CN104865487A - Sub-area fault diagnosis method for transformer station grounding network - Google Patents

Abstract

A sub-area fault diagnosis method for a transformer station grounding network aims at a given grounding network design topology structure and performs layered reduction on the grounding network design topology structure. The sub-area fault diagnosis method comprises the steps of calculating nominal value parameters of branch resistors according to original designing data, selecting a common node, generating an associated matrix A and a branched admittance matrix Y; building a simulated circuit model, applying a DC source excitation I0 between nodes i and j which are selected in the circuit; testing the voltage Uij of a selected accessible node, and obtaining a port resistance Rij between the nodes i and j; after the grounding network fails and the measured port resistance between the nodes i and j is changed to R'ij, comparing the measured port resistance with the accessible port resistance in the normal state of the grounding network, and obtaining a port resistance difference vector deltaRij, and establishing a fault diagnosis equation set according to a fault simulation model; solving the fault diagnosis equation set and acquiring a final calculation result; and according to a solving result, calculating a nominal value multiple which corresponds with a branch resistance value after an intrinsic grounding network fails, and determining a fault condition.

Description

The subregion method for diagnosing faults of grounding net of transformer substation

Technical field

The present invention relates to technical field of electric power, particularly, relate to a kind of subregion method for diagnosing faults of grounding net of transformer substation.

Background technology

Grounding net of transformer substation with band steel or round steel horizontal laying, is arranged in elongated hole type or square groove usually, imbeds underground 0.6 ~ 0.8m, and its area is substantially identical with the area of transformer station with generating plant.The safe operation of grounded screen to electrical equipment is most important, in recent years, the substation operation accident caused because grounded screen electric property reduces increases year by year, the wherein corrosion of conductor, fracture or solder skip etc. are the latencies causing ground connection hydraulic performance decline, if meet electric system generation ground short circuit fault, the partial potential difference of earth mat own and earth mat potential anomalies will be caused to raise, except giving the safety of operations staff and bringing threat, also the insulation of secondary device may be destroyed because of counterattack or cable skin circulation, high pressure scurries into pulpit, make monitoring or opertaing device generation malfunction or tripping and expansion accident, bring huge economic loss and bad social influence.As can be seen here, the fault of grounded screen has been a mortal malady of safe operation of power system, and the diagnosis breakpoint of grounded screen and the corrosion condition of earth mat have become a great anti-accident measures of power department.The ground connection performance of grounded screen is generally judged indirectly by the size of measure field stake resistance, but cannot judge ground net corrosion situation accordingly, and when the corrosion of earth mat conductor is even ruptured, stake resistance still may be normal.Even if grounding resistance measurement display is abnormal, also cannot learn the particular location of fault, and need extensive excavation looking up the fault point, workload is huge and with high costs.Fault Diagnosis for Grounding Grids is for Timeliness coverage hidden danger and take corresponding measure to have directive significance, and owing to being subject to the restriction of accessible node number and distributing position thereof, difficulty of this work is very large.

At present, Chinese scholars has achieved some achievements in research in Fault Diagnosis for Grounding Grids field, be mainly reflected in two class methods: a class is the detection method based on electromagnetic field method or surface potential, the crack conditions of sub-surface conductors is judged by the physical signalling such as electromagnetic field parameters or potential parameters feedback signal of ground surface, its result lacks good criterion at present, the precision of heavy dependence equipment and be vulnerable to on-the-spot interference, and fracture whether diagnostic result can only be made and concrete corrosion condition cannot be known.A class is also had to be set up the method for Fault Diagnosis for Grounding Grids equation based on electric network theory, by setting up equivalent model to grounded screen, apply based on this model the relation equation that conservation of the similar power principle sets up port resistive value and branch resistance value, and adopt the alternative manner solving equation of least square to obtain the optimum solution of nonlinear equation.There is scholar to further study novel intelligent optimized algorithm and solving the application in diagnosis equation, achieve certain effect, but because the Degree of Ill Condition of diagnosis equation is high, the obtainable data of institute are relatively less, and the result reliability that said method draws is still on the low side.For improving diagnostic reliability, researchist proposes and carries out layering and yojan at accessible node place to network according to the structure of grounded screen, obtain only containing the intrinsic grounded screen of accessible node, and the method that employing is successively traced back further determines the resistance situation of clear-branch branch road at all levels, reduce the Degree of Ill Condition of diagnostic equation, but wherein uncertain-branch is still more, and algorithm structure is complicated, calculated amount is very large.

Ground lead due to its power transformation station equipment is limited, and the Fault Diagnosis for Grounding Grids equation that therefore which kind of method builds is all underdetermined equation, and the result drawn has uncertainty.With regard to engineering is actual, if the position, fault zone of grounded screen can be determined, maintenance excavated targetedly for guide field very meaningful, therefore, how according to this equivalent model, using a kind of new method to improve validity to Fault Diagnosis for Grounding Grids and accuracy, is the problem special procuring solution at present.

Summary of the invention

The present invention the object of the present invention is to provide a kind of subregion method for diagnosing faults of grounding net of transformer substation, the method is a kind of grounded screen subregion method for diagnosing faults based on topological hierarchy yojan, theme is to grounded screen topological structure subregion for the distribution situation of grounded screen accessible node, according to division result, layer reduction is carried out to grounded screen and obtain intrinsic grounded screen, this intrinsic grounded screen application and trouble diagnostic equation group model and optimized algorithm are calculated to the changing value of each branch resistance, according to the failure condition in the grounded screen region decision region that every bar branch road is corresponding, the method avoids underdetermined problem during solving equation group, significantly improve reliability and the accuracy of diagnostic result.

