G ), complete the excitation characteristic detection of the capacitive voltage transformer.

Claims

1. A method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control, characterized in that, Includes the following steps: S1: Construct a model to predict the optimal controller: ,in For the current moment, For the next control moment, The control quantity output by the controller at the next moment. This represents the system response at the current moment. The system's target response at the next moment. For model predictive controller; S2: Set initial parameters; set the excitation characteristic distortion coefficient of the capacitive voltage transformer. ; Set the initial excitation voltage to It then outputs the current to a capacitive voltage transformer, which responds with the initial excitation current. ; S3: Acquire and record the initial excitation detection point, and number the detection point; acquire the response excitation current. Record the excitation voltage With response excitation current for , To detect the sequence number, at this time ; S4: Current Prediction Control; This will predict the current response excitation current. and the next target excitation current Input to the model predicts the optimal controller And obtain the excitation voltage for the next excitation detection. ,Right now ; excitation voltage The output is supplied to a capacitive voltage transformer, which then responds with an excitation current. ; S5: Obtain the response excitation current and calculate the distortion coefficient between detection points; Obtain the response excitation current. Detection sequence number Record the excitation voltage With response excitation current for ;calculate and ... distortion coefficient sequence ... That is, calculation The distortion coefficients between the original and all previous detection points specifically include: calculate and ... distortion coefficient sequence ... The formula is as follows: ； in Indicates taking Other testing sites Larger excitation current values Indicates taking Other testing sites The smaller the excitation current value, Indicates taking Other testing sites Larger excitation voltage values Indicates taking Other testing sites The smaller value of the excitation current; S6: Determine if an inflection point has occurred. ; That is, to determine the distortion coefficient set in S2. Does it exist in the distortion coefficient sequence? ... That is, if it does not exist, execute S7; if it exists, execute S8. S7: Distortion coefficient prediction control; (Set) The distortion coefficients at the current moment and the target distortion coefficients set by S2. The input is given to the model predictive optimization controller. And obtain the excitation voltage for the next excitation detection. ,Right now ; excitation voltage The output is given to the capacitive voltage transformer, which then responds with an excitation current. S8: Locate and determine the inflection point ; Query the distortion coefficient sequence ... The distortion coefficient set by S2 Two detection points with equal distortion coefficients are used to determine and record the inflection point. ; S9: Check if the number of detection points is greater than or equal to 3; if If so, then execute S10; if If so, then execute S11; S10: Supplement detection points in the low-voltage linear region; detection sequence number. ,make , excitation voltage The output is supplied to a capacitive voltage transformer, which then responds with an excitation current. ,Record ; S11: Stop applying excitation voltage to the capacitive voltage transformer; set the output excitation voltage to 0; S12: Fitting and constructing the vector expression of the excitation characteristic curve; constructing the general expression of the excitation characteristic curve. and all testing points , ... Substitute into the general expression of the excitation characteristic curve The vector expression corresponding to the measured excitation characteristic curve of the capacitive voltage transformer is determined by fitting. ; S13: Plot the excitation characteristic curve, mark the inflection point, and complete the excitation characteristic test.

2. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control according to claim 1, characterized in that, The vector expression corresponding to the measured excitation characteristic curve of the capacitive voltage transformer. Plot the excitation characteristic curve on the display device and mark the inflection points on the curve. Complete the excitation characteristic test of the capacitive voltage transformer.

3. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control according to claim 2, characterized in that, S1: Construct a model-predictive optimization controller; Construct a model-predictive optimization controller: ,in For the current moment, For the next control moment, The control quantity output by the controller at the next moment. This represents the system response at the current moment. The system's target response at the next moment. For model predictive controllers, specifically including: S1a: Constructing a capacitive voltage transformer system model: First, we construct a dynamic model of the system, using a discrete-time state-space model to describe the dynamic behavior of the system. The state-space model of the system is as follows: ； in, Indicates the current moment. This represents the system's state variables at the current moment. Indicates the control quantity. These are the state transition coefficients. The response coefficient of the control quantity; The system's output model is given by the following equation: ； in, This represents the system's output. For output coefficients, To control the input influence coefficient; S1b: Constructing a predictive model for capacitive voltage transformers: At every moment Based on the current state and control input, and using the system's state-space model and output model constructed in S11, the future is predicted. The system state and output at time t are predicted by the following formula: ； ； S1c: Defines the cost function for optimal control of excitation detection. Define a cost function with the objective of minimizing the weighted sum of output error and control input costs, and use the prediction model built in S12 to predict the future. Output at time 1 , ... , and the future The target output at each moment , ... , calculate the applied individual control quantities , ... The subsequent cost function is as follows: ； in, For reference output, It is the cost coefficient for controlling output error. It is the cost of controlling output error and controlling input; S1d: Solving the optimization problem: At each time step, calculate the cost function defined by S13. Minimum solution optimization problem to obtain the optimal control input sequence: ； in To control the minimum boundary of the values ​​that the variable can take, To control the maximum boundary of variable values, the boundary values ​​are set according to the safety assurance rules of the test site. , ... To solve the cost function The optimal control sequence obtained from the minimum solution optimization problem; S1e: After optimization, take the first control input from the optimal control input sequence. If the output of the control variable is controlled and applied to the system, then... Model predictive controller Construction complete.

4. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control as described in claim 3. Its characteristic is that, S2: setting the distortion coefficient of the excitation characteristics of the capacitive voltage transformer. ; Set the initial excitation voltage to ;Will The output is given to a capacitive voltage transformer, which then responds with the initial excitation current. Specifically, it includes: S21: Let the capacity of the measured capacitive voltage transformer be... Protection factor is The rated secondary current is And the damage tolerance coefficient for the measured capacitive voltage transformer is Then the initial excitation voltage It can be determined by the following expression: ； Damage tolerance coefficient The value range is [0,1]; S22: Distortion coefficient A value greater than 1 is the inflection point distortion coefficient.

5. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control according to claim 4, characterized in that, S4: Current Prediction Control; This will predict the current response excitation current. and the next target excitation current Input to the model predicts the optimal controller And obtain the excitation voltage for the next excitation detection. ,Right now ; excitation voltage The output is supplied to a capacitive voltage transformer, which then responds with an excitation current. Specifically, it includes: Target excitation current Determined by the following expression: ； Among them, distortion coefficient It has been determined in S2. This is the current excitation current. This is the distortion scaling factor.

6. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control according to claim 5, characterized in that, S6: Determine if an inflection point has occurred. ; That is, to determine whether the distortion coefficient δ set in S2 exists in the distortion coefficient sequence. ... That is, if it does not exist, execute S7; if it exists, execute S8. Specifically, it includes: set up Distortion coefficient sequence ... A point satisfies the following condition: ； inflection point Appears, exists in the detection point sequence ... In, that is: 。 7. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control according to claim 6, characterized in that, S8: Locate and determine the inflection point ; Query the distortion coefficient sequence ... The distortion coefficient set by S2 Two detection points with equal distortion coefficients are used to determine and record the inflection point. Specifically, it includes: set up Distortion coefficient sequence ... A point satisfies the following condition: ； inflection point Existing in the distortion coefficient The two corresponding detection points , Then the inflection point The definite expression is: ； inflection point Distortion coefficient The two corresponding detection points , Points with relatively large excitation current.

8. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control according to claim 7, characterized in that, S10: Supplement detection points in the low-voltage linear region; detection sequence number. ,make , excitation voltage The output is supplied to a capacitive voltage transformer, which then responds with an excitation current. ,Record Specifically, it includes: The excitation voltage of the supplementary low-voltage linear region detection point The range of values ​​is .

9. The method for testing the excitation characteristics of a capacitive voltage transformer based on model predictive control according to claim 8, characterized in that, S12: Fitting and constructing the vector expression of the excitation characteristic curve; constructing the general expression of the excitation characteristic curve. and all testing points , ... Substitute into the general expression of the excitation characteristic curve The vector expression corresponding to the measured excitation characteristic curve of the capacitive voltage transformer is determined by fitting. Specifically, it includes: General expression for excitation characteristic curve It can be represented by the following parametric equation: ； ； In the formula, It is a parameter representing a point on the curve; It is the first Each testing point Voltage coordinates; It is the first Each testing point Current coordinates; These are binomial coefficients, representing the contribution of each detection point to the curve; All detection points , ... And midnight Substituting the parameters into the equation, the resulting equation is the vector expression corresponding to the measured excitation characteristic curve of the capacitive voltage transformer. .

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