CN110619192B - Transformer parameter online calculation method - Google Patents

Transformer parameter online calculation method Download PDF

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CN110619192B
CN110619192B CN201910987200.3A CN201910987200A CN110619192B CN 110619192 B CN110619192 B CN 110619192B CN 201910987200 A CN201910987200 A CN 201910987200A CN 110619192 B CN110619192 B CN 110619192B
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王雪
丁嘉
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North China Electric Power University
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Abstract

The invention provides an online calculation method for transformer parameters, which is characterized by comprising the following steps: 1) Establishing a T-shaped equivalent circuit model according to the transformer circuit structure; 2) Constructing an objective function J comprising a voltage loop equation, an active loss equation, an input impedance equation, an idle current equation and an idle loss equation for solving the high-side resistance R 1 High pressure side leakage reactance X 1 Low-voltage side resistance value R 2 ' Low pressure side leakage reactance reduction value X 2 ' excitation resistor R m Exciting reactance X m 3) taking the formula J as an objective function, selecting an optimization algorithm to perform optimization calculation to obtain R 1 、X 1 、R 2 '、X 2 '、R m 、X m Is a solution to the optimization of (3). The transformer parameter online calculation method can calculate and identify the transformer equivalent circuit parameters such as winding resistance, leakage reactance, equivalent excitation branch impedance and the like online by utilizing the electrical measurement data of the transformer in steady state operation, and has the advantages of small identification error and high precision.

Description

Transformer parameter online calculation method
Technical Field
The invention belongs to the technical field of transformer operation monitoring, and particularly relates to an online calculation method for transformer parameters.
Background
The operating conditions of the transformer directly affect the safety and stability of the power equipment and even the whole power grid. The existing transformer equivalent circuit parameter identification method mainly establishes a parameter identification model according to a voltage loop equation, and adopts a least square method to complete parameter identification. For example, chinese patent CN201610050892.5 discloses a method for measuring leakage inductance and dc resistance of a transformer, which can measure the leakage inductance and dc resistance of one side of the transformer at the same time.
However, the parameter identification result of the above method has a large error. The main reason is that: in the parameter identification process, exciting current is ignored, so that the exciting current is not matched with the actual value, and the identification value is greatly different from the actual value; by adopting a method of artificially giving resistance, under the condition that a given value is different from an actual resistance or the resistance is changed, larger identification errors can be brought to other parameters; for the method of determining parameters through the two identification processes, each parameter is not obtained in the same state, and the states of the transformers corresponding to the two identification processes may be different, which may also result in a larger parameter identification error. In addition, after the voltage loop equation is obtained by the existing method, induced potential is eliminated, so that the identification model does not contain an excitation branch and the parameters of the branch cannot be identified.
Disclosure of Invention
The invention aims to provide an online calculation method for parameters of a transformer, which can calculate and identify the parameters of equivalent circuits of the transformer such as winding resistance, leakage reactance, equivalent excitation branch impedance and the like on line by using electrical measurement data during steady-state operation of the transformer and has the advantages of small identification error and high precision.
The specific technical scheme of the invention is an online calculation method for parameters of a transformer, which is characterized by comprising the following steps:
1) Establishing a T-shaped equivalent circuit model according to the transformer circuit structure;
2) Constructing an objective function J, shown in the following formula (I), for solving the high-voltage side resistance R 1 High pressure side leakage reactance X 1 Low-voltage side resistance value R 2 ' Low pressure side leakage reactance reduction value X 2 ' excitation resistor R m Exciting reactance X m
Figure BDA0002237062290000021
In the method, in the process of the invention,
Figure BDA0002237062290000022
for high-side voltage, +.>
Figure BDA0002237062290000023
For high-side current, +.>
Figure BDA0002237062290000024
For exciting current +.>
Figure BDA0002237062290000025
For low side voltage, +.>
Figure BDA0002237062290000026
To be reduced to the low-side voltage of the high-side, +.>
Figure BDA0002237062290000027
To refer to the low-side current to the high-side, Z 1 For high voltage side leakage impedance, Z 2 ' to be reduced to the low-side leakage impedance of the high-side, U N 、S N Rated voltage, rated capacity, P given to transformer nameplate 0 、I 0 % is the no-load loss and no-load current percentage given by the transformer nameplate, I N For the rated current of the transformer, which is determined from the data given by the transformer nameplate,/for the transformer>
Figure BDA0002237062290000028
I 1 Respectively->
Figure BDA0002237062290000029
Conjugate and modulus of->
Figure BDA00022370622900000210
For low-side current->
Figure BDA00022370622900000211
Is used for the conjugation of (a),
3) No-load loss P given by transformer nameplate 0 Percentage of no-load current I 0 Percent, rated voltage U N Rated capacity S N And the voltage at two sides of the transformer obtained by on-line measurement
Figure BDA00022370622900000212
And current->
Figure BDA00022370622900000213
Selecting an optimization algorithm by taking the J as an objective functionOptimizing calculation by the method to obtain R 1 、X 1 、R 2 ’、X 2 ’、R m 、X m Is a solution to the optimization of (3).
