CN106777610B - Oil-immersed transformer oil-paper resistivity inversion method based on Newton-Raphson approach - Google Patents
Oil-immersed transformer oil-paper resistivity inversion method based on Newton-Raphson approach Download PDFInfo
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- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract
The invention discloses a kind of oil-immersed transformer oil-paper resistivity inversion methods based on Newton-Raphson approach, comprising steps of step 1, respectively under N kind pressuring method measuring transformer entirety N group stable insulation resistance actual value Rjr, consider oil-paper basic structure, oil-paper be divided into N number of inverting region；Step 2, the finite element model of inside transformer insulation system is established using FInite Element, is input with the resistivity of each inverting region oil-paper, and FEM calculation is carried out based on finite element model, constructs the corresponding stable insulation resistance calculations model of each pressuring method；Step 3, according to the actual value of transformer oil resistivity and N group stable insulation resistance, it is based on stable insulation resistance calculations model, inverting is carried out using resistivity of the Newton-Raphson approach to each inverting region oil-paper.The present invention can avoid the inconvenience of sampling and measuring and the damage to transformer insulation structure, while also can get the aging area distribution of oil-paper.
Description
Technical field
The present invention relates to a kind of oil-immersed power transformer paper oil insulation status assessment technologies, more particularly to one kind to be based on ox
- the oil-immersed transformer oil-paper resistivity inversion method of the inferior method of pressgang.
Background technique
There are mainly of two types for inside transformer insulating materials: liquid insulating material (transformer oil) and solid insulating material
(oil-paper).With long term high temperature, the effect of hyperbaric environment, aging, every material parameter, such as electricity can gradually occur for insulating materials
Resistance rate etc. can also change therewith.It can thus reflect its ageing state with parameters such as resistivity.Transformer oil is due to it
Fluid behaviour, material parameter distribution is relatively uniform, can be measured by direct sample to its insulation characterisitic.Solid insulation material
Expect the weak link as transformer interior insulation, its deterioration all occurs in regional area under normal circumstances, and direct sample measures not
Only process is cumbersome, has damage to insulation system, and sampling cost is high, and there are certain dispersibilities, it is difficult to obtain different zones
Aging characteristics.
Technology of numerical simulation may be implemented to be based on corresponding number using electric parameters such as the resistivity of insulating materials as input quantity
It is worth model, simulation calculation is carried out to measurable electrical quantity such as the stable insulation resistance of transformer.Especially finite element method, by
It is good to the adaptability of complex model in it, it can preferably realize the simulation analysis of inside transformer insulation system.Due to transformer
Oily resistivity and transformer stable insulation resistance value are all the electrical quantity being convenient for measuring, and the resistivity of each region oil-paper with it is whole
It is dull continuous relationship between the stable insulation resistance of body, therefore oil-paper electricity can be set up by finite element numerical model
The relationship of resistance and transformer stable insulation resistance, the resistivity of oil-paper is obtained by iterative inversion.
According to the design feature of transformer, the stable insulation resistance of three classes or more, their measurement process can be at least obtained
In pressuring method include: high-voltage winding pressurization, low pressure winding and cabinet ground connection；Low pressure winding pressurization, high-voltage winding and cabinet
Ground connection；High-low pressure winding pressurizes simultaneously, cabinet ground connection etc..And the resistivity of each region oil-paper is to steady under different pressurized conditions
Determine insulation resistance contribution to be not quite similar, therefore can be realized according to multiple groups stable insulation resistance to different zones oil-paper resistivity
Inverting.
Newton-Raphson approach obtains Nonlinear System of Equations by successive ignition by the way that nonlinear problem is linearized
Solution, has the characteristics that iteration is high-efficient, and is suitable for the iterative solution of nonlinear multivariable equation.Thus for different zones oil immersion
The iterative inversion of paper resistivity, Newton-Raphson approach are a kind of more appropriate methods.
Summary of the invention
The object of the present invention is to provide a kind of oil-immersed transformer oil-paper resistivity inversion based on Newton-Raphson approach
Method, using the present invention can inverting obtain the resistivity of different inverting regions oil-paper.