For achieving the above object, the invention provides a kind of subregion method for diagnosing faults of grounding net of transformer substation, the method, comprises the following steps:

Step 1: for given grounded screen original design topological structure, application circuit network theory carries out yojan to grounded screen topological structure, to prune unreachable node: a grounded screen is decomposed into grounded screen, accurate first column, first column, metanetwork, can and grounded screen and intrinsic grounded screen 6 levels;

Step 2: according to the geographic location area of the result division grounded screen that the first column stage topology of standard is decomposed, and number consecutively;

Step 3: each branch road region successively reviewed to the every bar branch road in intrinsic grounded screen or by which region yojan is obtained, and recording zone number corresponding to each branch road in the table;

Step 4: according to the original design data of grounded screen, calculates the nominal value parameter of the branch resistance of intrinsic grounded screen, selects common node, generates incidence matrix A and branch admittance matrix Y;

Step 5: according to intrinsic grounded screen topological structure, build simulation circuit model, application fully measures scheme, chooses node i in circuit, applies DC source excitation I between j ₀, the voltage U of the accessible node that test is selected _ij, obtain i, the port resistive R between j _ij;

Step 6: after grounded screen fault, node i, the port resistive measured value between j becomes R ' _ij, with under grounded screen normal condition can and port resistive contrast, obtain port resistive difference value vector Δ R _ij, according to Fault Diagnosis for Grounding Grids model, set up diagnosis equation group;

Step 7: application Least-squares minimization algorithm solves diagnosis equation group, obtains last result of calculation;

Step 8: according to the solving result in step 7, calculates the multiple of the relative nominal value of branch resistance value after intrinsic grounded screen fault, according to the failure condition in the region decision regional of each bar intrinsic branch trouble situation and its correspondence.

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, in step 1:

The first column of described standard is the minimum unit network obtained after one group of accessible node place tears grounded screen;

Described first column is obtained by the series and parallel branch road merging in the first column of standard, retains all accessible nodes simultaneously;

Described metanetwork changes into only containing the equivalent network of accessible node by each block in first column by conversion of circuits;

Described can and grounded screen be the branch road in whole metanetwork with same node point carry out connecting and composing only containing the network of accessible node;

Described intrinsic grounded screen be by can and grounded screen in whole parallel branches merge and obtain, have a branch road at the most between its any two accessible nodes, be called intrinsic branch road.

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, in step 4, definition A is the incidence matrix of network after a selected reference mode; Y _bfor branch admittance matrix; Y _nfor bus admittance matrix; There is between branch admittance matrix and bus admittance matrix following relation:

Y _n＝A*Y _b*A ^T(1)

In formula, A ^tfor the transposed matrix of incidence matrix A.

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, step 5 is specially:

If a normal grounded screen model N has b+1 bar branch road, n+1 node, to all nodes of this grounded screen equivalent resistance network and branch road by following rule numbers: node serial number: be as the criterion with final topology figure, from top to down, right to a left side, be numbered, a rear point is not numbered, be set to reference point, also do not allow during measurement to use; Branch number: be as the criterion with final topology figure, from top to down, right to a left side, be numbered, first to transverse legs numbering, then to longitudinal branch number.B+1 article of branch road is connected to the i of ground lead, and j holds, and add DC current source forcing at the i-th, j port, its current value is I ₀, ask R according to circuit theory _ij, definition I _bfor branch current square; U _nfor node voltage column vector; I _nfor the current source column vector of node, the current value of non-actuated node is 0;

Kirchhoff's current law (KCL) and the Kirchhoff's second law the Representation Equation of resistor network are:

AI _b＝0 (2)

U _b＝A ^TU _n(3)

U in formula _brepresent the voltage of node b.

Can obtain in conjunction with formula (1), (2), (3)

Y _nU _n＝I _n(4)

Port resistive R _ijcalculating formula is:

R _ij＝U _b+1/I ₀(5)

U in formula _b+1represent the voltage of node b+1.

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, step 6 is specially:

Illustraton of model after grounded screen generation corrosion failure is considered as network N ', still its i, j end add current source, current value is I ₀, obtain R _ij'; Network N and network N ' topological structure is identical; To circuit N and N' with identical topological structure, and the branch road of correspondence and node get identical numbering, and the reference direction of each bar branch road is identical, then have with theorem according to Teller:

$\underset{k=1}{\overset{b+1}{\mathrm{\Σ}}}{U_k}^{\′}{I}_k=0---\left(6\right)$

$\underset{k=1}{\overset{b+1}{\mathrm{\Σ}}}{U}_k{I_k}^{\′}=0---\left(7\right)$

In formula, I _k', U _k' be respectively branch current and the branch voltage of electric network N', I _k, U _kbe respectively branch current and the branch voltage of electric network N; When corrosion or fracture defect occur branch road k, its branch resistance is by R _kbecome R _k', that is:

ΔR _k＝R _k'-R _k(8)

Now the resistance at i, j two ends is by R _ijbecome R _ij' namely:

ΔR _ij＝R _ij'-R _ij(9)

Because the electric current of the b+1 article of branch road at i, j end of two networks is all I ₀, that is:

I _b+1＝I' _b+1＝I ₀(10)

U _b+1＝-R _ijI ₀(11)

U' _b+1＝-R' _ijI ₀(12)

Formula (10), (11), (12) are substituted into formula (6), in (7):

$R_{\mathrm{ij}}{I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}{U}_k{I^{\′}}_k---\left(13\right)$

