The Surge Voltage Test in High Power Transformers by the Finite Element Method Aránzazu Fernández Andrés, Luis Fontán Agorreta Centre of Studies and Technical Investigations of Guipuzcoa (CEIT) Technological Studies of the University of Navarra (TECNUN) Paseo de Manuel Lardizabal, 13 y 15, 20016 - San Sebastián, Spain Abstract The present paper tries to emphasize the importance of surge voltage tests in High Power Transformers and the main advantages of developing them by a Finite Element Method (FEM). The sequence of steps to define the model, the geometry and the conditions that characterize the real transformer are presented. The electric parameters that describe the problem are calculated via an electric circuit model generated by the finite element program, and are used in a transient simulation to obtain the electric field value along the windings at different time steps. The critical points can be easily obtained, which allow us to determine the probability of an insulation failure in case of an electric discharge occurs. In addition, this technique also represents graphically the wave displacement for each time step. Introduction Testing is a very important issue in the manufacture of transformers. A satisfactory test result is not only a guarantee that the equipment meets the required specification, but it is also a proof to the designers that their models and calculations can be used for future designs. Nowadays, the Surge Voltage Test is one of the main tests to be carried out in transformers. It is a way to prove that the insulation level will resist the high voltage conditions of electric discharges. Real tests simulate a traveling wave caused by a discharge from the high-voltage generator situated some distance from the transformer. Usually, a standard wave-shape is applied, with a front time of 1.2µs and a time to half-value of 50µs (Figure 1). The peak voltage reached depends on the system highest tension and on the insulation layers properties. The surge generator consists of high voltage capacitors, which are charged in parallel from a DC source, and are subsequently discharged in series over an electric circuit with several resistors. The voltage wave is applied to one end of the winding, while the other end is connected to ground, either directly or via a low resistance. The ends of the windings that are not tested are connected to ground in order to avoid induced voltages on them. This is described in more detail in references [1],[2].
Figure 1. Voltage Wave applied during the Surge Voltage Test The Source Voltage Test is in practice difficult to accomplish and, in many cases, considered a destructive test. Actually, designers tend to use other techniques, which permit to know the behaviour of the system under these voltage conditions even before the manufacturing of the transformer. One of these methods is the simulation with a finite element program. The FEM Method The simulation of the Source Voltage Test consists in developing a valid geometric model which allows determine the value of the electric parameters that integrate the electric circuit model used to calculate the distribution of the electric field along the transformer. A three-dimensional problem should be defined in this type of analysis to calculate the field magnitude, but in this paper it has been simplified to a two-dimensional study because of the symmetry. Simulations have been carried out for a high power three-phase transformer. Additional documentation about other problems resolved by FEM methods is described in [3],[4],[5],[6]. The Geometric Model The first step in developing the simulation has been to create a 2D geometric model of the transformer, assigning the corresponding material properties, defining boundary conditions and loads, and carrying out a mapped meshing. In order to parameterize the process, four different macros have been defined for building up the model. These are the winding, the insulation layer, the aluminum screen layer and the
complementary winding used in some particular cases. In this way, the designer only needs to determine the sequence of macros to be run by the program for generating the geometry. The winding layer is made up of copper piled rectangular elements that represent the transverse section of the spires in the real transformer. Each spire is separated from the next one above by a thin paper layer of trapezoidal shape. The insulation level in the model depends on the thickness and electrical properties assigned to the paper elements between the winding rows and spires. Different types of paper have been displaced for the insulation layers. The aluminum screen layer can be represented with rounded edges, so that the distortion effects that the field lines experiment in those areas are minimized. The complementary winding is used in real tests for increasing the number of spires to avoid the field magnitude going under critical values. Table 1 presents the dimensions and material properties of the elements described in this paragraph. Table1. Properties of the objects in the model High (Inches) Width (Inches) Material Spires of main winding 0.32 0.35 Copper Screen Layer 51.57 0.064 Aluminum Insulation Layer 1 52.36 0.20 Paper ( Store ) Insulation Layer 2 52.36 0.27 Paper ( Tertrans ) Insulation Layer 3 52.36 0.20 Paper ( TBD ) Spires of complementary winding 0.41 0.26 Copper Once the geometry has been generated, the region model is broken up into a set of nodes in which the field magnitude is calculated. This step in the analysis process is called mesh generation and is one of the main stages during the definition of the problem. The origin of many errors observed in the results originated by a finite element program is in most cases a bad discretization of the model components. Another important point to consider is the necessity of checking that surfaces in contact in the geometry have been overlapped or glued and consequently present continuity. The mesh has been generated running a regular or mapped grid. The element type used has been PLANE121. This is a bidimensional eight-node solid appropriate to obtain the voltage and electrostatic energy in an axisymmetric model. Figure 2 shows the middle cross section of a 30MVA three-phase transformer. The main and complementary windings have been represented separately by different types of paper layers. The figure also shows the aluminum screen layer before the first row of spires. The upper region of the model simulates the oil flow used for the refrigeration of the transformer (see references [7],[8],[9]).