In order to achieve the above objectives, The technical solution adopted by the invention is as follows:
Oil-immersed transformer oil-paper resistivity inversion method based on Newton-Raphson approach, comprising steps of
Step 1, inverting region is divided:
According to each position of oil-paper to the influence degree of electric field, oil-paper is artificially divided into several inverting regions, it will be anti-
It drills region quantity and is denoted as N；The N group stable insulation resistance actual value R of measuring transformer entirety under N kind making alive modejr, Rjr
The stable insulation resistance actual value measured under expression jth kind making alive mode, j=1,2 ... N；
Step 2, the corresponding stable insulation resistance calculations model of each making alive mode is established:
The finite element model of inside transformer insulation system is established, using FInite Element with the oil-paper electricity in each inverting region
Resistance rate is that independent variable carries out limited respectively using the stable insulation resistance of transformer entirety as dependent variable under each making alive mode
Member calculates, and constructs the numerical relation model between the oil-paper resistivity and stable insulation resistance in each inverting region, i.e. stable insulation
Resistance calculations model, wherein transformer oil resistivity is as preset parameter；
Step 3, using the oil-paper resistivity in each inverting region of Newton-Raphson approach inverting:
According to the actual value of transformer oil resistivity and N group stable insulation resistance, it is based on stable insulation resistance calculations model,
Inverting is carried out using resistivity of the Newton-Raphson approach to each inverting region oil-paper, specifically includes following sub-step:
The preliminary oil-paper resistivity in 3.1 each inverting regions of setting:
By inverting region 1, inverting region 2 ... the oil-paper resistivity of inverting region N is denoted as ρ respectively1、ρ2、…ρN, right
The preliminary oil-paper resistivity answered is denoted as ρ respectively10、ρ20、…ρN0；
3.2 calculate the preliminary corresponding stable insulation resistance theoretical value of oil-paper resistivity:
According to transformer oil resistivity actual value, in conjunction with stable insulation resistance calculations model, under each making alive mode, point
The corresponding stable insulation resistance theoretical value R of current oil-paper resistivity is not calculated1c、R2c、…RNc；Current oil-paper resistivity
Initial value is the preliminary oil-paper resistivity that sub-step 3.1 is arranged；
3.3 calculate separately stable insulation resistance theoretical value RjcWith corresponding stable insulation resistance actual value RjrIt is opposite accidentally
Poor εjIf all relative error εjRespectively less than preset termination error threshold epsilonstop, then current oil-paper resistivity is final oil
Impregnated paper resistivity terminates；Otherwise, sub-step 3.4 is executed；
3.4 couples of each Rjc, calculate separately RjcEach inverting region current oil-paper resistivity neighborhood to each inverting region
Oil-paper resistivity partial derivative, by element of gained partial derivative construct size for N × N Jacobian matrix；
With R1c(ρ10、ρ20、…ρN0) in (ρ10,ρ20,...ρN0) nearby to ρ1Partial derivative for this sub-step is said
It is bright:
Keep ρ1The oil-paper resistivity in other outer inverting regions is constant, makes ρ1There is Tiny increment dt δ ρ1, inverting region 1 is set
Oil-paper resistivity be ρ10+δρ1, recalculate R1c(ρ10+δρ1、ρ20、…ρN0)。R1c(ρ10+δρ1、ρ20、...ρN0) indicate each
The oil-paper resistivity in inverting region is respectively ρ10+δρ1、ρ20、…ρN0When, using sub-step 3.2 obtained the 1st in making alive
Stable insulation resistance theoretical value under mode.R1c(ρ10、ρ20、…ρN0) indicate that the oil-paper resistivity in each inverting region is distinguished
ρ10、ρ20、…ρN0When, the stable insulation resistance theoretical value under the 1st kind of making alive mode obtained using sub-step 3.2.
Pass through formula (1) approximate calculation R1c(ρ10、ρ20、…ρN0) in (ρ10,ρ20,...ρN0) nearby to ρ1Partial derivative
Construct following Jacobian matrix J:
3.5 according to the correction amount ρ of each inverting region oil-paper resistivity1、Δρ2、…ΔρNBetween Jacobian matrix J
Relationship, computed correction；Δρ1、Δρ2、…ΔρNRespectively indicate inverting region 1, inverting region 2 ... the oil of inverting region N
Impregnated paper resistivity correction amount.
Correction amount ρ1、Δρ2、…ΔρNThere are following relationships between Jacobin matrix J:
In formula (3), Δ Rj=Rjr-Rjc, j=1,2 ... N；
According to formula (3), correction amount is solved:
3.6 correct the current oil-paper electricity in each inverting region using the oil-paper resistivity correction amount in each inverting region respectively
Resistance rate executes sub-step 3.2 using revised oil-paper resistivity as current oil-paper resistivity.