${R^{\′}}_{\mathrm{ij}}{I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}{U^{\′}}_k{I}_k---\left(14\right)$

Formula formula (13) deducts formula (14) and obtains:

$\begin{array}{c}(R_{\mathrm{ij}}-{R^{\′}}_{\mathrm{ij}}){I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}{U}_k{I^{\′}}_k-\underset{k=1}{\overset{b}{\mathrm{\Σ}}}{U^{\′}}_k{I}_k\\ =\underset{k=1}{\overset{b}{\mathrm{\Σ}}}(R_k{I}_k{I^{\′}}_k-{R^{\′}}_k{I^{\′}}_k{I}_k)=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}(R_k-{R^{\′}}_k){I^{\′}}_k{I}_k\end{array}---\left(15\right)$

Formula (8), (9) are substituted into formula (15) and obtain:

$\mathrm{\Δ}{R}_{\mathrm{ij}}=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}\mathrm{\Δ}{R}_k{I^{\′}}_k{I}_k/{I_0}^2---\left(16\right)$

Formula (16) represents the relation of branch resistance changing value and the change of port resistive value, because the variable of branch resistance in this network has b, therefore need to measure a series of port resistive, suppose that the different port number measured is m, thus draw system of equations:

$\left\{\begin{array}{c}\mathrm{\Δ}{R}_{\mathrm{ij}\left(1\right)}=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}\mathrm{\Δ}{R}_k{I^{\′}}_{k\left(1\right)}{I}_{k\left(1\right)}/{I_0}^2\\ \mathrm{\Δ}{R}_{\mathrm{ij}\left(2\right)}=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}\mathrm{\Δ}{R}_k{I^{\′}}_{k\left(2\right)}{I}_{k\left(2\right)}/{I_0}^2\\ \·\·\·\·\·\·\\ \mathrm{\Δ}{R}_{\mathrm{ij}\left(m\right)}=\underset{k=1}{\overset{b}{\mathrm{\Σ}}}\mathrm{\Δ}{R}_k{I^{\′}}_{k\left(m\right)}{I}_{k\left(m\right)}/{I_0}^2\end{array}\right\}---\left(17\right).$

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, step 7 comprises the following steps:

Step 71: the topological structure and the branch resistance R that obtain grounded screen from design drawing _k; I is calculated according to circuit theory _{k (s)}, choose measured node group and obtain resistance R between theoretical node _{ij (s)}(s=1 ~ m);

Step 72: measurement port resistance R ' _{ij (s)}, calculate port resistive changing value Δ R _{ij (s)}=R ' _{ij (s)}-R _{ij (s)};

Step 73: make I ' _{k (s)}(0)=I _{k (s)}, I ' _{k (s)}(0) current value of each bar branch road when being first iteration;

Step 74: calculate Δ R in conjunction with least square optimization by system of equations (17) _k ^(t)(s), t=0,1 ..., t is iterations, Δ R _k ^(t)the difference of branch resistance when () is the t time iteration s; Because original leg resistance is R _k, add the difference DELTA R of branch resistance during the t time iteration _k ^(t)s (), obtains the t time branch resistance value $R_k^{\′\left(t\right)}\left(s\right)=R_k+\mathrm{\Δ}{R_k}^{\left(t\right)}\left(s\right);$

Step 75: if t>=1 and | Δ R _k ^(t)-Δ R _k ^(t-1)| < ε, so stops iterative computation, obtains for end product, ε is the constant of setting; Otherwise perform step 76;

Step 76: use calculate the current value of each article of branch road when being the t+1 time iteration; Repeat step 74 and step 75.

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, described least square optimization formula is:

$\min f(\mathrm{\&Delta;}{R}_1^{\left(t\right)},\mathrm{\&Delta;}{R}_2^{\left(t\right)},...,\mathrm{\&Delta;}{R}_b^{\left(t\right)})=\underset{s=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{\&Delta;R}}_{\mathrm{ij}\left(s\right)}^{\left(t\right)}-\mathrm{\&Delta;}{R}_{\mathrm{ij}\left(s\right)})}^2---\left(18\right)$

$s.t.0\&le;\mathrm{\&Delta;}{R}_k^{\left(t\right)}\&le;\mathrm{\&Delta;}{R}_k^{(t-1)}+R_t(k=\mathrm{1,2},...,b)$

In formula, the resistance calculations difference of b article of branch road when being the t time iteration, be the t time and t-1 iteration time port resistive difference.

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, the value lower limit of the parameter in least square optimization is the nominal value of branch resistance, the upper limit is 50 times of nominal value, the constraint condition in the corresponding formula (18) of this higher limit, lower limit.

According to the subregion method for diagnosing faults of the grounding net of transformer substation described in present pre-ferred embodiments, in step 8, it is as follows that resistance value increases multiple situation corresponding to fault degree:

If it is μ that resistance value increases multiple, if μ is 1 ~ 2, normal; If μ is 2 ~ 4, there is minor failure; If μ is 4 ~ 10, there is moderate fault; If μ is 10 ~ 20, there is heavier fault; If μ is 20 ~ 40, there is catastrophic failure; If μ is more than 40, there is fracture.

Compared with prior art, the present invention, owing to taking above technical scheme, has the following advantages:

1, establish the mathematical model of grounded screen subregion fault diagnosis in the present invention, the Fault Diagnosis for Grounding Grids problem of complexity is converted into solving mathematical model, quantizes grounded screen fault degree, diagnostic result is easy to understand.