Furthermore, the optimization algorithm in the step 3) is a particle swarm algorithm, and the specific steps are as follows:
3.1 Setting inertia weight and learning factor of particle swarm algorithm;
3.2 Setting transformer parameter constraint conditions including parameter value constraint conditions and parameter correction constraint conditions;
3.3 Initializing the particle swarm according to the constraint condition, and determining an initial value of the optimal position of the particle and an initial value of the optimal position of the population;
3.4 And (3) carrying out iterative optimization, updating the speed and the position of the particles by adopting a particle speed and position updating formula, comparing the speed and the position of the particles with constraint conditions, calculating the fitness corresponding to each particle, evaluating the position of the particles, updating the optimal position of the particles and the optimal position of the population, judging whether the iteration ending condition is met, and finally outputting the transformer parameter identification value if the iteration ending condition is met.
The method has the beneficial effects that 1) the method for on-line calculation of the parameters of the transformer is based on the method for identifying the parameters of the multidimensional objective function, takes the leakage impedance and the excitation impedance as the to-be-identified quantity, synthesizes the transformer equations of five dimensions such as a voltage loop equation, an active loss equation, an input impedance equation, an idle loss equation and an idle current percentage equation, constructs the multidimensional objective function for parameter identification, combines the nameplate parameters of the transformer and the measured voltage and current at two sides of the transformer, and completes the parameter identification by adopting a particle swarm algorithm according to the objective function; 2) The active loss equation and the input impedance equation are introduced on the basis of the voltage loop equation, so that the factors of excitation impedance can be considered, the objective function equation not only contains leakage impedance, but also contains excitation impedance, and the influence of an excitation branch can be reflected; 3) The fact that no-load loss and no-load current of the transformer are not changed greatly in normal operation is fully considered, so that no-load current and no-load loss equations of the transformer can be introduced, the limiting capacity on an objective function is stronger, the two equations are mainly related to excitation impedance, the identification precision of the excitation impedance can be greatly improved, and other parameters are identified more accurately; 4) The particle swarm algorithm with the characteristics of simplicity, easiness, high precision and fast convergence is adopted for identification calculation, and no assumption limitation is required to be made on the running state and parameters of the transformer.
Drawings
FIG. 1 is a T-type equivalent circuit diagram of the transformer parameter on-line calculation method of the invention;
fig. 2 is a flowchart of a particle swarm optimization algorithm adopted in the transformer parameter online calculation method of the present invention.
FIG. 3 is a diagram of the high side voltage and current collected by an embodiment of the transformer parameter on-line calculation method of the present invention;
FIG. 4 is a diagram of low side voltage and current collected by an embodiment of an on-line calculation method for transformer parameters according to the present invention;
FIG. 5 is a graph showing the change in fitness obtained by applying an embodiment of the method for online calculation of transformer parameters according to the present invention;
FIG. 6 is a graph showing a resistance change curve obtained by applying an embodiment of the transformer parameter on-line calculation method of the present invention;
FIG. 7 is a plot of leakage reactance change obtained by an embodiment of an on-line calculation method for transformer parameters according to the present invention;
fig. 8 is a graph showing the excitation impedance variation obtained by applying the embodiment of the transformer parameter on-line calculation method of the present invention.
Detailed Description
The following structural description and the accompanying drawings further describe the specific technical scheme of the present invention.