In step 1, pressuring method is the pressurization of 1. high-voltage winding, low pressure winding and cabinet ground connection；2. low pressure winding is pressurizeed, high
Press winding and cabinet ground connection；And 3. high-low pressure winding simultaneously pressurize, cabinet ground connection one of or it is a variety of.
In step 2, stable insulation resistance calculations model is constructed respectively under each making alive mode, specifically:
A series of oil-paper resistivity are respectively set to each inverting region, it is combined to obtain a series of oil-paper resistivity
Group, the oil-paper resistivity group are made of the oil-paper resistivity value in N number of inverting region；In each oil-paper resistivity group
Under, the potential value of node is obtained using FEM calculation under current power pressure mode, according to the potential value and note of node
Enter electric current and calculates stable insulation resistance value；It is exhausted according to the stabilization calculated under each oil-paper resistivity group and each oil-paper resistivity group
Edge resistance value, the numerical relation model of building current power pressure mode corresponding oil-paper resistivity and stable insulation resistance, i.e.,
Stable insulation resistance calculations model.
Compared to the prior art, the present invention has a characteristic that
In oil-immersed power transformer operational process, oil-paper is in long-term high temperature and high pressure environment, meeting gradually aging,
Resistivity is gradually changed also with ageing process.Due to the solid property of oil-paper, ageing state shows spatial distribution,
Therefore the resistivity of oil-paper different zones is also not quite similar.When parameter assesses its ageing state characterized by oil-paper resistivity
When, not only process is cumbersome for direct sample measurement, has damage to insulation system, and sampling cost is high, and there are certain dispersibility,
It is difficult to obtain the aging characteristics of different zones.
For the spatial distribution of oil-paper aging, the present invention is electric according to the stable insulation resistance and transformer oil of transformer
Resistance rate can be finally inversed by the oil-paper resistivity in different inverting regions.One aspect of the present invention can avoid the inconvenience of sampling and measuring
And the damage to transformer insulation structure, on the other hand the old of oil-paper can be judged according to the resistivity of different zones oil-paper
Change region and degree of aging.
Detailed description of the invention
Fig. 1 is the idiographic flow schematic diagram of the method for the present invention；
Fig. 2 is the finite element model established in embodiment.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
The present embodiment is implemented premised on technical solution of the present invention, gives detailed embodiment and specific behaviour
Make process, but protection scope of the present invention is not limited to following embodiments.
By taking certain 110kV oil-immersed transformer as an example, the refutation process of its oil-paper resistivity is illustrated, stable insulation resistance,
The actual value and termination error threshold epsilon of transformer oil resistivity and oil-paper resistivitystopIt is shown in Table 1.
Each electric parameter actual value of table 1
Specific step is as follows for the present embodiment:
In step (1), three groups of pressuring methods according to shown in table 1, in conjunction with inside transformer insulation system feature, by transformation
Oil-paper is divided into 3 inverting regions inside device:
Inverting region 1: the cardboard between low pressure winding surface oil-paper and low pressure winding and iron core, the inverting region
Resistivity is denoted as ρ1；
Inverting region 2: cardboard and square ring between high-low pressure winding, the resistivity in the inverting region are denoted as ρ2；
Inverting region 3: the cardboard between high-voltage winding and the oil-paper and high-voltage winding and cabinet of electrostatic ring surface,
The resistivity in the inverting region is denoted as ρ3。
In step (2), according to inside transformer structure, having for inside transformer insulation system is established using finite element software
Meta-model is limited, sees Fig. 2.Finite element model includes winding, oil duct, cardboard, the basic structure inside the isallobaric device of electrostatic ring.With each
The oil-paper resistivity in inverting region is input quantity, carries out finite element simulation calculation based on finite element model, establishes each making alive
Stable insulation resistance calculations model under mode.
The specific implementation of this step are as follows:
According to specific making alive mode, the current potential of coupled high voltage part conductive surface node injects 1A electric current to node.
The grounded parts such as other non-pressurised windings and cabinet, iron core load 0 current potential.The current potential number on node is obtained by FEM calculation
Value, numerical value, that is, stable insulation resistance value.According to oil-paper resistivity and corresponding stable insulation resistance value, building and making alive
The corresponding stable insulation resistance calculations model of mode.