2. underdetermined problem when, the present invention avoids solving equation group, by topological structure layer reduction, grounded screen is changed into only containing the intrinsic network of accessible node, apply abundant testing scheme, reduce diagnostic equation group less qualitative, significantly improve reliability and the accuracy of diagnostic result.

3., the present invention to grounded screen zoning, diagnostic result is for the failure condition in region, and reliable results is accurate, can be used as reference when grounded screen excavation checks, more effective and practical for instructing substation field to safeguard, is easy to apply in Practical Project.

Accompanying drawing explanation

Fig. 1 is the subregion method for diagnosing faults method flow diagram of grounding net of transformer substation of the present invention;

Fig. 2 is grounded screen equivalent model figure of the present invention;

Fig. 3 is grounded screen topological diagram of the present invention;

Fig. 4 is the first column figure of standard of the present invention;

Fig. 5 is first column figure of the present invention;

Fig. 6 is metanetwork figure of the present invention;

Fig. 7 be of the present invention can and grounded screen figure;

Fig. 8 is intrinsic grounded screen figure of the present invention;

Fig. 9 is grounded screen subregion figure of the present invention;

Figure 10 is that Matlab exports branch resistance relative nominal value multiple histogram.

Embodiment

Below with reference to accompanying drawing of the present invention; clear, complete description and discussion are carried out to the technical scheme in the embodiment of the present invention; obviously; as described herein is only a part of example of the present invention; it is not whole examples; based on the embodiment in the present invention, the every other embodiment that those of ordinary skill in the art obtain under the prerequisite not making creative work, all belongs to protection scope of the present invention.

For the ease of the understanding to the embodiment of the present invention, be further explained for specific embodiment below in conjunction with accompanying drawing, and embodiment does not form the restriction to the embodiment of the present invention.

First principles analysis:

The grounded screen water mean pressure conductor being embedded in underground is connected with each other forming circuit network, and ignore the impact of edphic factor, grounded screen can regard pure resistance network as.After net is completed, because the length of each section of conductor, sectional area and conductivity are determined, their resistance value can be calculated, i.e. nominal value; During rear certain section of conductor generation fracture or the appearance corrosion for many years of local network operation (its topological structure does not become), now its branch resistance becomes large compared with nominal value.Meanwhile, Substation Electric Equipment has the ground lead be connected with earth mat, if grounded screen is regarded as " black box " of a resistive network, and ground lead just can regard as it can and port, as shown in Figure 2., because of topological structure, branch resistance is known for wherein original network port resistance (resistance namely between ground lead, lower same), can calculate according to electric network theory; And the port resistive value of the rear grounded screen of corrosion, because Substation Electric Equipment has the ground lead be connected with grounded screen, the port resistive value of the rear grounded screen of corrosion can be measured by ground lead.So just can obtain port resistive changing value, utilize Tellegen can obtain the relation of port resistive changing value and branch resistance changing value, apply suitable mathematical method again, the increased resistance value of grounded screen branch road can be released from node-resistance changing value, thus judge Grounding Grid and breakpoint situation.

A subregion method for diagnosing faults for grounding net of transformer substation, comprises the following steps:

Step 1: for given grounded screen original design topological structure, application circuit network theory carries out yojan to grounded screen topological structure, to prune unreachable node, a grounded screen is decomposed into grounded screen, accurate first column, first column, metanetwork, can and grounded screen and intrinsic grounded screen 6 levels;

The first column of described standard is the minimum unit network obtained after one group of accessible node place tears grounded screen;

Described first column is obtained by the series and parallel branch road merging in the first column of standard, retains all accessible nodes simultaneously;

Described metanetwork changes into only containing the equivalent network of accessible node by each block in first column by conversion of circuits;

Described can and grounded screen be the branch road in whole metanetwork with same node point carry out connecting and composing only containing the network of accessible node;

Described intrinsic grounded screen be by can and grounded screen in whole parallel branches merge and obtain, have a branch road at the most between its any two accessible nodes, be called intrinsic branch road.

Step 2: according to the geographic location area of the result division grounded screen that the first column stage topology of standard is decomposed, and number consecutively;

Step 3: each branch road region successively reviewed to the every bar branch road in intrinsic grounded screen or by which region yojan is obtained, and recording zone number corresponding to each branch road in the table;

Step 4: according to the original design data of grounded screen, calculates the nominal value parameter of the branch resistance of intrinsic grounded screen, selects common node, generates incidence matrix A and branch admittance matrix Y.

Definition A is the incidence matrix of network after a selected reference mode; Y _bfor branch admittance matrix; Y _nfor bus admittance matrix; There is between branch admittance matrix and bus admittance matrix following relation:

Y _n＝A*Y _b*A ^T(1)

In formula, A ^tfor the transposed matrix of incidence matrix A.

Step 5: according to intrinsic grounded screen topological structure, build simulation circuit model in Multisim simulation software, application fully measures scheme, chooses node i in circuit, applies DC source excitation I between j ₀, the voltage U of the accessible node that test is selected _ij, obtain i, the port resistive R between j _ij.

