Automatic identification of transformer excitation inrush based on second-order Taylor coefficient

In order to solve the time-consuming problem of the existing automatic identification methods of transformer inrush current, an automatic identification method of transformer inrush current based on second-order Taylor coefficient was designed. Ignore the leakage resistance and winding resistance of transformer winding, get the second harmonic characteristic quantity, assume the transformer variable ratio value is fixed, identify the transformer winding parameters, introduce the decay coefficient to describe the characteristic of excitation inrush current gradually decaying with time, construct the excitation inrush current Taylor expansion phase model, and set the automatic identification mode based on the second order Taylor coefficient. Experimental results: The designed transformer excitation inrush current automatic identification method and the other two transformer excitation inrush current automatic identification method of the elapsed time were: 55.32ms, 71.52ms, 71.04ms, indicating that after the integration of the second-order Taylor coefficient, the designed transformer excitation inrush current automatic identification method better performance.


Introduction
Power transformer is a very important equipment in the power system because it is not only expensive, but also directly related to the safe and stable operation of the whole power system.If the unbalance current exceeds a certain limit value will lead to transformer differential protection false operation, so we need to find ways to eliminate or minimize the unbalance current.Transformer maintenance is difficult and long, if the transformer is damaged due to failure, it will not only affect the safe operation of the power grid, but may even cause incalculable economic losses and social impact.The transformer generates an unbalanced current by regulating the tap of the load.Transformer with load regulation function is often used in power system to keep the operating voltage of the system stable, or to change the transformer ratio by moving the tap position of transformer, but once the Current to voltage ratio is determined before operation, it cannot be changed during operation.The transformer may generate several times the rated current excitation inrush on one side of the transformer when it is put into operation at no load or when the voltage is restored by external fault removal [1][2] .The size of the excitation inrush current is related to the remanence of the transformer before closing, closing angle, system impedance, etc.Therefore, the transformer's ratio and the current transformer's ratio do not agree to produce unbalanced current.The excitation inrush current in the transformer also gets unbalanced current.During normal and external faults, the transformer does not saturate and the excitation inrush current is relatively small, so the effect on differential protection can be neglected.Current differential protection is widely used in the main protection of transformers.Under normal operation and external fault conditions, the current size (converted to the primary side) and phase flowing through both ends of the transformer are basically the same, and the differential current is very small.When a fault occurs inside the transformer, the phase of the current at both ends is basically opposite and the differential current is large, thus the transformer differential protection operates 2 correctly to protect the transformer when an internal fault occurs.When the transformer is closed at no load, or when an external fault is removed making the grid system resume power supply, it may be severely saturated, thus generating a large excitation inrush current (up to the rated current) and producing an unbalanced current in the differential circuit.The excitation inrush current belongs to the unconnected branch, and this unconnected branch current may greatly exceed the start current of the differential protection, thus causing the differential protection to malfunction.So far, in addition to the differential protection principle, a better performance of the main protection principle of the transformer has not been found.Then, only under the premise of differential protection, continue to study the excitation inrush current and internal fault current identification method of transformer differential protection.