The invention discloses a transformer parameter online calculation method which is characterized by comprising the following steps of:
1) Establishing a T-shaped equivalent circuit model according to a transformer circuit structure, as shown in figure 1;
2) Constructing an objective function J, shown in the following formula (I), for solving the high-voltage side resistance R 1 High pressure side leakage reactance X 1 Low-voltage side resistance value R 2 'low'Pressure side leakage reactance reduction value X 2 ' excitation resistor R m Exciting reactance X m
Figure BDA0002237062290000051
In the method, in the process of the invention,
Figure BDA0002237062290000052
for high-side voltage, +.>
Figure BDA0002237062290000053
For high-side current, +.>
Figure BDA0002237062290000054
For exciting current +.>
Figure BDA0002237062290000055
For low side voltage, +.>
Figure BDA0002237062290000056
To be reduced to the low-side voltage of the high-side, +.>
Figure BDA0002237062290000057
To refer to the low-side current to the high-side, Z 1 For high voltage side leakage impedance, Z 2 ' to be reduced to the low-side leakage impedance of the high-side, U N 、S N Rated voltage, rated capacity, P given to transformer nameplate 0 、I 0 % is the no-load loss and no-load current percentage given by the transformer nameplate, I N For the rated current of the transformer, which is determined from the data given by the transformer nameplate,/for the transformer>
Figure BDA0002237062290000058
I 1 Respectively->
Figure BDA0002237062290000059
Conjugate and modulus of->
Figure BDA00022370622900000510
For low-side current->
Figure BDA00022370622900000511
Is a conjugate of (c).
The above formula (I) is a multidimensional objective function constructed from five-dimensional transformer equations, including a voltage loop equation, an active loss equation, a transformer high-voltage side input impedance equation, an idle current equation, an idle loss equation, and the like. These five equations are each described below.
2.1 Voltage loop equation
From fig. 1, a voltage loop equation can be established as shown in the following formula (II).
Figure BDA00022370622900000512
Wherein Z is 1 =R 1 +jX 1 ,Z’ 2 =R’ 2 +jX’ 2
Figure BDA00022370622900000513
And->
Figure BDA00022370622900000514
Respectively indicate->
Figure BDA00022370622900000515
And->
Figure BDA00022370622900000516
To the high-side value.
2.2 Equation of active loss
The transformer winding resistance and the equivalent excitation resistance both generate active loss which is equal to the difference between the input active power and the output active power of the transformer. And accordingly, establishing an active loss equation of the transformer, wherein the active loss equation is shown in the following formula (III).
Figure BDA0002237062290000061
2.3 Input impedance equation
The ratio of the voltage and current at the high voltage side is the input impedance at the high voltage side of the transformer, which is related to the parameters of the transformer itself and the load impedance, as shown in the following formula (IV).
Figure BDA0002237062290000062
In the middle of
Figure BDA0002237062290000063
2.4 Equation of no-load current
The transformer is not loaded, and the current is no-load current in the secondary open circuit. The calculation expression thereof is obtained as follows.
Figure BDA0002237062290000064
2.5 Equation of no-load loss
When the transformer runs in an idle state, the active loss on the high-voltage side coil resistor and the equivalent exciting resistor is no-load loss, and the calculation expression is as follows.
P 0 =(U N /|Z 1 +Z m |) 2 (R 1 +R m ) (VI)
If the objective function is built only by using the voltage loop equation, the equation only contains drain impedance, no excitation impedance, an excitation branch cannot be represented, and when the drain impedance, particularly the winding resistance is small, the identification accuracy is insufficient.
The leakage impedance and the excitation impedance are important components of the transformer equivalent circuit, so that the input impedance of the transformer obtained by the transformer equivalent circuit can show the excitation impedance, can well limit the leakage impedance, and can better improve the identification accuracy of each parameter.
In order to enhance the identification accuracy of the excitation impedance, the method introduces no-load current and no-load loss equation. Because the transformer has little change in no-load loss and no-load current when in normal operation and even when some faults (such as winding deformation and turn-to-turn short circuit) occur, the two are mainly related to excitation impedance, and the limitation capacity on the excitation impedance is strong. Therefore, the identification accuracy of exciting impedance can be greatly improved by introducing no-load current and no-load loss equation of the transformer, and the identification of other parameters can be more accurate indirectly.
In addition, the active loss of the transformer is correspondingly generated by the resistance parts of the drain impedance and the exciting impedance, so that the method introduces an active loss equation again in order to ensure that the winding resistance with smaller value can be identified more accurately and the constraint on the exciting resistance can be enhanced.
And (3) taking the minimum sum of squares of residual errors of the five sets of equations (II) - (VI) as an identification criterion to obtain the multidimensional objective function J shown in the formula (I).
3) No-load loss P given by transformer nameplate 0 Percentage of no-load current I 0 Percent, rated voltage U N Rated capacity S N And the voltage at two sides of the transformer obtained by on-line measurement
Figure BDA0002237062290000071
And current->
Figure BDA0002237062290000072
Taking the formula J as an objective function, selecting an optimization algorithm to perform optimization calculation to obtain R 1 、X 1 、R 2 ’、X 2 ’、R m 、X m Is a solution to the optimization of (3).
