CN115296299B - Earth surface potential correction method based on transformer neutral point direct current measurement data - Google Patents
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- H—ELECTRICITY
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
The invention relates to a ground surface potential correction method based on transformer neutral point direct current measurement data, which utilizes transformer neutral point direct current measurement data of transformers in a plurality of different transformer substations and combines a power grid direct current magnetic bias simulation model, forms a target function through comparison between a calculation result of the direct current magnetic bias simulation model and measured data, and corrects the power station ground surface potential of the direct current magnetic bias simulation model by using a Zoutendijk feasible direction method. According to the method, the correction potential column vector of the transformer substation is introduced, so that the deviation between the direct current bias magnetic simulation model and the measured data can be effectively made up.
Description
Technical Field
The invention belongs to the technical field of power grid direct current magnetic biasing risk assessment, and particularly relates to an earth surface potential correction method based on transformer neutral point direct current measurement data.
Background
The direct current transmission mostly adopts a single-pole earth return operation mode during fault. Under the condition, a large amount of direct current can invade an alternating current power grid indirectly through the ground, so that a transformer winding passes direct current magnetic biasing current with different numbers of amperes to dozens of amperes, and an iron core of the transformer is in a saturated working state. In order to evaluate and manage the risk of the direct current magnetic bias of the transformer, a general method is to establish a direct current magnetic bias current distribution calculation model of an alternating current power grid through a computer simulation technology, and then confirm relevant sites needing to adopt a transformer neutral point series type magnetic bias management device by combining calculation results and actual measurement data of partial sites.
The direct current magnetic bias simulation model comprises two steps: (1) The relative position of the power station-direct current grounding electrode is arranged, and the mutual resistance between the earth potential and the transformer substation is calculated; (2) And solving according to a field-path direct coupling model to obtain the direct current distribution of the system. But there is a more outstanding problem at present: the calculated result of the magnetic biasing model is inconsistent with the measured data of partial sites, and although the site adopting the transformer neutral point series type magnetic biasing treatment device can be determined according to the measured result in the actual engineering, the adverse effects of treatment measures on other transformer substations cannot be accurately analyzed through the model of simulation evaluation in the follow-up process.
Disclosure of Invention
The invention provides a method for correcting the earth surface potential based on transformer neutral point direct current measurement data, which aims at the defects of the prior art, and comprises the steps of utilizing the neutral point direct current measurement data of transformers in a plurality of different substations, combining a direct current magnetic bias simulation model, forming a target function through the comparison between the calculation result of the direct current magnetic bias simulation model and the measured data, correcting the earth surface potential of a power station of the direct current magnetic bias simulation model by using a Zoutendijk feasible direction method, and indicating the substation with the possibility of error collection of wiring data.
The invention adopts the following technical scheme that an earth surface potential correction method based on transformer neutral point direct current measurement data comprises the following steps:
step 1, constructing a direct current magnetic bias simulation model;
step 2, importing the direct current measurement data of the neutral point of the transformer, establishing a comparison relation between a simulation calculation result of the direct current magnetic bias simulation model and an actual measurement value, and forming an objective functionF：
WhereinI Aj Is as followsjThe direct current measured value of the neutral point of each transformer substation,
is a firstjThe direct current simulation calculation value of the neutral point of each transformer substation,qis the number of measured values;
step 3, correcting the potential column vector of the initial transformer stationΔV (0) = {0}, solving the second step according to the direct current magnetic bias simulation model in the step 1jNeutral point DC simulation initial value of individual transformer substation
；
Step 4, making the number of iterationsk=1, objective function threshold
=0.01, secondjNeutral point DC simulation initial value of individual transformer substation
Substituting the objective functionFAfter k iterations, the objective function value of the k iteration is obtainedF k() ；
Step 5, if it iskTarget function absolute value of sub-iteration
Ending the iteration; otherwise, the next iteration is carried out, andk= k+1, and go to step 6;
step 6, constructing a Zoutendijk feasible direction optimization problem:
in the formula, min represents an optimization operator for solving a minimum value, s.t. represents a constraint condition,
