Due to the AC-DC converter connected to the transformer, electrical stresses such as AC, DC and DC polarity reversal (DCPR) are excited in the transformer, while only AC stress is excited in conventional AC power transmission systems. This thesis focuses on optimizing the design of two types of insulation, parallel oil barrier insulation between conductors and end wrap insulation, because the electric fields in those areas are stronger than other areas. The suggested algorithm produces parallel oil barrier insulations that have 5% less insulation length than the reference insulations on average under AC and HVDC stresses, maintaining their stability, which means achieving the design objective.
Introduction
Chapter II explains the field analysis method (Finite Element Method) used for analyzing insulation materials. In Chapter IV, the reliability analysis method used for this work is explained with the term “safety factor” that estimates the robustness of insulation. In Section V, the design purpose of this work will first be clarified, and the proposed optimization method will be explained in detail.
Electric Field Analysis
Governing Equation
Finite Element Method
- Construction of matrix system
- Imposition of boundary condition
By combining the three equations, which can be obtained by varying the value of the index i in Equation 11, we can develop the matrix equation by resolving 𝑟𝑒(𝜎𝑒+ 𝜀𝑒 𝜕 . 𝜕𝑡) into 𝑟𝑒𝜎𝑒+ 𝑟𝑒𝜀 𝑒𝜕/𝜕𝑡. For time-harmonic analysis, replacing 𝜕/𝜕𝑡 in Equation 14 with 𝑗𝜔 gives the equation below. With the initial condition {𝜙̂(𝑡0)} with time-varying conditions, {𝜙̂(𝑡)} can be obtained by computing Equation 20 in an iterative manner.
Insulation of HVDC Converter Transformer
Insulation Structure
The outer shell represents a container, red and blue dotted cylinders are conductors (coil), and the green dotted line is a slice to see a two-dimensional cross-section later. Each material has different dielectric strengths, that is, barriers have constant dielectric strengths and oil has a dielectric strength that is a function of the length of the oil gap between barriers. The length d is along the contour perpendicular to the equipotential line, on which electrical breakdown or partial discharge may occur.
Design optimization of the entire insulation at once is expected to be difficult to implement due to the large number of design variables expected to be handled, but optimizing only small key components independently, while taking into account the physical continuity of each component, will this is expected to be simpler and possible. . In this work, the two red-framed areas in Figure 3 are the likely areas where an electrical fault or partial discharge may occur, due to the small distances between the high-voltage and low-voltage conditioned boundaries that cause a high electric field intensity. For the sequential optimization, the lower region (parallel oil barrier insulation or main insulation) where parallel barriers are placed between two conductors is optimized first, and then the upper region (end winding insulation) is optimized, taking into account the physical continuity with the first optimization result.
Boundary conditions must also be applied to each conductor boundary and the surrounding outer boundaries of the structure. In this work, high voltages (HV) are applied to the right conductors (coil and electrostatic ring), zero voltages (ground) are applied to the left conductors and surrounding outer limits except the lower ones, and the Neumann condition is applied to the lower surrounding edges. outer border. The design variables and limitations of parallel oil barrier insulation are summarized in Tables III and IV, and they can be seen.
Those for end winding insulation are summarized in Tables V and VI, and they can be seen in Figure 6.
Field Characteristic
For parallel oil barrier insulation, the electric field distributions obtained from one-dimensional and two-dimensional analyzes are almost the same because, if it is far enough from the end winding insulation, along the vertical direction (z direction), the structural form can be approximated as infinite vertical barriers. For comparison, the analysis results of an example of isolation using one-dimensional FEM and two-dimensional FEM are shown in Figure 10 using the isolation shown in Figure 9.
Reliability Analysis
Safety Factor
In addition, the minimum safety factor of the isolation may be reduced, and as a result the isolation length of the reliable optimal solution may be greater than that of the analytical optimal solution. First, to determine whether the design objectives are met, a reference AC insulation designed for 282.6 kV (AC@60Hz, magnitude) on the right conductor with the values shown in Table VII is introduced and compared with the insulation optimized by the algorithm developed in previous chapters. The result of the analysis of the reference structure shown in Table VII is shown in Figure 21.
