Transformer parameter estimation in distribution network based on deformable transformer

With the large number of distributed power sources and the dynamic change of load, the abnormal parameters of distribution transformers become more and more complicated. So it is particularly important to estimate their parameters accurately. For a low voltage distribution network with a limited number of measuring equipment, a Transformer parameter estimation method based on a Deformable Transformer is proposed in this paper. Firstly, a Transformer parameter estimation model based on a Deformable Transformer network is established by using historical measurement data. Then, a quality evaluation method of parameter estimation is proposed to test the accuracy of parameter estimation. Finally, the effectiveness of the proposed method is verified by practical data.


Introduction
As the core equipment of the distribution network, the distribution transformer plays an important role in power transmission and distribution.Due to its extensive presence within the distribution network, the operational condition of the transformer assumes critical importance in ensuring the safe and stable functioning of the overarching power grid.The accurate estimation of transformer parameters can effectively grasp its operating state, thereby significantly contributing to the assurance of stable power system operation.
The dynamic fluctuations in load, the widespread integration of distributed power sources, and the effects of equipment aging have collectively contributed to the increasing complexity of abnormal conditions in distribution transformers.These abnormal conditions may lead to the deterioration of the performance of the power system, the reduction of power transmission efficiency, and the shortening of equipment life, and have a serious impact on the stable operation of the power system.Therefore, the detection and diagnosis of distribution transformer parameter anomalies becomes particularly important.However, there are many difficulties in the parameter estimation of distribution transformers.Firstly, constrained by the constrained availability and spatial distribution of measurement devices in distribution networks [1], the quantity of independent equations derived from the parameter estimation of distribution transformers typically falls short of the total count of static parameters necessitating estimation.Consequently, achieving a comprehensive determination of all static parameters becomes a formidable challenge.Secondly, the load of the distribution transformer will change with time and the environment, making the parameter estimation of the transformer more challenging [2].
At present, there are three main methods for parameter estimation of distribution transformers, which are the theoretical calculation method [3], the parameter measurement method [4], and the data-driven method [5,6].The theoretical calculation method and the parameter measurement method cannot obtain enough measurement data for calculation because there are few measuring devices in the distribution network.The most widely used data-driven method is the method based on the principle of least square estimation.By collecting the input and output voltage, current, power, and other data of the transformer, a mathematical model is established to calculate the error between the actual data and the predicted data of the model, and the model parameters are adjusted to minimize the error and achieve parameter estimation.However, the problem of the ill-conditioned coefficient matrix will occur in this method.And the engineering practicability is poor.Considering the above problems, this paper analyzes the relationship between voltage, current and static parameters on the high/low voltage side of different types of distribution transformers, uses a neural network to fit the relationship, and obtains the parameter estimation model.
A transformer parameter estimation method based on a Deformable transformer network is proposed in this paper.Firstly, a Deformable Transformer network is used to fit the measurement data of the distribution transformer with the parameters to be estimated.The transformer parameters can be estimated directly through the measurement data.Secondly, a quality evaluation method of transformer parameter estimation is proposed to reflect the accuracy of parameter estimation.Finally, the proposed method is tested on several three-phase double-winding transformers, and the accuracy and effectiveness of the proposed method are verified.

Basic principles of parameter estimation
In a transformer, there are 12 parameters that need to be estimated.These parameters encompass the winding resistance RT, short circuit reactance XT, excitation conductance GT, and excitation susceptance BT of each phase.Taking the Dyn11 transformer as an example, the complex power of each winding flowing into the high voltage side can be expressed as follows: where SA,H, SB,H, and SC,H respectively represent the complex power of the three windings on the high voltage side.UA,H, UB,H, and UC,H represent the voltage phasors of the three windings on the high voltage side respectively.I * A,H , I * B,H , and I * C,H represent the conjugate values of the current phasors of the three windings on the high voltage side, respectively.
The three-phase complex power on the low voltage side can also be expressed as follows: ,,, , where Sa,L, Sb,L, and Sc,L respectively represent the complex power of the three-phase at the low voltage side.Pa,L, Pb,L, and Pc,L and Qa,L, Qb,L, and Qc,L respectively represent the three-phase active and reactive power on the low voltage side.
The excitation active power loss in a transformer can be expressed as: 222 ,,, ,, where ΔPA, ΔPB, and ΔPC respectively excitation active power loss; UA, UB and UC respectively represent the effective value of each winding voltage on the high voltage side of the transformer.
The active power loss of each winding in the transformer can be expressed as: where ΔPa, ΔPb and ΔPc respectively represent the active power loss of the winding.Ia, Ib and Ic respectively represent the effective value of a three-phase current on the low voltage side of the transformer.
The excitation reactive power loss in a transformer can be expressed as: 222 ,,, ,, where ΔQA, ΔQB and ΔQC respectively represent excitation reactive power loss.Short-circuit reactance reactive power loss in a transformer can be expressed as: 222 ,,, ,, where ΔQa, ΔQb and ΔQc respectively represent short-circuit reactance reactive power loss.The relationship between the power of the various windings of the transformer can be expressed as: , By plugging the above six equations into Equation (7), we get: where PL, QL and Ia can be measured from the TTU on the low voltage side of the transformer, UA,H and IA,H can be obtained by installing a voltage and current transformer on the high voltage side of the transformer.From Equation (8), it can be seen that the transformer parameters GT, BT, RT, and XT can be estimated by measuring these known quantities.