Obtaining the second harmonic characteristic quantity
Power transformers are very important equipment in power systems because they transfer power between different voltage levels through electromagnetic energy conversion.Second harmonic identification method also has many problems: one is due to the different transformer models and transformer no-load into the system before the remanence of different will lead to brake adjustment value is not easy to determine.Power transformer structure is complex, but basically can be divided into the following main parts: winding, core, shell, insulation medium, insulation bushing, plus the relevant measurement transformer and the connection line between each part.Second, when the system capacity is too large, the second harmonic content of the transformer will also be higher when an internal fault occurs, which affects the accuracy of this criterion and leads to the misoperation of the relay protection device [3][4][5] .During operation, faults or abnormalities can occur in all parts.The task of relay protection is to make the correct decision in case of a fault, so that the accident causes the least damage to the power system and to the equipment.In addition, winding and its lead faults are basically short-circuit faults.Lead wire breakage and disconnection are generally accompanied by a short circuit.Third, the magnetic saturation point of the current improved core material is lower than before, so it is easier to saturate, when the remanent magnetism is higher and the closing angle meets certain conditions, the second harmonic content in the excitation surge may be less than the set threshold, which will lead to the rejection of the relay protection device.Ignoring the leakage resistance of the transformer winding and winding resistance, the voltage equation of the transformer can be expressed by the following equation.
In formula (1),  indicates the transformer core flux, h indicates the voltage amplitude on the primary side bus of the transformer, Q indicates the angular velocity, and  indicates the initial phase angle of the voltage.The short circuit is very harmful to the equipment and the system, and the main protection is required to remove the fault without delay.The main protection can be divided into current differential protection which does not require voltage and differential current impedance protection which requires voltage, parameter identification protection and so on.If voltage is not required, there are less problems caused by voltage, such as the installation position of voltage transformer, primary and secondary circuit disconnection of voltage transformer, secondary circuit cable induction voltage or secondary circuit voltage tampering, etc.It can be seen that in the event of an excitation inrush, the transformer primary side line current will appear a steep rise, followed by a slow decline, in the process there is a certain interruption in the waveform, as the part is a certain remanent magnetization situation, so its value will not decay to the size of the normal current, but slightly larger than normal.On this basis, the integration of equation (1) becomes the following form.
In formula (2), W indicates the integration constant associated with the closing angle.Therefore, current differential protection is widely used in the main protection of transformers.The biggest challenge for current differential protection comes from two main aspects: one aspect is the unbalanced current constituted by the current transformer excitation branch current, and the other is the excitation current of the excitation branch of the transformer being protected.During the transient process when the transformer is put into operation at no load, the latter is often referred to as excitation inrush.The voltage distortion occurs on all three sides of a three-winding transformer, and the second harmonic content of this distortion rate as a characteristic excitation inrush has the highest percentage of all harmonics and can be used as a criterion for the same.The DC component decays more slowly, but eventually all decay to 0. When a power transformer has a sudden voltage rise when the supply voltage is put in or an external fault is removed, its excitation branch may produce an excitation inrush current of high amplitude.This unconnected branch current may greatly exceed the start current of the differential protection.In order to prevent the protection from false operation, we must try to block the protection.Among them, the second harmonic braking method is most widely used.The second harmonic method is to use the feature that the excitation inrush current waveform contains a large number of second harmonic components to latch the protection when the second harmonic component of the differential current flowing into the differential relay is detected to be higher than the threshold value, in order to avoid the differential protection from false operation due to the excitation inrush current.Based on the above description, the step of obtaining the second harmonic characteristic quantity is completed.

Identifying transformer winding parameters
Transformer is not a pure circuit, it has not only internal circuit but also magnetic circuit, the principle can not meet the requirements of KCL law for linear components.From the circuit point of view, the transformer primary and secondary windings are not a node, and the transformer current differential protection is based on the steady-state magnetic circuit balance of the transformer, which can also be seen as an extension of the differential protection.By identifying transformer winding parameters, the excitation inrush current and internal fault current are identified based on whether the parameters change [6][7] .This provides an accurate signal for transformer protection, however, as soon as the transformer undergoes a transient process and the core is saturated, this balance can easily be broken, resulting in a false operation of the differential protection.This balance can only be re-established when the transformer returns to steady state again.When a fault occurs outside the transformer, no matter how severe the fault is, the differential current flowing through the relay is constantly equal to zero, as shown in the equation.
In formula (3), R indicates the short-circuit current at the internal short-circuit point of the outflow voltage,  indicates the current phase of the  terminal of the protected voltage, and W has the same meaning as formula (2).The advantage of this method is that only the physical parameters of each side winding of the transformer are used as the differential protection criterion, which does not need to do complicated adjustment calculation and establish the blocking conditions, and has good sensitivity and quick-action.Therefore, it is not necessary to have a transformer internal fault to generate unbalanced differential current, but as long as the transformer is in the transient process, unbalanced current will appear.It shows that the inrush current is the main cause of transformer misoperation.For the power sector, most of its identification models are grey-box models, i.e. some parameters of the system are known, such as model structure, order, or system parameters to be measured.In general, the excitation inrush of a transformer is much smaller than the rated current and its influence on the protection action can be disregarded.However, when the transformer will not run from the state suddenly without the load of the start, the voltage will change abruptly, due to the first and second winding mutual inductance flux size is equal, so the non-linear amount can be eliminated, assuming that the transformer variable ratio value is fixed, the side resistance can be expressed as.
In Equation ( 4),  indicates the side resistance, Y indicates the leakage inductance of the side winding, v indicates the number of turns of the side winding, S indicates the mutual inductance flux between the side windings.Boosted directly from zero or very small values to rated voltage, the transformer core may be severely saturated, resulting in large excitation inrush currents, the maximum of which may be as high as four to eight times the rated current.Although the power domain is by nature a high-order, nonlinear, and complex system, the same system identification techniques can be used to identify the model parameters in the power system, which can be broadly divided into two categories, one belonging to the structural parameters, also called network parameters, from which it can be seen if the excitation inrush current is evaded by increasing the action current threshold [8][9] .The discriminant principle of flux characteristics is used to derive from the flux characteristics of transformers, which differ in various aspects under excitation inrush current and internal fault current.Since all electrical quantities of the transformer are transferred through the magnetic flux, it is somewhat more accurate in principle than the method based on waveform characteristics.Based on this, the steps to identify the transformer winding parameters are completed.