is shown askA second iteration ofjThe direct current simulation calculation value of the neutral point of each transformer substation,I Aj k() denotes the firstkA second iteration ofjThe direct current measured value of the neutral point of each transformer substation,ΔVthe potential column vector is corrected for the substation,I dc the earth current is injected to the direct current grounding electrode,Nis the mutual resistance between two substations,Mthe mutual resistance between the direct current grounding electrode and the transformer substation;
step 7, selecting the feasible direction of the Zoutendijk feasible direction optimization problemd 1 k() And the direction of constraintd 2 k() Comprises the following steps:
wherein,Bis provided withThe correlation matrix of the neutral point of the measured data to all nodes,E m is composed ofmA matrix of the order of the unit,Zis an overground-underground network correction matrix of a direct current magnetic bias simulation model,ΔV k() correcting the potential column vector for the transformer substation of the kth iteration;
overground-underground network correction matrix of direct current magnetic bias simulation modelZThe specific expression of (A) is as follows:
in the formula,Hfor the incidence matrix between the substation node and all nodes,H T is composed ofHTransposing;Qa node conductance matrix of the AC power grid ground network;Gis a ground conductance matrix of the substation,G= R –1 ，Ris a matrix of the ground resistance of the substation,R= diag ( R 1 , R 2 , …, R i , …,R m )，R i is as followsiThe grounding resistance of each transformer substation is controlled by a controller,i=1，2，…，m；
calculating to obtain feasible directiond 1 k() And direction of constraintd 2 k() Turning to step 8;
step 8, passing the feasible directiond 1 k() And direction of constraintd 2 k() Generating feasible search directions under constraintsd 3 k() ：
Wherein,
is a number smaller than 0 and is,Trepresenting a transposition; if it cannot generated 3 k() Go to step 6, if it can generated 3 k() Turning to step 9;
step 9, determining the feasible direction by the steepest descent methodd 1 k() And direction of constraintd 2 k() Searching for the optimal direction of the Zoutendijk feasible direction optimization problemd 4 k() ：
To find outd 4 k() Turning to step 10;
step 10, by linear search method, according to the optimum directiond 4 k() Determining an optimal step size for a Zoutendijk feasible direction optimization problems k() ：
UpdatingΔV k(+1) =ΔV k() + d 4 k() s k() ，ΔV k+(1) And (5) correcting the potential column vector for the transformer substation of the (k + 1) th iteration, and turning to the step 5.
Further preferably, the process of constructing the dc magnetic bias simulation model includes:
step 1.1, sorting the relative positions of a power station and a direct current grounding electrode, and calculating mutual resistance between the earth potential and a transformer substation;
and step 1.2, solving according to a field direct coupling model to obtain a transformer substation neutral point direct current simulation calculated value.
Further preferably, the mutual resistance between the two substationsNComprises the following steps:
wherein,α p is as followspThe amplitude of the individual earth potential characteristic components,β p is a firstpThe attenuation modes of the individual earth potential characteristic components,rthe distance between the direct current grounding electrode and the transformer substation.
Further preferably, the first stepjNeutral point DC simulation calculated value of individual transformer substation
Calculated as follows:
wherein "\\" is a left division operator.
Compared with the prior art, the invention has the following beneficial effects: the existing direct current magnetic bias simulation model is improved moderately, but the solving method and the related theoretical basis of the existing direct current magnetic bias simulation model are not damaged; the introduction of the substation correction potential column vector can be regarded as further refinement and supplement of a ground potential distribution mode which cannot be accurately predicted by the direct current bias simulation model, and the deviation between the direct current bias simulation model and the measured data can be effectively compensated. The method is suitable for improving the precision of the direct current magnetic bias simulation model, and the effect evaluation of the transformer direct current magnetic bias treatment measures by adopting the corrected direct current magnetic bias simulation model, and solves the problems that the measurement data cannot be introduced by the past calculation means for correction and the calculation precision is low.
Detailed Description
For better understanding of the present invention, the following examples are provided to further illustrate the present invention, and the examples described are only a part of the present invention, but the present invention is not limited to the following examples. Various changes or modifications may be effected therein by one skilled in the art and such equivalents are intended to be within the scope of the invention as defined by the claims appended hereto.
The earth surface potential correction method based on the transformer neutral point direct current measurement data comprises the following steps:
step 1, constructing a direct current magnetic bias simulation model.
Step 1.1, the relative position of the power station-direct current grounding electrode is arranged, and the mutual resistance between the earth potential and the transformer substation is calculated.