Parameter estimation model based on deformable transformer network
Through the analysis of the above principles, the unique transformer parameter value can be estimated by the known quantity measurement, and the parameter estimation of the transformer can be realized.In this paper, a Deformable transformer network is selected to learn the mapping relationship between various measurements and transformer parameters, and it is fitted to obtain a transformer parameter estimation model.Compared with traditional methods, a Deformable transformer network has good adaptability, which can automatically adapt to different scenarios and data distribution, so as to obtain more accurate parameter estimation results.
Taking Phase a as an example, the measurement data and parameters of Phase a are input into the Deformable transformer network for training: where x and y represent the input and output of the network, and h(x) represents the hidden layer; LN is treated by layer normalization.MLP is a multi-layer perceptron.MHDA is a multi-head deformable attention mechanism.
Phase b and Phase c are similar to Phase a, and the transformer parameter estimation model is obtained through training.

Quality evaluation of parameter estimation
Through the established transformer parameter estimation model, the data of Phase a, Phase b and Phase c are respectively input at the input end of the model, and the estimation matrix y* of transformer threephase static parameters is obtained.The matrix is T× 12-dimensional, yij represents the elements of row i and column j, and T represents the total number of collection periods.
The accuracy of parameter estimation is verified by using the parameter estimation quality evaluation method.According to the parameter estimation results obtained at different times, the estimated mean value of each parameter at each time_y and the quality comprehensive evaluation index η can be calculated respectively.For the i th parameter data, there are: where ηi represents the comprehensive evaluation index, the front part is the standard deviation of the estimated parameter, the back part is the maximum deviation of the estimated parameter at different times, and Ω represents the weight value.
The size of η is the method proposed in this paper to evaluate the accuracy of parameter estimation.The smaller the value of η is, the more accurate the estimation performed by this method will be.

Case studies
To verify the effectiveness of the proposed method, a three-phase double-winding transformer of S11-M-80/10 with multiple Dyn11 connections in a low-voltage distribution network is selected for testing.Before delivery, the parameters reduced to the high voltage side are: RT = 19.53Ω, XT = 50 Ω, GT =1.8× 10 -6 S, and BT =7.2×10 -6 S. The local measurement information of the distribution transformer is obtained through the same TTU (or fusion terminal) configured in the distribution transformer, and the value can be sampled at the same time.As can be seen from the two figures in Figure 1, by comparing the parameter estimation quality of 10 transformers, it can be found that the accuracy of the transformer parameter estimation method adopted in this paper fluctuates around 4%, while the accuracy of the two traditional methods fluctuates around 6% to 7%.By comparison, it can be seen that the error of the estimation method proposed in this paper is smaller than that of the ordinary estimation method.The estimated parameters are of higher quality and can be more accurate in transformer parameter estimation.By comparing Figures 1(a) and 1(b), it can be found that the parameter estimation quality evaluation method proposed in this paper can effectively evaluate the estimation quality compared with the traditional evaluation method using Mean Absolute Percentage Error.In comparison, the method proposed in this paper is more distinguishable.The accuracy of the estimate can be better judged.
Then, different neural networks are used to train the transformer parameters, and their training time and training accuracy are compared.The results are as follows: As can be seen from Table 1, compared with the other three traditional neural network methods, the Deformable Transformer method used in this paper has the most accurate Transformer parameters and the shortest training time.Deformable Transformer is the most suitable neural network for transformer parameter estimation, which can save a lot of training time.That's why this neural network is selected for training in this paper.
Then test the estimation results of the proposed method for distribution transformers under abnormal operation.10 transformers in normal operation and abnormal operation were selected for testing.The results are shown in Figure 2: As can be seen from Figure 2, the accuracy of the proposed method for estimating transformers under normal and abnormal operating conditions is between 4% and 5%, and there is no obvious difference between the two.Thus, it can be seen that the proposed method can accurately estimate both the transformer under normal operating conditions and the transformer under abnormal operating conditions.The method in this paper has good generalization.

Conclusion
For the distribution network with limited measuring equipment, a transformer parameter estimation method based on a Deformable transformer is proposed in this paper.The mapping relationship between measurement data and transformer parameters is learned through the Deformable transformer network, and real-time measurement data is used to estimate transformer parameter values.Moreover, the effectiveness of this method is verified by the quality evaluation method.

Figure 1 .
Figure 1.Quality of parameter estimation under different methods.

Figure 2 .
Figure 2.Estimated mass under abnormal operating conditions. +j

Table 1 .
Different neural network training effects.