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3D modeling of an HVDC converter transformer and its application on the electrical field of windings subject to voltage harmonics
Electrical Power and Energy Systems 117 (2020) 105581
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
3D modeling of an HVDC converter transformer and its application on the electrical field of windings subject to voltage harmonics
T
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Weidong Suna, Lijun Yanga, , Firuz Zareb, YanWei Xiac, Li Chenga, Kuiyu Zhoua a
State Key Laboratory of Power Equipment & System Security and New Technology, College of Electrical Engineering, Chongqing University, Chongqing 400044, China School of Information Technology and Electrical Engineering, The University of Queensland, St Lucia, Qld 4072, Australia c Hebei Electric Power Research Institute, Shijiazhuang 050000, Hebei, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Converter transformer Voltage harmonics HVDC Voltage changing rate Partial discharge
Converter transformers are key facilities in HVDC systems. The operation condition of converter transformers is more complex than that of conventional AC transformers. Because of the superposition of the voltage harmonics, the valve voltage wave is more serrated than a pure AC voltage. As a result, the insulation system withstands severe stress. Several tasks are accomplished in this study to obtain a better understanding of the electrical field distribution in converter transformers as well as analyze the effects of voltage harmonics on the main insulation of converter transformers. First, an HVDC system with a voltage of ± 800 kV is simulated and the voltage harmonics at the valve side are obtained. The simulation is verified based on the measurement in a real ± 800 kV HVDC substation. The harmonics in valve winding are mainly characterized by components with frequencies of 6k, 12k, 12k ± 1, and 6k ± 1. Then, a full-scaled 3D converter transformer model is proposed. The electric field of the proposed model is calculated under AC, DC, and polarity reversal voltages. Compared with conventional 2D models, the inhomogeneity of the electric field distribution is obtained, and the difference can reach 30%. Finally, the valve voltage waveform is applied on the 3D model to calculate the electric field using finite element method. Results show that the voltage harmonics in valve side further deepen the inhomogeneity of electric field in insulation structures. Moreover, a high value of voltage changing rate (dV / dt ) with value 2.96 kV/ μs is observed in simulation. The influence of defects on partial discharge within insulation materials under the voltage harmonics is also analyzed.
1. Introduction The converter transformer is an important facility in a HVDC system. Since the first HVDC system in China Southern Power Grid was constructed in 2003 [1], an increasing number of DC transmission lines have been applied in Chinese power systems. Compared with the conventional condition of AC systems, the converter transformers in HVDC systems need to withstand not only the AC and DC voltages but also the voltage harmonics. Thus, manufacturers and researchers have increasing concerns over the insulation safety of converter transformers. Harmonics in AC power systems increase because of the increasing of the non-linear loads. However, in HVDC systems, the harmonic pollution is much more severe due to the operation of rectifiers or inverters. The voltage waveform, especially at the valve side of the converter transformers, is mostly different from that in traditional AC transformers. Not only harmonics will cause high losses in converter transformers, but also the distorted valve voltage may increase the danger of
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insulation fault [2–4]. They also lead to commutation failures for the entire system [5]. Thirty faults have occurred in operational converter transformers in the State Grid and China South Power Grid by 2016 due to the severe operation condition [6–8]. Meanwhile, a report made by CIGRE stated that 14 out of 22 failures happened in the valve windings of converter transformers [9]. Much effort has been conducted by now to investigate the voltage harmonics in HVDC systems for guaranteeing the safety of power systems. In field conditions, various methods are adopted to eliminate or suppress harmonics by applying filters or developing novel configurations of the converter transformer winding [10,11]. As for the analysis of the converter transformer insulation system, the finite element method (FEM) is widely adopted to calculate the electric field distribution of the inner structures. Simulations based on 2D models have been established to calculate the electric field of converter transformers in recent years [12–14]. In these studies, the 2D models are usually applied to calculate the electric field distribution in
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.ijepes.2019.105581 Received 13 November 2018; Received in revised form 20 June 2019; Accepted 26 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
Electrical Power and Energy Systems 117 (2020) 105581