The optimization algorithm can be selected from an immune algorithm, a genetic algorithm, an ant colony algorithm, a particle swarm algorithm, a fish swarm algorithm, a drosophila algorithm and the like in the prior art. The method of the invention selects the particle swarm algorithm with simple and easy operation, high precision and fast convergence for identification calculation, as shown in figure 2.
The following describes the procedure of each step of the particle swarm algorithm in combination with the parameter identification of an actual transformer. The transformer is known as a 242+/-1 multiplied by 5%/13.8kV three-phase transformer, and the parameters are respectively as follows: the calculated values of the high-voltage side resistor and the low-voltage side resistor are approximately equal and are 0.4637 omega; the high-pressure side leakage inductance is 0.1614H, and the low-pressure side leakage inductance is 0.0003431H; the excitation resistance is 100491.2 omega and the excitation reactance is 252894.1 omega.
For this example, the voltage and current are obtained by simulation, and since the simulation adopts a single-phase transformer model, the identification adopted transformer nameplate parameters are all single-phase values obtained by converting the three-phase parameters of the transformer. The single-phase values of each nameplate parameter are: the single-phase no-load loss is 0.0795/3MW, the single-phase no-load current percentage is 0.1%, and the single-phase rated voltage is
Figure BDA0002237062290000082
The single-phase rated capacity is 200/3MVA. The voltage and current on both sides of the transformer are measured as shown in figures 3 and 4.
(3.1) setting parameters of particle swarm algorithm
In general application of the particle swarm algorithm, the inertia weight is generally 0.2-1.2, and the learning factor is generally 0-4. The inertia weight omega is taken to be 0.4, and the learning factor c is taken 1 0.5, c 2 2.5.
(3.2) setting parameter constraints
According to the nameplate data, the sum of the resistances of the two sides, the sum of the leakage resistances of the two sides and the excitation impedance can be calculated, and a certain range of floating up and down is used as a constraint condition of corresponding parameter values according to the values. In this embodiment, the sum of resistances at both sides of the transformer is 0.9274 Ω, the sum of leakage reactance at both sides is 61.7479 Ω, the excitation resistance is 100491.2 Ω, and the excitation reactance is 252894.1 Ω. According to the constraint condition of parameter value, the constraint condition of parameter correction quantity can be set, and generally V is taken max =kx max ,V min =-kx max In V max 、V min Respectively the maximum and minimum correction amounts of the parameters, x max K is a value smaller than 1 for the maximum value of the parameter.
Constraint conditions for setting the values and correction amounts of the parameters are shown in table 1:
table 1 transformer parameter constraints
Figure BDA0002237062290000081
Figure BDA0002237062290000091
(3.3) particle parameter initialization
A population of initial particles is given. According to the size range corresponding to the parameter value and correction quantity constraint condition, randomly selecting the initial position { R } of each particle 10 X 10 R 20 ’X 20 ’R m0 X m0 } initial velocity { v 10 v 20 v 30 v 40 v 50 v 60 -a }; taking the initial position of the particle as the initial value of the self optimal position; and (3) taking the formula (I) as a fitness function, calculating the fitness of the initial particles, and determining the initial value of the optimal position of the population according to the fitness.
When the parameters of the transformer are identified, the initial position and initial speed of a particle are shown in table 2, and the fitness of the particle is 2.5592 according to the fitness function.
TABLE 2 initial position and initial velocity of particles
Figure BDA0002237062290000092
(3.4) iterative optimization
And during iteration, the speed and the position of each particle are updated by a particle speed and position updating formula. The particle velocity and location update formula is as follows:
v kid =ωv(k-1) id +c 1 r i (gbest-x (k-1)id )+
c 2 r 2 (zbest-x (k-1)id )
x kid =x (k-1)id +v (k-1)id
in the formula, v kid 、v (k-1)id Respectively the d-th dimensional velocity of particle i in the kth, k-1 iterationsA degree; x is x kid 、x (k-1)id Respectively refers to the d-th dimensional position of the particle i in the kth and the kth-1 iteration; omega is the inertial weight; c 1 、c 2 Is a learning factor; r is (r) 1 、r 2 A random number between 0 and 1; gbest and zbest are the historical optimal positions of the population and the historical optimal positions of the population in each iteration. After updating, the position and speed of the particles are required to be compared with the parameter value constraint condition and the parameter correction quantity constraint condition set in the prior art, and when the value of the particle is larger or smaller than the range corresponding to the constraint condition, the particle is modified into the upper bound or the lower bound of the range.