Figure 2. Detail of a section of the transformer generated by the FEM Method Parameter Values in the Model To develop an electric circuit that simulates the tension wave traveling along the transformer, it is necessary to determine the value of the electric parameters in the problem, that is, the capacitances, inductances and resistances of the conductive elements. Capacitances in the model are defined by the paper between two consecutive winding layers or between two consecutive spires at the same winding layer. To determine these values, different levels of voltages have been applied to the copper windings. By this way, a previously calculated tension gradient has been imposed between opposite elements. This procedure enables to obtain the electrostatic energy stored by each element using a specific function of the FEM Method. These calculations are substituted in expression (1) to obtain the corresponding capacitance value. 2 W C = (1) 2 V Where: C = Capacitance value. W = Electrostatic energy stored by the elements which define the capacitance. V = Tension gradient applied to the opposite copper elements.
On other hand, each conductive element in the model has an inductance and resistance value depending on its geometry and material properties. The numeric value of these parameters has been calculated via equations (2) and (3). The geometrical variables taken into account to calculate these parameters have been measured on the geometric model described in previous section using the finite element program. n L = 2 µ µ A r l o (2) l R = ρ (3) A Where; n = Number of spires in the winding (n=1 if we are considering a single spire). µ r = Relative permeability of the winding material with respect to the vacuum permeability. µ o = Vacuum permeability. A = Area of a conductor element in the model. l = Length of a conductor element in the model. ρ = Conductor resistivity. Some of the results obtained via the finite element method for the electric parameters in the model are presented in table 2. Table2. Electric Parameter values in the model via the FEM Method Minimum Value Maximum Value Capacitance between layers 1-2 Capacitance between layers 2-3 Capacitance between layers 3-4 Capacitance between layers 4-5 Capacitance between layers 5-6 8.106 10-12 F 8.106 10-12 F 1.199 10-11 F 1.199 10-11 F 1.398 10-11 F 1.398 10-11 F 1.065 10-11 F 1.065 10-11 F 4.129 10-13 F 1.065 10-11 F Resistances 0.000757 Ω 0.000961 Ω Inductances 0.00033 H 0.00042 H
The Electric Circuit Model With the electric parameter values obtained in previous section, the electric circuit of the transformer is fixed. This model lets the designer calculate, when a high voltage source is applied, the tension magnitude at each node in the circuit for different periods. In the electric circuit model, spires appear represented by their resistance and inductance. The connection of these elements with the rest of the circuit has been carried out by the corresponding capacitances in parallel. The extreme of each pair of electric components have been short-circuited with the following one. The dimensions of the components and the distances between nodes are very similar to those in the geometric model. The total length of an inductance and a resistance is equal to the height of one spire. The time-varying voltages obtained via the simulation are calculated in three different nodes located at the top, middle and bottom region of each spire in the model. In the same way, the length of a capacitance element in the circuit corresponds to the thickness of the insulation layer between the spires connected by the capacitance. The element used for modelling the electric behaviour has been CIRCU124, which has up to six degrees of freedom per node to simulate the circuit response. This element allows us to generate different types of electrical circuit components. When setting up the elements options, the designer has to specify what type of electric parameter must be placed in the circuit when the simulation is run. Figure 3 shows a detail of the electric circuit model obtained for the transformer analysed in this paper. Figure 3. Detail of one section of the electric circuit model of the transformer An example of the voltages obtained in the present analysis for the nodes of the electric circuit, are shown by curves in figures 4 and 5, where the tension wave for two different spires of consecutive winding layers has been represented for the total number of time steps considered. These values are collected in a data
table that will be used in the transient simulation to establish the voltage level that each node of the transformer would present over the time if a discharge occurred. Figures 4 and 5 also represent the decrement that the tension magnitude experiments as consequence of the losses in the electric loads of the circuit. Figure 4. Voltage Wave shape in two spires of first and second winding layer Figure 5. Voltage Wave shape in two spires of third and fourth winding layer