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pressboard and oil under AC, DC, and polarity reversal voltages. The anisotropic characteristic of insulation materials is also considered to obtain more reliable results [15]. Genetic algorithms are applied in simulation as well to optimize the insulation structure designing [16]. However, the influence of the voltage harmonics on converter transformer insulation system is rarely researched. Meanwhile, in those 2D models, the inner insulation structures are partly given to guarantee computation feasibility of the models in simulation. In real conditions, the inner structure of converter transformers is asymmetric, and the voltage superposition exists between insulation parts. Moreover, the 2D models provide only a section of the insulation structure, in which the electric field cannot be fully represented. The electric field analysis of converter transformers based on 3D models is rarely presented. As for the converter transformer manufacturers, 3D models may have been proposed and analyzed, but the models are confidential and are unavailable to researchers. Thus, for a better understanding of the converter transformers under voltage harmonics condition, it is necessary to build a 3D model for analysis. Several works are essential in this study to conduct the analysis of the influence of voltage harmonics on inner insulation in converter transformers. First, a ± 800 kV HVDC system will be simulated to obtain the valve voltage waves in converter transformers. Experiment will be conducted in a real ± 800kV HVDC system to obtain the valve voltage waves to verify the validation and rationality of the simulated results. The voltage harmonics in both simulation and experiment will be compared and analyzed. Then, a 3D converter transformer model will be established to conduct electric field analysis with harmonics. The electric field under AC, DC, and polarity reversal voltages will be calculated using the finite element method to ensure that the electric field is within the designing limitation. Finally, the simulated valve voltage is applied on the valve winding in the 3D model, to calculate the electric field of this model for estimating the influence of voltage harmonics on the insulation system.
Fig. 1. Simulation model of a ± 800 kV HVDC system.
Y/Δ configuration and two with Y/Y configuration). Furthermore, every two different transformers and two valve bridges form into a 12pulse voltage conversion system with a voltage level of ± 400 kV. Thus, a voltage of ± 800 kV can be reached by connecting two 12-pulse converters in series. The capacities and other parameters of converter transformers of inverter sides are shown in Table 1. The rated voltage of AC1 system is 525 kV. Converter transformers with rated voltages of line winding of 520 kV and valve winding of 165.65 kV are placed at the inverter side. The line voltage at the inverter side is 520 kV. In this paper, to analyze the voltage harmonics generated from the operation of converters, no external harmonic source is introduced. The AC system is simulated by connecting the voltage source and impedance in series according to Thevenin’s theorem. The control system is also the key component for the voltage conversion. The control flow of the HVDC system simulation is based on the benchmark model published by CIGRE in the 1990s [17–20]. The current margin control is adopted in this system. A current controller and given reference value are involved in the voltage conversion of rectifier. First, DC current measured from transmission line is compared with the current reference output of voltage-dependent current limit unit. The PI controller generates the alpha-order with an angle between 1° and 170°. The alpha-order signal is sent to the six-pulse converters of rectifier. Under normal condition, this control adjusts DC current in a short time to guarantee that the current is within the limits. As for the inverter side, a current controller and a gamma controller are applied for voltage conversion from DC to AC. The basic rules of the current controller of inverter are similar to those in rectifier control. The measured DC current is compared with the reference current with a current margin of 0.1 pu. Then, the inverter PI controller generates the alpha-order signal with a limitation between 110° and 150°. Meanwhile, the implementation of a gamma controller is introduced into this system. The measured value of gamma is compared with the reference value. Then, the error signal is sent to the PI controller to
2. Modeling of a ± 800 kV HVDC system 2.1. Basic definition of harmonics in power systems The voltage harmonic components are mainly produced by the switching of electronic facilities. High-frequency harmonic components can affect the grid current and the voltage. Harmonics are periodic nonsinusoidal signals with a frequency that is an integral multiple of the fundamental frequency in power systems. To evaluate the electric quality of the voltage in power systems, indexes such as harmonic distortion (HD) and total harmonic distortion (THD) are introduced to depict the influence of harmonics and given by the following equations: N = 50
THDU =
HDh =
∑h = 2 Uh2 U1
× 100%
Uh × 100% U1
(1)
(2)
where h is the harmonic order of the fundamental wave, U1 is the root mean square value of the fundamental wave, and Uh is the effective value of the h-order voltage harmonic. In an HVDC system, harmonics are determined by various factors and not only injected from the AC system but also generated by the application of six-pulse converters [6].