Constructing a Taylor expansion phase model for excitation inrush current
Due to the nonlinearity of the core material flux of the transformer, it is easy to generate unbalanced current with high amplitude and harmonic content in the process of no-load operation or cutting off external faults, which is called excitation inrush.The frequency component of the excitation inrush is complex, and contains attenuated DC components, second harmonic components and higher harmonic components in addition to fundamental components, and the signal waveform shows dynamic decay characteristics.When the core of the transformer is in saturation, the transformer excitation current is influenced by the remanent magnetism and can be further decomposed into periodic and non-periodic components [10] .This is because the transformer is in a saturated state, there is remanent magnetism in the core, and the flux is not mutable, so there is a non-periodic transient component.Excitation inrush current generation and transformer winding wiring, power system operation, closing angle, remanent magnetism, and current mutual inductance saturation are closely related.As the excitation inrush contains fundamental components, attenuated DC components and harmonic components, in most cases the second harmonic component of the excitation inrush is greater than 30%, the third / fourth harmonic component than the fundamental, the second harmonic and DC component is smaller.Therefore, in the establishment of the excitation inrush current signal model, each frequency component should be considered.
In Equation ( 5 When the transformer core becomes saturated with flux, the AC flux is superimposed, and the characteristics of the excitation inrush can be obtained based on the nonlinear characteristics of the transformer core magnetization curve, and the transformer flux curve containing remanence.The generation of the excitation inrush current can be seen as a charging process of the capacitor, where the sudden change in voltage produces an inrush current during the instantaneous access to the voltage of the transformer.In summary, the hysteresis effect makes the transformer contain remanent magnetism, which often leads to core saturation when the transformer encounters no-load closing, voltage recovery after external fault removal, etc.After core saturation, the transformer operating point enters the saturation zone of the magnetization curve, which is affected by the nonlinear characteristics of the transformer, resulting in the generation of excitation inrush current containing a large number of harmonic components.Therefore, when considering the excitation inrush current signal model, the dynamic decay characteristics of the excitation inrush current should be modeled for the introduction of the decay coefficient to describe the characteristics of the gradual decay of the excitation inrush current with time, resulting in the current decay rate of: In Equation ( 6), 1 D indicates the attenuation coefficient of the DC component, 0 D indicates the attenuation factor of the DC component, and t indicates the attenuation factor of the fundamental component.The magnitude of the inrush current is related to the core type of the transformer, winding method, impedance, etc.In addition, the voltage closing phase angle and breaking phase angle are also influencing factors of the inrush current, but they have different degrees of influence on the inrush current magnitude.The excitation inrush current Taylor expansion phase model characterizing the frequency composition is obtained as follows.
In Equation ( 7), g represents the attenuated DC component, d represents the higher harmonic phase, c represents the steady state frequency, and l represents the second harmonic frequency domain information.The distortion of the excitation surge waveform and the complexity of the components make this phase volume model contain more frequency components, which will lead to a huge amount of computational burden.In terms of achieving accurate measurement of the fundamental phase quantity, the impact on the measurement accuracy, so the need to find the key components affecting the measurement effect is not all frequency components will simplify the measurement pair model.The inrush current is supposed to be the normal current state during the closing process, but the current transformer equates it to the short-circuit current, which means that if the algorithm is not specifically set, the normal relay protection devices will recognize it as a fault current, leading to transformer misoperation and thus affecting the power supply of the power system.Based on the above description, the steps to construct the excitation inrush current Taylor unfolding phase model are completed.