According to the relation between the longitude and latitude of the earth and the distance, a certain transformer substationS(x i , y i ) And a DC ground electrode (x, y) North-south distance betweenL N Comprises the following steps:
whereinx i For the longitude of the substation, it is,y i in order to be the latitude of the substation,xis the longitude of the dc earth electrode,yis the latitude of the direct current grounding electrode,
equator radiusa=6 378.137 km, eccentricitye 2 = 0.006 694 38. In the same way, the east-west distanceL E Comprises the following steps:
distance between DC grounding electrode and transformer substationrAndL N andL E the relationship between them is:
the earth surface potential of the transformer substation can be completed by substituting the formula (3) into the following formulaUSolving:
wherein,I dc the earth current is injected to the direct current grounding electrode,α p is as followspThe amplitude of the individual components of the earth potential signature,β p is a firstpThe attenuation modes of the individual earth potential characteristic components,Mis the mutual resistance between the direct current grounding electrode and the transformer substation.
On the basis of the formula (4), the longitude and latitude coordinates of the direct current grounding electrode in the formula (1) are replaced by the longitude and latitude coordinates of another transformer substation, so that the mutual resistance between the two transformer substations can be derivedNComprises the following steps:
similarly, the direct current simulation calculation value of the neutral point of the transformer substation
And the influence of mutual resistance between substations on the earth potential of peripheral substationsU N The simplified algorithm described above can also be used to calculate:
and step 1.2, solving according to a field direct coupling model to obtain a transformer substation neutral point direct current simulation calculated value.
The column-write grid node voltage model is as follows:
in the formula:Vis a column vector of the grid node voltages,V = [V S ，V B ，V N ]，V S 、V B 、V N are respectively asmMaintaining the voltage column vector of the node of the transformer substation,bThe dimensional bus voltage column vector,nMaintaining the column vector of the neutral point of the transformer,Yis a conductance matrix of the nodes of the power grid,Jand injecting a current column vector for the grid node.
In the formulaHFor the incidence matrix between the substation node and all nodes,H T is composed ofHThe method (2) is implemented by the following steps,H m× m b n( ++) = [E m 0 m b× 0 m n× ]，E m is composed ofmAn order identity matrix;Qa node conductance matrix of the AC power grid ground network;Gis a grounded conductance matrix of the substation,G= R –1 ，R= diag ( R 1 , R 2 , …, R i , …,R m )，R i is as followsiThe grounding resistance of each transformer substation is provided with a plurality of grounding resistors,i=1，2，…，m。
if the measured data of the grounding resistance of the transformer substation cannot be collected and the condition that the grounding resistance of the transformer substation is locally considered as uniform soil is determined, the grounding resistance of the transformer substation can be calculated by the following formula:
in the formula,
the resistivity of the soil at the location of the substation,Ais the total area of the grounded screen.
In formula (10):J S 、J B 、J N respectively are the injection current column vectors of a transformer substation node, a bus node and a transformer neutral point;Pthe induction potential column vector of the transformer substation is represented by the following grounding theory:
the definition of the substation induced potential, namely the entrance potential between the neutral point and the earth zero point, and the substation ground resistance and the induced potential can be called as 'thevenin equivalent'. At the moment, the simulation calculation value of the direct current of the neutral point of the transformer substation is as follows:
in the formulaV A Is the voltage of a substation node, and is defined as:
by combining the above formulas, the relation between the simulation calculation value of the direct current of the neutral point of the transformer substation and the direct current grounding electrode injection earth current can be finally deduced as follows:
in the formula,
，E m is composed ofmAn order unit matrix. Then the simulation calculation value of the dc current at the neutral point of the substation can be represented by the following formula:
wherein "\\" is a left division operator and is expressed as an equation
The solution of (1). Solving the formula (15) to obtain the neutral point direct current of the transformer substation.
Step 2, importing the direct current measurement data of the neutral point of the transformer, establishing a comparison relation between a simulation calculation result of the direct current magnetic bias simulation model and an actual measurement value, and forming an objective functionF：
WhereinI Aj Is as followsjThe direct current measured value of the neutral point of each transformer substation,
is as followsjThe direct current simulation calculation value of the neutral point of each transformer substation,qis the number of measured values.
Step 3, correcting the potential column vector of the initial transformer stationΔV (0) =0, the second direct current magnetic bias simulation model in step 1 is solvedjNeutral point DC simulation initial value of individual transformer substation
。
Step 4, making the number of iterationsk=1, objective function threshold
=0.01, secondjNeutral point DC simulation initial value of individual transformer substation
Substituting formula (16), and obtaining the objective function value of the kth iteration after k iterationsF k() 。
Step 5, if it iskTarget function absolute value of sub-iteration
Ending the iteration; otherwise, the next iteration is carried out, andk= k+1, and go to step 6.
