Prediction of Gas Dissolved in Power Transformer Oil by Non-equidistant Multivariable Grey Model

Power transformer is an essential component in the power systems.The concentration of fault characteristic gases dissolved transformer oil is essential to the insulation fault diagnosis.The concentration prediction of the gases is an important supplement for periodical testing.A NMGM(1,5)model using Non-equidistance Multivariable grey theory for the five characteristic gases dissolved in transformer oil, i.e.hydrogen, methane,ethane,ethylene,acetylene,was constructed.In the built model, the interaction among these gases was comprehensively considered and the disadvantage that only one index extracted from the signal or each index that was dealt with separately was made up, meanwhile, the scope of application is enlarged. Two actual prediction cases were analyzed and the results were compared with those obtained by Non-equidistant GM(1,1)mode1.The comparison result indicates the validity and efficiency of the proposed mode1.


Introduction
As test data processing, some information is known and some is unknown, test data processing system is a grey system．Making use of grey system, we can forecast data to unknown information in future．Grey system theory is established in poor information (few sample), which build differential equation model with alone feature by data transform process to fully dig up apparent and latent information in relying on few data and discover knowing orderliness from un-orderliness data and reason the rule in future [1][2][3][4] ． Fault mechanism of transformer is complex, the relationship between the insulation latent faults and fault feature, some is known, some is unknown, has uncertainty．The insulation fault diagnosis of power transformer is grey system, in recent years, grey model has been predicted the concentration of the gas dissolved in power transformer oil . The Ref. [5] predicts the gas dissolved in power transformer oil by grey GM(1,1) model, the Ref. [6] predicts the gas dissolved in power transformer oil by improved grey GM(1,1) model, the Ref. [7] predicts the gas dissolved in power transformer oil by Multivariable Grey Model (MGM(1,n) )which is extended from GM(1,1)in n variables condition but is not simple combination and is also differ from GM(1,n) which only builds one differential equation with multi-variable one order． But the period of transformer fault detection is non-equidistant ,so the GM(1,1) and MGM(1,n) model is not work．The Ref. [8] introduced non-equidistant multi-variable grey model GM (1,M) which has high fitting precision and high forecasting precision． In this study, we predict concentration of gas dissolved in power transformer oil by non-equidistance multivariable grey model which based on the Ref. [8] ． This proposed model not only has high forecasting precision, but also provides the guidance basis to forecasting gas dissolved in power transformer oil, this model and method possesses the vast application foreground in the data processing of domain at other engineering.

Non-equidistance Multivariable Grey Model (NMGM (1, n))
This section describes the main structures and operations of the Non-equidistant Multivariable Grey Model (NMGM(1,n)). NMGM(1,n)model with n-variable 1-order differential equations is as follows: Then, the formula (2) can be expressed as: The prediction accuracy of grey model depends on distinguishing values A and B, while, A and B depend on the background value, the general background value is as follows: The actual background value is as follows: Using exponential function vector fit (1) () i xt the formula (6) can be expressed as follows: square method, the estimated value i a of parameter i a is as follows:
By the inverse accumulated generating operation, the fitting data or forecast of the original data is as follows: (1) () k i xt is fitting value and when km  The mean value of relative error of the I variable is The mean value of relative error of all data is the ref. [9] introduced the accuracy detecting method, the grades of mean relative error accuracy is as tab.1

3Concentration prediction of fault gases in power transformer oil by NMGM (1,5)
A NMGM(1 ， 5)model using Non-equidistance Multivariable grey theory for the five characteristic gases dissolved in transformer oil，i．e．hydrogen，methane， ethane ， ethylene ， acetylene ， was constructed. The interaction among these gases was comprehensively considered .

Case I
The DGA data is come from Ref. [6], as table. From the results, it is obvious that NMGM(1,5) model can better reflect the relation between hydrogen and methane ， ethane ， ethylene and acetylene. the proposed model has high fitting precision and high forecasting precision.

Case II
From August 17th 1984 to March 5th 1985, The 5 th transformer of Liu Jia-Xia had collected seven sets of DGA data．As Tab.3 ."Gas ratios" of DGA prediction on march 5th 1985 by non-equidistant multivariable grey model is C 2 H 2 ／C 2 H 4 =0.0746，CH 4 ／H 2 =1.0224，C 2 H 4 ／C 2 H 6 =1.875, nodes for "gas ratios" should be 022 , Thus can predict the transformer faults is hyperthermia and superheating fault which is confirmed by the operation department.From the results, it is obvious that NMGM(1,5) model has higher forecasting precision than Non-equidistant GM(1,1) model.

CONCLUSIONS
Dissolved gas analysis ( DGA ) is the essence to evaluate the state of transformer insulation and analyze transformer insulation faults. With non-equidistance multi-variable grey model the interaction among these gases was comprehensively considered and the disadvantage that only one index extracted from the signal or each index was dealt with separately was made up, meanwhile, the proposed model overcome the deficiency that the MGM(1,n) model don't fit the nonequidistant , The method can be used for model establishing on equal interval, as well as on non-interval. Moreover, non-equidistance multi-variable grey model's fitting precision and prediction is advanced and the scope of application is enlarged.