Setting automatic recognition mode based on second-order Taylor coefficient
With the improvement of transformer core materials, the saturation flux is constantly reduced, resulting in smaller and smaller second harmonic components in the excitation surge, which leads to the disadvantages of a series of identification methods based on the second harmonic content criterion as a principle.The excitation inrush current contains a large number of higher harmonic components, especially the second harmonic component.By detecting the size of the second harmonic content in the three-phase differential current to determine whether the excitation surge, so as to achieve timely blocking of the longitudinal differential protection, to prevent the purpose of the protection of false operation.In particular, in some cases, the second harmonic content of the three-phase excitation surge will be lower than the threshold value of 15% for differential protection.Transformers transmit energy by electromagnetic induction between the primary and secondary windings.This is known as the second harmonic braking element of the transformer longitudinal differential protection.At this time, the protection system will be misjudged and open differential protection, that is, the second harmonic blocking criterion fails, but at this time the second harmonic content of the zero sequence current generated by the asymmetric excitation inrush of the three-phase transformer is high, and for this feature, this paper uses the second-order Taylor coefficient as the core of the excitation inrush automatic identification method [11] .Through the study found that the normal operation of the transformer, active losses and other stray losses, the sum is relatively small and basically stable, especially for large power transformers, active losses are basically m-ohm losses, this value can be small to negligible, while the reactive power generated on behalf of the transformer excitation winding reactance component, will follow the flux change and constantly change.The transformer three-phase voltage and current waveforms are standard sine waves and are symmetrical, and the expression for instantaneous reactive power is obtained as: In Formula (8), K represents the initial phase Angle of transformer voltage, r represents the initial phase Angle of transformer current, and L represents the zero-sequence component of current.Since the excitation inrush current of transformers is transient, it is not suitable for harmonic analysis by Fourier series, the reason being that the Fourier series method will lead to incorrect results for transient signals.However, the second harmonic principle has its own limitations.With the development of modern transformers, the electrical transfer properties of ferromagnetic materials are fully utilized, leading to an earlier core saturation point.When the remanence of the transformer is large, the second harmonic content of the excitation inrush is less distinctive.The transformer excitation current always changes slightly faster than the main flux because of eddy current losses and hysteresis in the magnetic circuit of the transformer, so that the main flux and excitation current are two standard sinusoidal quantities with phase differences when a short-circuit fault occurs in the transformer.Therefore, the trajectory of the main flux is approximately an ellipse, and the excitation current is similar.When the transformer has an internal fault, the excitation circuit voltage will be reduced, the excitation circuit voltage will be reduced, the excitation current flowing through the excitation circuit will be reduced even more, and the excitation circuit can be regarded as an open circuit.On the basis of equation ( 8), the corresponding expressions for the secondary side current and voltage are derived as follows:   In Equation ( 9) and ( 10), x indicates the corresponding DC component of the two differences, a indicates the instantaneous active power on the secondary side, and b indicates the instantaneous reactive power on the secondary side.In addition, when a transformer is connected to a fixed capacitor in the event of an internal fault, the resulting transient current will contain a large amount of second harmonic components, which means that a large second harmonic in the current is no longer unique to excitation inrush, but may also be generated under certain conditions of internal faults.If the calculated magnitude is larger than the braking ratio, the inrush is judged to be an excitation inrush.When the transformer is put into operation at no load and the power supply is restored after the fault is removed, the core flux saturation and various other factors can cause an excitation inrush to be generated, and this excitation inrush is composed of two parts: the core magnetization current and the basic iron consumption current.At the same time the reactive current corresponds to that part of the energy exchanged, which often varies considerably.At the same time, all the total equivalent resistances at the fault point are numerically compared to the equivalent reactance values of the short-circuit winding, and the power factor of the transformer will increase and the active power consumption will increase.Based on the above two aspects it can be found that the ratio of three-phase differential reactive power to three-phase differential active power is smaller when an internal fault occurs.This method has become a widely used method at present because of its practicality.However, with the increase of installed transformer capacity, the popularity of long-distance high-voltage transmission lines and the improvement of transformer core materials, the second harmonic component of the excitation inrush current will become smaller and smaller, and thus the harmonic component of the fault current will increase, which leads to a decrease in the reliability as well as applicability of the traditional second harmonic blocking criterion.However, the increase of active power of the transformer is relatively small, so the active iron consumption current of the transformer is relatively small compared to the reactive magnetization current, reactive power accounts for the main component, and the ratio of reactive power to active power is correspondingly larger, that is, for the excitation inrush current appearing in the three-phase transformer, the ratio of the three-phase reactive power difference to the three-phase active power difference is often larger.In summary, the steps to complete the automatic identification mode based on the second-order Taylor coefficient settings.