Table1 Parameters of converter transformer at inverter side in simulation and measurement.
2.2. General introduction of the HVDC simulation In this study, a bipolar DC transmission system with a rated capacity of 5000 MW and a voltage level of ± 800 kV is simulated to obtain the valve voltage of converter transformers. The rated DC current of each polarity is 3.125 kA. Fig. 1 shows that, at the rectifier side, each polarity is equipped with four converter transformers for each phase (two with 2
Voltage level
Simulation
Measurement
Rated voltage line winding Rated voltage valve winding Rated capacity impedance
520 kV 165.65 kV 750.63 MVA 0.18 pu
520 kV 165.65 kV 390.43 MVA 0.18 pu
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results indicate that the AC voltage is no longer the standard sinusoidal wave, and various harmonics are involved in the valve side. Measurements have been conducted in a real ± 800 kV HVDC substation to verify the rationality and validity of simulation results of harmonics in valve winding. The substation is called Huainan Converter Station, which is in Jiangsu Province and is one of the West to East Power Transmission Projects of China. The substation, located at the end of transmission terminal in the HVDC system, works as an inverter to convert the DC voltage to the AC one. The rated capacity of this converter station is 6400 MW. As for the inverter side, the rated voltage of AC system is 520 kV, and the rated voltages of both line windings are 520 and 165.65 kV, respectively. The AC part of the valve voltage has been measured from the first two converter transformers (with Y/Y and Y/Δ configurations, respectively) at negative polarity. The measured and simulated voltages are at the same voltage level even if the shape of the simulated curves is slightly different from the measured ones. Harmonics of the waveforms above are extracted by fast Fourier transform and depicted in Fig. 2. The harmonic order is considered to be fifty times the fundamental frequency of 50 Hz. The voltage harmonics in valve winding are made of two parts: one is the result of current harmonics in line winding, and the other is from the operation of converters. First, with the operation of converters, voltage harmonics with orders of 6k and 12k are generated (k is an integer that represents a multiple of the harmonic frequency relative to the fundamental frequency). Second, harmonics with orders 12k ± 1 and 6k ± 1 are mainly originated from the current harmonics of line winding. Other harmonics with orders 5, 7, 17, 19… will be balanced in the output of each 12-pulse converter due to the parallel connection of Y/Y and Y/Δ configurations between converter transformers. However, in each phase, harmonics still exist in the valve winding of the converter transformer. The voltage harmonics in the valve winding shown in Table 2 are divided into five major categories with orders of 12k ± 1, 6k ± 1, 12k, 6k, and 3k (k = 1, 2, …). In each category, the HD of each frequency is calculated using Eq. (2), and the THD is also presented. Evidently, the voltage harmonics with lower frequencies have higher magnitude. The THD of the simulation is higher than that in the measurement. According to the results of Y/Δ configuration, in the simulation, the highest harmonic distortion of 6k and 12k are 9.19% and 5.62%, respectively. In the measurement, these two values are 10.64% and 10.35%. As for categories 6k ± 1, 12k ± 1, the highest harmonic distortions in simulation are higher than the measurement. As for the Y/Y configuration, the highest harmonic distortion of 12k in simulation is 10.43%, which is higher than the value 3.52% obtained in measurement. Compared with the serrated voltage in Y/Δ configuration, the voltage waveform in Y/Y configuration is also featured with rippled wave. Considering the similar harmonic content in both two configurations, this kind of difference is caused by the various phase in voltage superposition. Overall, the calculation in Table 2 shows an excellent agreement between the simulation and the measurement, even if the harmonics distortion obtained in the simulation is slightly higher than the measurement. This disparity may be explained by the following reasons: First, the harmonics are strictly restrained by the application of filters in a real HVDC system. Second, in the real system, various loads are linked to the real AC system, wherein harmonics may be generated by other factors. The voltage harmonics originate from different sources. As for the harmonics with orders of 6k are generated by the 6-pulse converters. When two 6-pulse bridges are connected in series to form into a 12pulse converter, the harmonics with orders 12k will be generated. But as for the output, the DC voltage will not contain the harmonics with an order of 6k due to the offset of the voltage superposition. However, harmonics with orders of 6k and 12k still exist in the valve windings of each phase of the transformers. As for the voltage harmonics with
Fig. 2. Valve voltage comparison between simulation and measurement (a) Y/Δ configuration (b) Y/Y configuration.