Results of the Transient Simulation The voltage distribution obtained with the previous circuit becomes a load in the initial geometric model. Under these conditions a transient simulation was run. Results of this procedure enable us to determine the points where the electric field presents maximum values. These are called the critical points, that is, the points where the probability of an insulation failure is bigger when an electric discharge takes place. In addition to this, this test lets also observe the wave displacement along the winding of the transformer for each time step. Some of the graphical results obtained in the simulation carried out in this paper are shown in figures 6 and 7. The electric field distributions on the critical points of the transformer and the voltage gradient have been represented for the time step at which these variables reach their maximum values. Figure 6. Voltage distribution of the transformer at 1.2µs time step
Figure 7. Electric Field distribution at 1.2µs time step Critical values for electric field are reached at a time step of 1.2 µs between the first and second winding layers. This maximum is 54,4 kv/mm and is lower than the maximum allowed by the insulation paper. This seems to be a reasonable result if we consider that the highest levels of tension occur during the initial time steps of the simulation, due that the wave front presents its maximum magnitude. In addition to this, simulation results also show a maximum gradient that appears at one quarter of the total height from the bottom region of the transformer at time step t=13,8µs (See Figure 8). The maximum value for this gradient is 27, 3 kv/mm between the first and second winding layers, and 48,7kV/mm between the third and fourth winding layers. The rest of the electric field values obtained in the simulation are lower than the ones mentioned in this section, and consequently do not require a special attention.
Figure 8. Electric Field distribution at t=13,8 µs (¼ the height of the transformer) The results calculated via the FEM Method have been compared with the ones obtained in a real test by the Spanish company for the manufacture of transformers OASA Transformadores. Figures 9 and 10 show the voltage waves in the simulation and in a real transformer respectively. The wave shape tends to decrease along time with maximum values occurring at the same time step. Figure 9. Voltage Wave Shape during the Surge Voltage Test simulation
Figure 10. Voltage Wave Shape in a real Surge Voltage Test Conclusions Damages from electrical discharges are one of the main problems occurring in high power transformers. The FEM Method can be considered a very useful tool in order to obtain testing results before the transformer manufacture, which induces in a considerable reduction of costs and development time, particularly if the designer carries out the analysis at the first steps of a process. By other hand, the method described at this paper presents many advantages over real tests. The flexibility of the designing steps allows simulate any type of transformer geometry. It can be possible to study an entire structure rather than isolated components and some complex aspects, such as nonlinear effects, can be taken into account in the analysis. Therefore, finite element methods are more indicated for indeterminate structures, the material properties can be defined as dependent of other variables and displacements and rotations in case that exist mobile parts in the model can also be simulated. At the time of developing a simulation, it is necessary to consider that although some numerical problems can appear due to quantization errors in number representation and round off errors in arithmetic operations, the results obtained with this method show a good proximity with the ones obtained by real tests. Results obtained with the analysis described in the present paper have been compared with the response of transformers in a real Surge Voltage Test. In those cases when the transformer has been damaged or destructed, the simulation results show gradient values higher than the maximum limits allowed by the characteristics of insulation layers. In other cases in which the behavior of the transformer was satisfactory after test, simulations show the tension gradients in the same areas than the real one, as it has been described in the results section of this paper. These comparisons contribute to verify the validity of the finite element method for this type of tests.
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