Step 6, constructing a Zoutendijk feasible direction optimization problem:
in the formula, min represents an optimization operator for solving a minimum value, s.t. represents a constraint condition,
is shown askA second iteration ofjThe direct current simulation calculation value of the neutral point of each transformer substation,I Aj k() is shown askA second iteration ofjAnd (6) a direct current measured value of a neutral point of each transformer substation.
Step 7, selecting the feasible direction of the Zoutendijk feasible direction optimization problemd 1 k() And direction of constraintd 2 k() Comprises the following steps:
wherein,Bfor the correlation matrix of the neutral point with the measurement data to all nodes,E m is composed ofmThe order unit matrix, R is the grounding resistance matrix of the transformer substation,Zis an overground-underground network correction matrix of a direct current magnetic bias simulation model,ΔV k() and correcting the potential column vector for the substation of the k iteration.
Overground-underground network correction matrix of direct current magnetic bias simulation modelZThe specific expression of (A) is as follows:
in the formula,Hfor the incidence matrix between the substation node and all nodes,H T is composed ofHThe method (2) is implemented by the following steps,H m× m b n( ++) = [E m 0 m b× 0 m n× ]；Qa node conductance matrix of the AC power grid ground network;Gis a ground conductance matrix of the substation,G= R –1 ，R= diag ( R 1 , R 2 , …, R i , …,R m )，R i is as followsiThe grounding resistance of each transformer substation is controlled by a controller,i=1，2，…，m。
calculating to obtain feasible directiond 1 k() And direction of constraintd 2 k() Go back to step 8.
Step 8, passing the feasible directiond 1 k() And the direction of constraintd 2 k() Generating feasible search directions under constraintsd 3 k() ：
Wherein,
is a number smaller than 0 and is,Trepresenting a transposition. If it cannot generated 3 k() Go to step 6, if it can generated 3 k() Go to step 9.
Step 9, determining the feasible direction by the steepest descent methodd 1 k() And the direction of constraintd 2 k() Searching for the optimal direction of the Zoutendijk feasible direction optimization problemd 4 k() ：
To obtaind 4 k() Go back to step 10.
Step 10, according to the optimal direction by a linear search methodd 4 k() Determining an optimal step size for a Zoutendijk feasible direction optimization problems k() ：
UpdatingΔV k(+1) =ΔV k() + d 4 k() s k() ，ΔV k+(1) And (5) correcting the potential column vector for the transformer substation of the (k + 1) th iteration, and turning to the step 5.
To further verify the applicability of the method of the present invention, in-situ measurements of the neutral point current of the primary transformer within 70km of the perimeter of the dc ground were organized during commissioning of the dc ground at some point. The direct current electrode grounding current is 6219A, and the deviation of the converted measured value and the calculated value is shown in Table 1. The result shows that the difference between the simulation calculated value and the measured value of 16 sites is more than 10A. The result shows that the traditional direct current magnetic bias simulation model has certain deviation with the measured value. Careful analysis finds that the causes of the deviation of the direct current magnetic bias simulation model mainly include the following three points: 1) Resistivity models of the earth are not accurate enough; 2) The model value of the grounding resistance of the transformer substation has deviation from the actual value; 3) The power grid wiring mode in the direct current magnetic bias simulation model is different from the actual operation mode of the power grid. All the factors can be solved by equivalently adding a surface potential correction term at the site of the substation.
The results of the correction of the surface potential based on the measured values and the method of the present invention are shown in Table 2.
The corrected earth surface potential is substituted into the direct current magnetic bias simulation model, and the obtained error between the direct current of the neutral point of the transformer and the measured value is shown in table 3.
After the method is applied, the deviation between the simulation calculated value and the measured value is less than 5A, and the engineering application requirements are met.
Those not described in detail in this specification are well within the skill of the art. Conventional substitutions made in accordance with the prior art within the spirit of the invention are also within the scope of the spirit of the invention.