If a normal grounded screen model N has b+1 bar branch road, n+1 node, to all nodes of this grounded screen equivalent resistance network and branch road by the rule numbers node serial number preset: be as the criterion with final topology figure, from top to down, right to a left side, be numbered, a rear point is not numbered, be set to reference point, also do not allow during measurement to use; Branch number: be as the criterion with final topology figure, from top to down, right to a left side, be numbered, first to transverse legs numbering, then to longitudinal branch number.B+1 article of branch road is connected to the i of ground lead, and j holds, and add DC current source forcing at the i-th, j port, its current value is I ₀, ask R according to circuit theory _ij, definition I _bfor branch current square; U _nfor node voltage column vector; I _nfor the current source column vector of node, the current value of non-actuated node is 0;

KCL (Kirchhoff's current law (KCL)) and KVL (Kirchhoff's second law) journey of resistor network are expressed as:

AI _b＝0 (2)

U _b＝A'U _n(3)

U in formula _brepresent the voltage of node b.

Can obtain in conjunction with formula (1), (2), (3)

Y _nU _n＝I _n(4)

Port resistive R _ijcalculating formula is:

R _ij＝U _b+1/I ₀(5)。

U in formula _b+1represent the voltage of node b+1.

Step 6: after grounded screen fault, node i, the port resistive measured value between j becomes R ' _ij, with under grounded screen normal condition can and port resistive contrast, obtain port resistive difference value vector Δ R _ij, according to Fault Diagnosis for Grounding Grids model, set up diagnosis equation group.

Illustraton of model after grounded screen generation corrosion failure is considered as network N ', still its i, j end add current source, current value is I ₀, obtain R _ij'; Network N and network N ' topological structure is identical; To circuit N and N' with identical topological structure, and the branch road of correspondence and node get identical numbering, and the reference direction of each bar branch road is identical, then have with theorem according to Teller:

$\underset{k=1}{\overset{b+1}{\mathrm{\&Sigma;}}}{U_k}^{\&prime;}{I}_k=0---\left(6\right)$

$\underset{k=1}{\overset{b+1}{\mathrm{\&Sigma;}}}{U}_k{I_k}^{\&prime;}=0---\left(7\right)$

In formula, I _k', U _k' be respectively branch current and the branch voltage of electric network N', I _k, U _kbe respectively branch current and the branch voltage of electric network N; When corrosion or fracture defect occur branch road k, its branch resistance is by R _kbecome R _k', that is:

ΔR _k＝R _k'-R _k(8)

Now the resistance at i, j two ends is by R _ijbecome R _ij' namely:

ΔR _ij＝R _ij'-R _ij(9)

Because the electric current of the b+1 article of branch road at i, j end of two networks is all I ₀, that is:

I _b+1＝I' _b+1＝I ₀(10)

U _b+1＝-R _ijI ₀(11)

U' _b+1＝-R' _ijI ₀(12)

Formula (10), (11), (12) are substituted into formula (6), in (7):

$R_{\mathrm{ij}}{I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U}_k{I^{\&prime;}}_k---\left(13\right)$

${R^{\&prime;}}_{\mathrm{ij}}{I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U^{\&prime;}}_k{I}_k---\left(14\right)$

Formula formula (13) deducts formula (14) and obtains:

$\begin{array}{c}(R_{\mathrm{ij}}-{R^{\&prime;}}_{\mathrm{ij}}){I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U}_k{I^{\&prime;}}_k-\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U^{\&prime;}}_k{I}_k\\ =\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}(R_k{I}_k{I^{\&prime;}}_k-{R^{\&prime;}}_k{I^{\&prime;}}_k{I}_k)=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}(R_k-{R^{\&prime;}}_k){I^{\&prime;}}_k{I}_k\end{array}---\left(15\right)$

Formula (8), (9) are substituted into formula (15) and obtain:

$\mathrm{\&Delta;}{R}_{\mathrm{ij}}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{R}_k{I^{\&prime;}}_k{I}_k/{I_0}^2---\left(16\right)$

Formula (16) represents the relation of branch resistance changing value and the change of port resistive value, because the variable of branch resistance in this network has b, therefore need to measure a series of port resistive, suppose that the different port number measured is m, thus draw system of equations:

$\left\{\begin{array}{c}\mathrm{\&Delta;}{R}_{\mathrm{ij}\left(1\right)}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{R}_k{I^{\&prime;}}_{k\left(1\right)}{I}_{k\left(1\right)}/{I_0}^2\\ \mathrm{\&Delta;}{R}_{\mathrm{ij}\left(2\right)}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{R}_k{I^{\&prime;}}_{k\left(2\right)}{I}_{k\left(2\right)}/{I_0}^2\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\\ \mathrm{\&Delta;}{R}_{\mathrm{ij}\left(m\right)}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{R}_k{I^{\&prime;}}_{k\left(m\right)}{I}_{k\left(m\right)}/{I_0}^2\end{array}\right\}---\left(17\right).$

Step 7: apply Least-squares minimization algorithm in MATLAB software diagnosis equation group is solved, obtain last result of calculation.

Formula (17) belongs to Nonlinear System of Equations, cannot direct solution, can introduce alternative manner.First, I ' is made _k(0)=I _k, system of equations becomes system of linear equations, but m<b system of equations owes fixed, need use Optimization Method, herein be nonnegative least.So just obtain Δ R _kand R ' (0) _k(0), then R ' is used _k(0) I ' is calculated _k(1); Then I ' is used _k(1) R ' is calculated _k(1).Repeat calculating above, until the resistance delta obtained meets the demands, obtain last result of calculation.Specifically comprise the following steps:

Step 71: the topological structure and the branch resistance R that obtain grounded screen from design drawing _k; I is calculated according to circuit theory _{k (s)}, choose measured node group and obtain resistance R between theoretical node _{ij (s)}(s=1 ~ m);

Step 72: measurement port resistance calculate port resistive changing value

Step 73: make I ' _{k (s)}(0)=I _{k (s)}, I ' _{k (s)}(0) current value of each bar branch road when being first iteration;