And after updating the particle speed and the particle position, evaluating the particle position by adopting a fitness function.
After evaluation, comparing the fitness between different iterations of the same particle and between the particles of the iteration, and selecting the particle with the lowest fitness to update the particle self optimal position gbest and the particle population optimal position zbest.
And finally judging whether the iteration termination condition is met, namely, whether the fitness of the optimal position of the population meets the condition or reaches the maximum iteration times. When the termination condition is not met, continuing iteration; and when the termination condition is met, the identification is finished, and the optimal position of the output population is the identification value of the transformer parameter.
In this embodiment, during iterative optimization, the change curve of the fitness of the objective function is shown in fig. 5, and the change curves of the transformer winding resistance, the leakage reactance and the excitation impedance along with the iteration are shown in fig. 6-8. Finally, the parameter identification value and the identification error of the transformer are shown in the table 3, and the corresponding fitness is 1.2302 multiplied by 10 -9
TABLE 3 Transformer parameter identification results
Figure BDA0002237062290000101
/>
Figure BDA0002237062290000111
While the invention has been disclosed in terms of preferred embodiments, the embodiments are not intended to limit the invention. Any equivalent changes or modifications can be made without departing from the spirit and scope of the present invention, and are intended to be within the scope of the present invention. The scope of the invention should therefore be determined by the following claims.

Claims (2)

1. The transformer parameter online calculation method is characterized by comprising the following steps of:
1) Establishing a T-shaped equivalent circuit model according to the transformer circuit structure;
2) Constructing an objective functionJThe formula (I) is shown as the specification and is used for solving the high-voltage side resistanceR 1 Leakage reactance of high pressure sideX 1 Low-voltage side resistance valueR 2 ' Low pressure side leakage reactance reduction valueX 2 ' Exciting resistorR m Exciting reactanceX m
Figure QLYQS_1
(I)
In the method, in the process of the invention,
Figure QLYQS_7
for high-side voltage, +.>
Figure QLYQS_8
For high-side current, +.>
Figure QLYQS_9
For low side voltage, +.>
Figure QLYQS_10
To be reduced to the low-side voltage of the high-side, +.>
Figure QLYQS_11
To account for the low side current to the high side,Z 1 for the high-voltage side-leakage impedance,Z 2 ' to account for the low side leakage impedance to the high side,U N S N rated voltage, rated capacity, given for transformer nameplate>
Figure QLYQS_12
The percentage of no-load current given for the transformer nameplate, < >>
Figure QLYQS_13
Respectively->
Figure QLYQS_2
Conjugate and modulus of->
Figure QLYQS_3
For low-side current->
Figure QLYQS_4
Conjugation of->
Figure QLYQS_5
,/>
Figure QLYQS_6
3) No-load loss according to transformer nameplate
Figure QLYQS_15
Percentage of no-load current->
Figure QLYQS_16
Rated voltage->
Figure QLYQS_17
And rated capacity->
Figure QLYQS_18
And the voltage on both sides of the transformer measured on line +.>
Figure QLYQS_19
、/>
Figure QLYQS_20
And current->
Figure QLYQS_21
、/>
Figure QLYQS_14
Above mentioned methodJSelecting an optimization algorithm for optimization calculation to obtain an objective functionR 1X 1 R 2 ' X 2 ' R m X m Is a solution to the optimization of (3).
2. The online calculation method of transformer parameters according to claim 1, wherein the optimization algorithm in the step 3) is a particle swarm algorithm, and specifically comprises the following steps:
3.1 Setting inertia weight and learning factor of particle swarm algorithm;
3.2 Setting transformer parameter constraint conditions including parameter value constraint conditions and parameter correction constraint conditions;
3.3 Initializing the particle swarm according to the constraint condition, and determining an initial value of the optimal position of the particle and an initial value of the optimal position of the population;
3.4 And (3) carrying out iterative optimization, updating the speed and the position of the particles by adopting a particle speed and position updating formula, comparing the speed and the position of the particles with constraint conditions, calculating the fitness corresponding to each particle, evaluating the position of the particles, updating the optimal position of the particles and the optimal position of the population, judging whether the iteration ending condition is met, and finally outputting the transformer parameter identification value if the iteration ending condition is met.
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Estimation of Equivalent Circuit Parameters of Transformer and Induction Motor from Load Data;Diptarshi Bhowmick;《IEEE Transactions on Industry Applications》;20180108;第54卷(第03期);全文 *

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