generate another alpha-order signal, which is also within the limitation from 110° to 150°. The minimum value will be chosen from the two alpha signals as the firing-pulse signal for the inverters. The time step of the simulation is 50 μs, and the entire simulation duration is 5 s. Both the DC voltage and current in outputs at the positive polarity of rectifier side are 796 kV and 3.1 kA, respectively. The power output of two polarities is 4935 MW. The angle of alpha order in rectifier is 5.00°–5.040°, and the gamma order in inverter is within 16.580°–16.620°.
2.3. Voltage harmonics in the valve winding The valve voltage waves for Y/Δ and Y/Y configurations are shown in Fig. 2(a) and (b), respectively. The DC voltage is 695 kV for Y/Δ connection and that is 496 kV for Y/Y connection. The simulation 3
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Table 2 Harmonic content in simulation and experiment. Harmonic orders
Harmonics distortion (HD) % Simulation
Measurement
Y/Y
Y/Δ
Y/Y
Y/Δ
5 7 17 19 29 31 41 43
14.91 13.03 1.83 2.21 2.74 1.94 1.99 2.06
14.91 13.24 1.68 2.43 2.46 1.93 1.86 2.25
5.22 5.14 3.42 3.55 2.08 1.88 0.53 0.09
3.57 3.68 3.6 3.39 2.64 2.34 1.06 0.89
11 13 23 25 35 37 47 49
7.44 6.49 3.86 3.58 1.17 1.08 1.18 1.15
7.23 6.46 3.77 3.72 1.17 1.25 0.93 1.15
4.5 3.82 2.89 2.85 1.4 1.06 0.39 0.89
4.56 3.56 3.25 2.81 1.96 1.59 0.12 0.1
6k
6 18 30 42
9.17 4.76 2.07 0.73
9.19 4.76 2.056 0.74
11.06 2.61 2.92 0.94
10.64 2.34 2.59 1.03
12k
12 24 36 48
10.43 4.13 5.56 3.14
5.62 2.23 3.02 1.70
3.52 0.75 0.33 0.81
10.35 1.46 2.58 3.66
3k
3 9 15 21 27 33 39 45
34.50 3.03 5.09 3.31 1.18 2.40 1.58 0.78
34.58 3.19 5.27 3.18 1.34 2.55 1.36 1.08
31.07 5.92 2.88 1.11 3.83 1.04 1.41 0.86
29.81 7.21 3.63 1.92 3.28 1.62 0.74 1.6
45.57
44.36
36.79
36.37
6k ± 1
12k ± 1
THD %
Fig. 3. Two basic arrangements of converter transformer T – Tap winding L – Line winding V – Valve winding.