Step 74: calculate Δ R in conjunction with least square optimization by system of equations (17) _k ^(t)(s) (t=0,1 ..., t is iterations), Δ R _k ^(t)the difference of branch resistance when () is the t time iteration s; Because original leg resistance is R _k, add the difference DELTA R of branch resistance during the t time iteration _k ^(t)s (), obtains the t time branch resistance value $R_k^{\&prime;\left(t\right)}\left(s\right)=R_k+\mathrm{\&Delta;}{R_k}^{\left(t\right)}\left(s\right);$

Step 75: if t>=1 and | Δ R _k ^(t)-Δ R _k ^(t-1)| < ε, so stops iterative computation, obtains for end product, ε is the constant of setting; Otherwise perform step 76;

Step 76: use calculate the current value of each article of branch road when being the t+1 time iteration; Repeat step 74 and step 75.

Because the number of unknown quantity is b in system of equations (17), obtain the exact value of these variablees, the number of equation number should be b, but the quantity of general substation grounding lead-in wire is less than the branch road quantity of grounded screen, and solution of equations is not unique.Consider engineering problem, in these solutions, often only have scope very small percentage to be rational, introduce constrained linear programming problem to obtain optimum solution.In order to obtain good exact value, need to use optimization technique, particularly, least square optimization formula is:

$\min f(\mathrm{\&Delta;}{R}_1^{\left(t\right)},\mathrm{\&Delta;}{R}_2^{\left(t\right)},...,\mathrm{\&Delta;}{R}_b^{\left(t\right)})=\underset{s=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{\&Delta;R}}_{\mathrm{ij}\left(s\right)}^{\left(t\right)}-\mathrm{\&Delta;}{R}_{\mathrm{ij}\left(s\right)})}^2---\left(18\right)$

$s.t.0\&le;\mathrm{\&Delta;}{R}_k^{\left(t\right)}\&le;\mathrm{\&Delta;}{R}_k^{(t-1)}+R_t(k=\mathrm{1,2},...,b)$

In formula, the resistance calculations difference of b article of branch road when being the t time iteration, be the t time and t-1 iteration time port resistive difference.This formula as adaptive value function, makes the difference of port resistive change and reaches minimum in the process of solution formula (17).

With the restriction of constraint condition to domain, solution can be made relatively more reasonable, be also conducive to the effect of planning problem in actual computation simultaneously.Lower variable be constrained to non-negative, ensure to solve and be of practical significance in engineering; Step-length restriction is done to upper variable, can ensure that the solution of trying to achieve is the optimum solution near every single-step iteration initial value, meet the actual conditions of iterative process.Particularly, the nominal value that the value lower limit (namely descending variable) of the parameter in least square optimization is branch resistance, 50 times that the upper limit (namely going up variable) is nominal value.

Step 8: according to the solving result in step 7, calculates the multiple of the relative nominal value of branch resistance value after intrinsic grounded screen fault, according to the failure condition in the region decision regional that each bar branch road is corresponding.

Particularly, resistance value increase multiple situation corresponding to fault degree is as shown in table 1.

Table 1 resistance value increases multiple situation corresponding to fault degree

Be described in further details below in conjunction with the subregion method for diagnosing faults of specific embodiment to grounding net of transformer substation of the present invention.

Embodiment one

Figure 3 shows that certain grounding net of transformer substation network topological diagram, have 16 nodes, wherein 2,4,5,7,8,10,11,14,16 is accessible node, and the concrete decomposition of this grounded screen can referring to this paper Fig. 4 ~ 8.Under normal condition, every bar branch road normal resistance is 60m Ω, and existing three branch roads break down, and be followed successively by: 1-2 branch road becomes 300m Ω, 7-8 branch road becomes 600m Ω, and 11-15 branch road becomes 900m Ω.

Fig. 4 ~ 8 be respectively this Grounding net topology structural stratification yojan obtain standard unit column, first column, metanetwork, can and grounded screen and intrinsic grounded screen, Fig. 9 is grounded screen zoning figure.Be then the process of intrinsic grounded screen according to the first column yojan of standard, successively trace back to grounded screen bar branch road every in intrinsic grounded screen, in Fig. 8, every bar props up shown in the corresponding information slip 1 that route grounded screen area transformation obtains.

Table 1 intrinsic branch road situation corresponding to grounded screen region

In Multisim, build grounded screen model, apply the continuous-current excitation of 10A, according to desirable optimum abundant testing scheme, select measurement port, the port resistive situation of change recording intrinsic grounded screen before and after fault is as shown in table 2.

Table 2 intrinsic grounded screen port resistive situation of change

Application the method for the invention, sets up diagnosis equation group, applies least-squares iteration algorithm and solve, obtain diagnostic result as shown in Figure 10 in Matlab calculation procedure.

As can be seen from diagnostic result, there is obvious fault in branch road 2-5,7-8,11-14,11-16, wherein branch road 2-5 resistance is increased to original 2.5 times, branch road 7-8 resistance is increased to original 9.4 times, branch road 11-14 resistance is increased to original 10.6 times, branch road 11-16 resistance is increased to original 1.9 times, according to the region of the corresponding grounded screen of branch road, can judge 1., 4., 5., 9., region memory is at fault branch.Because other branch roads of the intrinsic grounded screen 4., 9. corresponding to region do not have fault, thus 4., 9. region Shi Wei fault zone.Therefore, the region that there is fault in grounded screen be 1., 5., and 1. region is minor failure, 5., for comparatively catastrophic failure.This diagnostic result is consistent with the situation of actual set, illustrates that method for diagnosing faults herein correctly can diagnose out the failure condition in small-sized grounded screen regional.