In the sub-step 3.1 of step (3), the provisional value ρ of three inverting region oil-paper resistivity is set10、ρ20、ρ30
It is 1 × 1011Ω·m.In the sub-step 3.2 of step (3), provisional value ρ10、ρ20、ρ30Stabilization under corresponding each making alive mode
Insulation resistance theoretical value is shown in Table 2:
2 provisional value ρ of table10、ρ20、ρ30Corresponding insulation resistance theoretical value (unit: Ω)
| R1c | R2c | R3c |
| 2.1445×109 | 2.7247×109 | 2.0566×109 |
In the sub-step 3.3 of step (3), each stable insulation resistance theoretical value and actual value is opposite under each making alive mode
Error is shown in Table 3.
The relative error (unit: %) of 3 stable insulation resistance of table
| ε1 | ε2 | ε3 |
| 81.59 | 66.97 | 59.31 |
Each relative error is all larger than termination threshold epsilonstop, continue to execute sub-step 3.4.
In the sub-step 3.4 of step (3), individually make ρ1、ρ2、ρ3In (ρ10,ρ20,ρ30) nearby there is a Tiny increment dt δ ρ10、
δρ20、δρ30, three groups of stable insulation resistance values in corresponding situation are calculated, are shown in Table 4.Here Tiny increment dt takes 0.5%.
Stable insulation resistance calculations value (Ω) under the oil-paper resistivity of the different invertings of table 4 region
| ρ10+δρ10,ρ20,ρ30 | ρ10,ρ20+δρ20,ρ30 | ρ10,ρ20,ρ30+δρ30 | |
| R1c | 2.1445×109 | 2.1448×109 | 2.1446×109 |
| R2c | 2.7248×109 | 2.7252×109 | 2.7247×109 |
| R3c | 2.0567×109 | 2.0567×109 | 2.0567×109 |
Using above-mentioned calculated result, Jacobian matrix is calculated using formula (1):
In step (3) sub-step 3.5, the correction amount ρ of each inverting region oil-paper resistivity is calculated using formula (4)i,
It is shown in Table 5.
The correction amount (unit: Ω m) of the different invertings of table 5 region oil-paper resistivity
| Δρ1 | Δρ2 | Δρ3 |
| -1.0564×1013 | 8.4340×1012 | 1.3964×1013 |
Utilize correction amount ρiEach inverting region oil-paper resistivity is modified, wherein due to Δ ρ1< 0, here artificially
It is 1 × 10 that iteration lower limit, which is arranged,9Ω·m.Each inverting region oil-paper resistivity is shown in Table 6 after amendment.
The different revised oil-paper resistivity (Ω m) in inverting region of table 6
| ρ10 | ρ20 | ρ30 |
| 1×109 | 8.534×1012 | 1.406×1013 |
ρ in each secondary iteration10、ρ20、ρ30And relative error ε1、ε2、ε3It is shown in Table 7.
Parameter and calculated result used in each secondary iteration of table 7
According to iterative calculation as a result, the oil-paper resistrivity meter that termination error threshold value finally acquires in the case where being 0.1%
Calculation value is as follows:
Inverting region 1:2.810 × 1012Ω·m；
Inverting region 2:1.034 × 1014Ω·m；
Inverting region 3:1.298 × 1013Ω·m。
As can be seen that only having carried out 12 iteration just obtains the result below of stable insulation resistance relative error 0.1%.
Although the oil-paper different with the presence of degree of aging, resistivity are averaged to a certain extent in each inverting region, still
It can be with the aging conditions of oil-paper in each inverting region of significant reaction.Especially in inverting region 2 and inverting region 3 resistivity with
Difference is smaller between the cardboard resistivity of setting, illustrates present invention accuracy with higher.
Be described in above-described embodiment to illustrate this patent, though text in be illustrated by specific term, not
The protection scope that this patent can be limited with this, be familiar with this technical field personage can understand this patent spirit with it is right after principle
It changes or modifies and reaches equivalent purpose, and this equivalent change and modification, should all be covered by scope of the claims institute circle
Determine in scope.