The comparison shows that the optimization algorithm reduced the insulation length while maintaining the safety of the insulation, which previously clarified the satisfaction of the design objective. To see the effects of the reliability analysis on the design optimization, a design optimization with the reliability analysis is performed under voltages of 282.6 kV at 60 Hz, 500 kV DC and 500 kV DCPR. The resulting design parameters of the end winding insulation optimized based on that parallel oil barrier insulation are shown in Table XIII.
A standardized and automated method for optimizing the insulation design of an HVDC converter transformer is proposed, which aims to reduce the insulation length while maintaining robustness under HVDC loads. The design optimization is divided into two different optimizations for two important areas of insulation, which are parallel conductor-to-conductor oil barrier insulation and end winding insulation. Comparisons of the optimized parallel oil barrier isolation with reference parallel oil barrier isolations show that the proposed optimization algorithm performs well in the desired manner.
The optimization of the type of insulations requires two-dimensional FEM analysis, so the optimization required more calculation time than the oil barrier insulation optimization, which is sufficient with one-dimensional analysis.
Sensitivity Analysis
Design Optimization
Design Objective
Genetic Algorithm
- Encoding
- Decoding
- Fitness Function
- Selection, Crossover, and Mutation
Even if the volume of the transformer is small, the utility and total value of the transformer is expected to increase. The names or symbols of the variables in the figures can be given in Tables III to VI, and their representations on the structure in Figures 5 and 6, both in Chapter 3. For example, when 𝑛𝑏 = 3, the first barrier of width 𝑤𝑏,1 is placed first 𝑙𝑜,1 apart to the left of the conductor. Next, a second barrier of width 𝑤𝑏.2 is placed 𝑙𝑜.2 away from the first barrier.
Finally, the third barrier of width 𝑤𝑏.3 is placed 𝑙𝑜.3 apart from the second barrier and the last oil gap of length 𝑙𝑜.4 is inserted between the third barrier and the right conductor. The decoding process for end-wound insulation is complex compared to parallel oil barrier insulation. Apply the angles 𝑛𝑎, 𝑙𝑜,
Implement 𝑛𝑎− 𝑛𝑎,𝑙𝑒𝑓𝑡 right-curved corners of width 𝑤𝑎,𝑖's attached to the certain sides of parallel barriers indicated in 𝑝𝑎,𝑖's and separated from the electrostatic ring or the corner just below it by 𝑙𝑜,𝑖 is from right to left, where 𝑖 lies between 𝑛𝑎,𝑙𝑒𝑓𝑡+ 1 and 𝑛𝑎. However, for end winding insulation this is not as simple as the previous one, but curved contours are needed because the equipotential line is not parallel, as in the case of parallel oil barrier insulations. From each point, move a differential distance in the direction of the electric field vector at the point.
After the pairs cross, a mutation may occur in the chromosomes of each offspring.
Simulation and Results
Parallel Oil-Barrier Insulation
- Design Optimization Based on an AC Reference Insulation
- Design Optimization Based on a HVDC Reference Insulation
Comparing Tables VII and VIII, we can see that 𝑠𝑚𝑖𝑛 became closer to 𝑠0, the target safety factor, and also the insulation length 𝑙𝑖𝑛𝑠 decreased by 5 mm. However, because the insulation is largely designed for AC only, its safety under DC and DCPR loads cannot be guaranteed. To see its safety under 500kV DC and DCPR voltages, the insulation is analyzed with the voltages.
Using the optimization algorithm developed in this thesis, an optimization result under the same stresses is obtained, which is in Table IX. As shown in the table, the minimum safety factor is slightly higher than the target safety factor of 1.12, but the insulation length is increased to make the insulation stable even under DC and DC polarity stress conditions. The optimization result can be seen in Table X and its analysis result can be seen in Figure 25.
By comparing the result with the result optimized without the reliability analysis shown in Table IX, it can be seen that a longer insulation length is needed to handle the unpredictable deviations of the baffle positions. To see that the design optimization produces insulation that meets the design objective for HVDC loads as well, another reference insulation is introduced that is designed for 776 kV (AC@60Hz), 838 kV (DC) and 460 kV (DCPR) loads. Table XI. The result of optimizing the design with the same environment with isolation given in Table XI is shown in Table XII.
By comparing Tables
End-Winding Insulation
Conclusion
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