Be only several specific embodiment of the present invention above, but the present invention is not limited thereto, the changes that any person skilled in the art can think of, all should drops in protection scope of the present invention.

Claims (9)

1. a subregion method for diagnosing faults for grounding net of transformer substation, is characterized in that, comprise the following steps:

Step 1: for given grounded screen original design topological structure, application circuit network theory carries out yojan to grounded screen topological structure, to prune unreachable node, a grounded screen is decomposed into grounded screen, accurate first column, first column, metanetwork, can and grounded screen and intrinsic grounded screen 6 levels;

Step 2: according to the geographic location area of the result division grounded screen that the first column stage topology of standard is decomposed, and number consecutively;

Step 3: each branch road region successively reviewed to the every bar branch road in intrinsic grounded screen or by which region yojan is obtained, and recording zone number corresponding to each branch road in the table;

Step 4: according to the original design data of grounded screen, calculates the nominal value parameter of the branch resistance of intrinsic grounded screen, selects common node, generates incidence matrix A and branch admittance matrix Y;

Step 5: according to intrinsic grounded screen topological structure, build simulation circuit model, application fully measures scheme, chooses node i in circuit, applies DC source excitation I between j ₀, the voltage U of the accessible node that test is selected _ij, obtain i, the port resistive R between j _ij;

Step 6: after grounded screen fault, node i, the port resistive measured value between j becomes R ' _ij, with under grounded screen normal condition can and port resistive contrast, obtain port resistive difference value vector Δ R _ij, according to Fault Diagnosis for Grounding Grids model, set up diagnosis equation group;

Step 7: application Least-squares minimization algorithm solves diagnosis equation group, obtains last result of calculation;

Step 8: according to the solving result in step 7, calculates the multiple of the relative nominal value of branch resistance value after intrinsic grounded screen fault, according to the failure condition in the region decision regional of each bar intrinsic branch trouble situation and its correspondence.

2. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 1, is characterized in that, in step 1:

The first column of described standard is the minimum unit network obtained after one group of accessible node place tears grounded screen;

Described first column is obtained by the series and parallel branch road merging in the first column of standard, retains all accessible nodes simultaneously;

Described metanetwork changes into only containing the equivalent network of accessible node by each block in first column by conversion of circuits;

Described can and grounded screen be the branch road in whole metanetwork with same node point carry out connecting and composing only containing the network of accessible node;

Described intrinsic grounded screen be by can and grounded screen in whole parallel branches merge and obtain, have a branch road at the most between its any two accessible nodes, be called intrinsic branch road.

3. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 1, is characterized in that, in step 4, definition A is the incidence matrix of network after a selected reference mode; Y _bfor branch admittance matrix; Y _nfor bus admittance matrix; There is between branch admittance matrix and bus admittance matrix following relation:

Y _n＝A*Y _b*A ^T(1)

In formula, A ^tfor the transposed matrix of incidence matrix A.

4. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 3, it is characterized in that, step 5 is specially:

If a normal grounded screen model N has b+1 bar branch road, n+1 node, to all nodes of this grounded screen equivalent resistance network and branch road by following rule numbers: node serial number: be as the criterion with final topology figure, from top to down, right to a left side, be numbered, a rear point is not numbered, be set to reference point, also do not allow during measurement to use; Branch number: be as the criterion with final topology figure, from top to down, right to a left side, be numbered, first to transverse legs numbering, then to longitudinal branch number.B+1 article of branch road is connected to the i of ground lead, and j holds, and add DC current source forcing at the i-th, j port, its current value is I ₀, ask R according to circuit theory _ij, definition I _bfor branch current square; U _nfor node voltage column vector; I _nfor the current source column vector of node, the current value of non-actuated node is 0;

Kirchhoff's current law (KCL) and the Kirchhoff's second law the Representation Equation of resistor network are:

AI _b＝0 (2)

U _b＝A ^TU _n(3)

U in formula _brepresent the voltage of node b;

Can obtain in conjunction with formula (1), (2), (3)

Y _nU _n＝I _n(4)

Port resistive R _ijcalculating formula is:

R _ij＝U _b+1/I ₀(5)

U in formula _b+1represent the voltage of node b+1.

5. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 4, it is characterized in that, step 6 is specially:

Illustraton of model after grounded screen generation corrosion failure is considered as network N ', still its i, j end add current source, current value is I ₀, obtain R _ij'; Network N and network N ' topological structure is identical; To circuit N and N' with identical topological structure, and the branch road of correspondence and node get identical numbering, and the reference direction of each bar branch road is identical, then have with theorem according to Teller:

$\underset{k=1}{\overset{b+1}{\mathrm{\&Sigma;}}}{U_k}^{\&prime;}{I}_k=0---\left(6\right)$

$\underset{k=1}{\overset{b+1}{\mathrm{\&Sigma;}}}{U}_k{I_k}^{\&prime;}=0---\left(7\right)$ In formula, I _k', U _k' be respectively branch current and the branch voltage of electric network N', I _k, U _kbe respectively branch current and the branch voltage of electric network N; When corrosion or fracture defect occur branch road k, its branch resistance is by R _kbecome R _k', that is:

ΔR _k＝R _k'-R _k(8)

Now the resistance at i, j two ends is by R _ijbecome R _ij' namely:

ΔR _ij＝R _ij'-R _ij(9)