Claims (4)
1. the oil-immersed transformer oil-paper resistivity inversion methods based on Newton-Raphson approach, characterized in that comprising steps of
Step 1, according to each position of oil-paper to the influence degree of electric field, oil-paper is artificially divided into several inverting regions, it will
Inverting region quantity is denoted as N；The N group stable insulation resistance actual value R of measuring transformer entirety under N kind making alive modejr,
RjrThe stable insulation resistance actual value measured under expression jth kind making alive mode, j=1,2 ... N；
Step 2, the finite element model of inside transformer insulation system is established, using FInite Element with the oil-paper in each inverting region
Resistivity is independent variable, using the stable insulation resistance of transformer entirety as dependent variable, is had respectively under each making alive mode
Limit member calculates, and constructs the numerical relation model between the oil-paper resistivity and stable insulation resistance in each inverting region, i.e., stable exhausted
Edge resistance calculations model, wherein transformer oil resistivity is as preset parameter；
In step 2, stable insulation resistance calculations model is constructed respectively under each making alive mode, specifically:
A series of oil-paper resistivity are respectively set to each inverting region, it is combined to obtain a series of oil-paper resistivity groups, institute
The oil-paper resistivity group stated is made of the oil-paper resistivity value in N number of inverting region；Under each oil-paper resistivity group, working as
The potential value of node is obtained using FEM calculation under preceding making alive mode, according to the potential value of node and Injection Current meter
Calculate stable insulation resistance value；According to the stable insulation resistance calculated under each oil-paper resistivity group and each oil-paper resistivity group
Value, the numerical relation model of building current power pressure mode corresponding oil-paper resistivity and stable insulation resistance are that is, stable exhausted
Edge resistance calculations model；
Step 3, using the oil-paper resistivity in each inverting region of Newton-Raphson approach inverting, this step further comprises:
The preliminary oil-paper electricalresistivityρ in 3.1 each inverting regions of settingi0, ρi0For the preliminary oil-paper resistance in i-th of inverting region
Rate, i=1,2 ... N；
3.2 divide under each making alive mode according to the actual value of transformer oil resistivity in conjunction with stable insulation resistance calculations model
The corresponding stable insulation resistance theoretical value R of current oil-paper resistivity is not calculatedjc, RjcIndicate steady under jth kind making alive mode
Determine insulation resistance theoretical value, j=1,2 ... N；
3.3 calculate separately stable insulation resistance theoretical value RjcWith corresponding stable insulation resistance actual value RjrRelative error, if
All relative errors are respectively less than preset termination error threshold value, the oil-paper resistivity of current oil-paper resistivity, that is, final, knot
Beam；Otherwise, sub-step 3.4 is executed；
3.4 according to stable insulation resistance theoretical value RjcEstablish Jacobian matrix J；
3.5 according to the correction amount ρ of each inverting region oil-paper resistivityiWith the relationship of Jacobian matrix J, correction amount is solved
ρi, Δ ρiIndicate the oil-paper resistivity correction amount in i-th of inverting region；
3.6 use correction amount ρiThe current oil-paper resistivity in each inverting region is corrected, respectively with revised oil-paper resistance
Rate executes sub-step 3.2 as current oil-paper resistivity.
2. the oil-immersed transformer oil-paper resistivity inversion methods based on Newton-Raphson approach as described in claim 1,
Be characterized in: the making alive mode is the pressurization of 1. high-voltage winding, low pressure winding and cabinet ground connection；2. low pressure winding is pressurizeed, high
Press winding and cabinet ground connection；And 3. high-low pressure winding simultaneously pressurize, cabinet ground connection one of or it is a variety of.
3. the oil-immersed transformer oil-paper resistivity inversion methods based on Newton-Raphson approach as described in claim 1,
It is characterized in:
Sub-step 3.4 specifically:
To each Rjc, calculate separately RjcEach inverting region current oil-paper resistivity neighborhood to the oil-paper in each inverting region
The partial derivative of resistivity constructs size by element of gained partial derivative as the Jacobian matrix of N × N.
4. the oil-immersed transformer oil-paper resistivity inversion methods based on Newton-Raphson approach as claimed in claim 3,
It is characterized in:
Calculate RjcEach inverting region current oil-paper resistivity neighborhood to the inclined of the oil-paper resistivity in each inverting region
Derivative, specifically:
The oil-paper resistivity in each inverting region is carried out respectively:
The current oil-paper resistivity in i-th of inverting region is set to have a Tiny increment dt δ ρi, while keeping the current of other inverting regions
Oil-paper resistivity is constant；Stable insulation resistance theoretical value is recalculated under jth kind making alive mode using sub-step 3.2
Rjc'；Rjc' and RjcDifference and Tiny increment dt δ ρiRatio, that is, RjcTo the inclined of the current oil-paper resistivity in i-th of inverting region
Derivative.
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