Experiment preparation
Simulation verification of the method proposed in this paper based on the second-order Taylor coefficient for automatic identification of excitation inrush current, using the SIMULINK toolbox in MATLAB for simulation verification.At the same time, in order to facilitate the analysis, the parameters of the three transformers are set equal, the simulation system of the three-phase transformer for Y/△ wiring mode, capacity are set 100MVA; transformer parameters are set as follows: capacity: 5000KVA, frequency 50Hz; high-voltage side rated voltage: 35KV, using three-phase double winding, winding resistance primary side, secondary side are set to 0.002pu; high-voltage Side leakage inductance: 0. 08pu, the calculated rated current of the high-voltage side: 659.9A.Three single-phase transformers are selected instead of three-phase transformers to simulate internal transformer faults.Among them, the single-phase transformer element is composed of one primary-side winding and two secondary-side windings, the secondary-side windings are connected by first and last connection, the simulation duration of each arithmetic case is 1.2s, the sampling frequency of differential current and standard sine wave sequence is 2200Hz, and the weekly wave has 36 sampling points.Through setting parameters of secondary winding, it is more convenient to realize the simulation of transformer internal faults.

Experimental results
Selecting PSCAD-based automatic identification of transformer excitation inrush current method, based on convolutional neural network automatic identification of transformer excitation inrush current method, and this design of automatic identification of transformer excitation inrush current method for comparison testing.Separate test in different second harmonic content conditions, the three transformer excitation inrush current automatic identification method of time consumption, the experimental results are shown in Figure 1-3.
Through Figure 1 -Figure 3 can be derived from the average value of the time consumed by the three transformer excitation inrush current automatic identification methods, as shown in Table 1.Second harmonic content 60% three transformer excitation inrush current automatic identification method time consuming(ms) In the event of a fault within the zone, the other transformer excitation inrush current automatic identification method will first block the protection, while the second-order Taylor coefficient criterion can cooperate with the main protection directly remove the fault.As can be seen from Table 1, the design of the transformer excitation inrush current automatic identification method and the other two transformer excitation inrush current automatic identification method time consuming respectively: 55.32ms, 71.52ms, 71.04ms.In this case, the design of the transformer excitation inrush current automatic identification method can open protection in a shorter period of time.

Conclusion
The article is based on the second-order Taylor coefficient, through the commonly used transformer excitation inrush current identification methods for detailed analysis, discussing the transformer excitation inrush current on the longitudinal difference protection.As the excitation inrush waveform characteristics and many factors related to rely on its waveform characteristics to identify the excitation inrush method is more complex, combined with the second-order Taylor coefficient, the conclusion that the excitation inrush and and should be inrush current contain a large number of higher harmonics.The next step of work will focus on the spectral response level of the sampling window function, dedicated to achieve higher achievements.

), 0 G
indicates the DC component, 1 G indicates the fundamental component amplitude,  indicates the fundamental frequency, and  indicates the initial phase angle of the fundamental component.As the voltage is sinusoidal alternating, thus a periodic transient component appears.

Table 1 .
Mean value of elapsed time(ms)