Because the electric current of the b+1 article of branch road at i, j end of two networks is all I ₀, that is:

I _b+1＝I' _b+1＝I ₀(10)

U _b+1＝-R _ijI ₀(11)

U' _b+1＝-R' _ijI ₀(12)

Formula (10), (11), (12) are substituted into formula (6), in (7):

$R_{\mathrm{ij}}{I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U}_k{I^{\&prime;}}_k---\left(13\right)$

${R^{\&prime;}}_{\mathrm{ij}}{I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U^{\&prime;}}_k{I}_k---\left(14\right)$

Formula formula (13) deducts formula (14) and obtains:

$\begin{array}{c}(R_{\mathrm{ij}}-{R^{\&prime;}}_{\mathrm{ij}}){I_0}^2=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U}_k{I^{\&prime;}}_k-\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{U^{\&prime;}}_k{I}_k\\ =\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}(R_k{I}_k{I^{\&prime;}}_k-{R^{\&prime;}}_k{I^{\&prime;}}_k{I}_k)=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}(R_k-{R^{\&prime;}}_k){I^{\&prime;}}_k{I}_k\end{array}---\left(15\right)$

Formula (8), (9) are substituted into formula (15) and obtain:

${\mathrm{\&Delta;R}}_{\mathrm{ij}}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;R}}_k{I^{\&prime;}}_k{I}_k/{I_0}^2---\left(16\right)$

Formula (16) represents the relation of branch resistance changing value and the change of port resistive value, because the variable of branch resistance in this network has b, therefore need to measure a series of port resistive, suppose that the different port number measured is m, thus draw system of equations:

$\left\{\begin{array}{c}{\mathrm{\&Delta;R}}_{\mathrm{ij}\left(1\right)}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;R}}_k{I^{\&prime;}}_{k\left(1\right)}{I}_{k\left(1\right)}/{I_0}^2\\ {\mathrm{\&Delta;R}}_{\mathrm{ij}\left(2\right)}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;R}}_k{I^{\&prime;}}_{k\left(2\right)}{I}_{k\left(2\right)}/{I_0}^2\\ ......\\ {\mathrm{\&Delta;R}}_{\mathrm{ij}\left(m\right)}=\underset{k=1}{\overset{b}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;R}}_k{I^{\&prime;}}_{k\left(m\right)}{I}_{k\left(m\right)}/{I_0}^2\end{array}\right\}---\left(17\right).$

6. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 5, it is characterized in that, step 7 comprises the following steps:

Step 71: the topological structure and the branch resistance R that obtain grounded screen from design drawing _k; I is calculated according to circuit theory _{k (s)}, choose measured node group and obtain resistance R between theoretical node _{ij (s)}(s=1 ~ m);

Step 72: measurement port resistance R ' _{ij (s)}, calculate port resistive changing value Δ R _{ij (s)}=R ' _{ij (s)}-R _{ij (s)};

Step 73: make I ' _{k (s)}(0)=I _{k (s)}, I ' _{k (s)}(0) current value of each bar branch road when being first iteration;

Step 74: calculate Δ R in conjunction with least square optimization by system of equations (17) _k ^(t)(s), t=0,1 ..., t is iterations, Δ R _k ^(t)the difference of branch resistance when () is the t time iteration s; Because original leg resistance is R _k, add the difference DELTA R of branch resistance during the t time iteration _k ^(t)s (), obtains the t time branch resistance value $R_k^{\&prime;\left(t\right)}\left(s\right)=R_k+{{\mathrm{\&Delta;R}}_k}^{\left(t\right)}\left(s\right);$

Step 75: if t>=1 and | Δ R _k ^(t)-Δ R _k ^(t-1)| < ε, so stops iterative computation, obtains for end product, ε is the constant of setting; Otherwise perform step 76;

Step 76: use calculate the current value of each article of branch road when being the t+1 time iteration; Repeat step 74 and step 75.

7. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 6, is characterized in that, described least square optimization formula is:

$\begin{array}{cc}\min & f({\mathrm{\&Delta;R}}_1^{\left(t\right)},{\mathrm{\&Delta;R}}_2^{\left(t\right)},...,{\mathrm{\&Delta;R}}_b^{\left(t\right)})=\underset{s=1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{\&Delta;R}}_{\mathrm{ij}\left(s\right)}^{\left(t\right)}-{\mathrm{\&Delta;R}}_{\mathrm{ij}\left(s\right)})}^2---\left(18\right)\end{array}$

$s.t.0\&le;{\mathrm{\&Delta;R}}_k^{\left(t\right)}\&le;{\mathrm{\&Delta;R}}_k^{(t-1)}+R_k,(k=\mathrm{1,2},...,b)$

In formula, the resistance calculations difference of b article of branch road when being the t time iteration, be the t time and t-1 iteration time port resistive difference.

8. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 7, it is characterized in that, the value lower limit of the parameter in least square optimization is the nominal value of branch resistance, the upper limit is 50 times of nominal value, the constraint condition in the corresponding formula (18) of this higher limit, lower limit.

9. the subregion method for diagnosing faults of grounding net of transformer substation according to claim 1, is characterized in that, in step 8, it is as follows that resistance value increases multiple situation corresponding to fault degree:

If it is μ that resistance value increases multiple, if μ is 1 ~ 2, normal; If μ is 2 ~ 4, there is minor failure; If μ is 4 ~ 10, there is moderate fault; If μ is 10 ~ 20, there is heavier fault; If μ is 20 ~ 40, there is catastrophic failure; If μ is more than 40, there is fracture.