Claims (4)
1. A surface potential correction method based on transformer neutral point direct current measurement data is characterized by comprising the following steps:
step 1, constructing a direct current magnetic bias simulation model;
step 2, importing the direct current measurement data of the neutral point of the transformer, establishing a comparison relation between a simulation calculation result of the direct current magnetic bias simulation model and an actual measurement value, and forming an objective functionF：
WhereinI Aj Is as followsjThe direct current measured value of the neutral point of each transformer substation,
is as followsjThe direct current simulation calculation value of the neutral point of each transformer substation,qis the number of measured values;
step 3, correcting the potential column vector of the initial transformer stationΔV (0) ={0}Solving the second step according to the DC magnetic bias simulation model in the step 1jNeutral point DC simulation initial value of individual transformer substation
；
Step 4, making the number of iterationsk=1, objective function threshold
=0.01, secondjNeutral point DC simulation initial value of individual transformer substation
Substituting the objective functionFAfter k iterations, the objective function value of the k iteration is obtainedF k() ；
Step 5, if it iskTarget function absolute value of sub-iteration
Ending the iteration; otherwise, the next iteration is carried out, andk= k+1, and go to step 6;
step 6, constructing a Zoutendijk feasible direction optimization problem:
in the formula, min represents an optimization operator for obtaining a minimum value, s.t. represents a constraint condition,
is shown askA second iteration ofjThe direct current simulation calculation value of the neutral point of each transformer substation,I Aj k() denotes the firstkA second iteration ofjThe direct current measured value of the neutral point of each transformer substation,ΔVthe bit column vectors are corrected for the substation,I dc the earth current is injected to the direct current grounding electrode,Nbetween two substationsThe mutual resistance of (a) is greater than (b),Mthe mutual resistance between the direct current grounding electrode and the transformer substation;
step 7, selecting the feasible direction of the Zoutendijk feasible direction optimization problemd 1 k() And the direction of constraintd 2 k() Comprises the following steps:
wherein,Bfor the correlation matrix of the neutral point with the measurement data to all nodes,E m is composed ofmA matrix of the order of the unit,Zis an overground-underground network correction matrix of a direct current magnetic bias simulation model,ΔV k() correcting the potential column vector for the transformer substation of the kth iteration;
overground-underground network correction matrix of direct current magnetic bias simulation modelZThe specific expression of (A) is as follows:
in the formula,Hfor the incidence matrix between the substation node and all nodes,H T is composed ofHTransposing;Qa node conductance matrix of the AC power grid ground network;Gis a ground conductance matrix of the substation,G= R –1 ，Ris a matrix of the ground resistance of the substation,R= diag ( R 1 , R 2 , …, R i , …,R m )，R i is a firstiThe grounding resistance of each transformer substation is controlled by a controller,i=1，2，…，m；
calculating to obtain feasible directiond 1 k() And the direction of constraintd 2 k() Turning to step 8;
step 8, passing the feasible directiond 1 k() And direction of constraintd 2 k() Generating feasible search directions under constraintsd 3 k() ：
Wherein,
is a number smaller than 0 and is,Trepresenting a transpose; if it cannot generated 3 k() Go to step 6, if can generated 3 k() Turning to step 9;
step 9, determining the feasible direction by the steepest descent methodd 1 k() And the direction of constraintd 2 k() Searching for optimal direction of Zoutendijk feasible direction optimization problemd 4 k() ：
To find outd 4 k() Turning to step 10;
step 10, according to the optimal direction by a linear search methodd 4 k() Determining the optimal step size of the Zoutendijk feasible direction optimization problems k() ：
UpdatingΔV k(+1) =ΔV k() + d 4 k() s k() ，ΔV k+(1) For the (k + 1) th iterationThe potential column vector is corrected by the transformer substation, and the step 5 is carried out.
2. The method for correcting the earth surface potential based on the direct current measurement data of the neutral point of the transformer according to claim 1, wherein the process of constructing the direct current magnetic bias simulation model comprises the following steps:
step 1.1, sorting the relative positions of a power station and a direct current grounding electrode, and calculating mutual resistance between the earth potential and a transformer substation;
and step 1.2, solving according to a field direct coupling model to obtain a transformer substation neutral point direct current simulation calculated value.
3. The method of claim 2, wherein the mutual resistance between the two substations is a mutual resistanceNComprises the following steps:
wherein,α p is as followspThe amplitude of the individual earth potential characteristic components,β p is as followspThe attenuation modes of the individual earth potential characteristic components,rthe distance between the direct current grounding electrode and the transformer substation.
4. The method for correcting the earth's surface potential based on the DC measurement data of the neutral point of the transformer as claimed in claim 3, wherein the first stepjDC simulation calculated value of neutral point of each transformer substation
Calculated as follows:
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| JP2001037256A (en) * | 1999-07-21 | 2001-02-09 | Mitsubishi Electric Corp | Power converter |
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