converter transformers, namely the type of single-phase with three windings and the type of single-phase with dual windings. The choice of the converter transformer is mainly determined by the total capacity of the HVDC system, that is, the capacity of each converter transformer. When the capacity of each converter transformer is less than 300 MVA, the single-phase transformer with three windings is generally adopted, the winding arrangement is shown as Fig. 3(a). However, when the voltage level of the HVDC system is higher than ± 500 kV, the capacity of the HVDC system will be promoted to 3000 MW. Under this circumstance, once the converter transformer with three windings is adopted, the capacity of each transformer will be around 600 MVA, causing the transformer too big for transportation. Thus, the singlephase converter transformer with dual windings, is commonly selected when voltage level is higher than ± 500 kV. In Fig. 3(b), the valve winding is placed at the outermost circle to ensure the insulation strength [21]. 3.2. Theoretical analysis for model simplification As for the composition of main insulation of converter transformers, the pressboards are adopted to form the surrounding barriers in the insulation system between windings. In transformer designing and manufacturing, the thickness of each pressboard generally ranges from 1.6 mm to 6 mm [22]. The thickness 5 mm is generally adopted in 2D models to calculate the electric field [16]. When the thickness of each pressboard is given as 5 mm in a full-scale 3D model, the difficulty of the grid meshing will be increased. Meanwhile, the number of tetrahedral finite elements will exceed 200 million after the grid meshing. To improve the computing efficiency, an appropriate simplification is necessary before the simulation. In a transformer tank, cylinder pressboards are placed between windings at certain distance to form into the main insulation system. Insulation oil are filled between pressboards. Theoretically, the pressboard barriers of the main insulation are similar with the plate capacitance, which is illustrated in Fig. 4(a). The pressboard is represented by the shadow area with thickness d1 and the thickness of insulation oil is d2. When the distance between the electrodes remain unchanged, as the thickness of both pressboards is doubled, the number of pressboards is halved. In ideal condition, when the two structures are applied with
orders of 12k ± 1 and 6k ± 1, are mainly derived from the current harmonics of the line winding. When the current harmonics flow through the line winding, voltage harmonics are generated because of the impedance of the line winding. Thus, voltage harmonics will be injected into valve winding from the line winding. Harmonics with an order of 3k mainly come from the power system of line side. Because various voltage harmonics are involved in the valve voltage, thereby causing the voltage curve serrated. Moreover, not only the frequencies of the harmonics are different from the fundamental wave, but also phase varies among the voltage harmonics. Although the valve voltage is obtained in measurement, the measurement step is 100 μs. In the simulation, the data size of the voltage wave is doubled by the finer step 50 μs. Considering the simulated wave can provide more information as well as the difference between simulation and measurement is acceptable. Therefore, in the subsequent finite element simulation, the simulated waveform will be used to calculate the electric field for analysis. 3. 3D converter transformer model After obtaining the valve voltage curve in the simulated HVDC system, a 3D converter transformer model is discussed and proposed in this section. 3.1. Winding arrangement of converter transformers
Fig. 4. Equivalent plate electrode of pressboard-oil system (a) Thinner insulation layers (b) Thicker insulation layers.
In general, there are two types of winding arrangement for 4
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Fig. 5. Electric field comparison between two different thickness settings (a) Each pressboard 5 mm. (b) Each pressboard 10 mm.
the same voltage, the electric field strength in pressboard or oil of Fig. 4(b) will be the same with that in Fig. 4(a). Simulation is conducted to verify the validation of the simplification. A 2D model is established in Fig. 5(a), there are 22 pressboards in total between the valve and line windings, the thickness of each pressboard is 5 mm. Then based on the same dimension, the model is simplified to 11 pressboards, the thickness of each pressboard is increased to 10 mm. The width of oil duct between pressboards is also doubled. The conductivity and relative permittivity of mineral oil and pressboard are shown in Table 3. By giving the same material settings, both the original and simplified models are calculated under the same AC and DC voltages. The AC and DC voltages are 902 kV and 1246 kV, respectively, which are calculated in accordance with the standard IEC 60076-57. The outcomes in Fig. 5 indicate the electric field distribution in these two models are similar with each other regardless AC or DC voltage. The electric field distribution along the red arrow lines in Fig. 5 is acquired. In AC withstand voltage simulation, the electric field in the insulation oil area between pressboards is shown in Fig. 6(a). The dash curve shows that results of the simplified model is highly in consistent with the former one. As for the DC withstand voltage simulation, the electric field in pressboard is slightly changed after the simplification. However, the deviation is within 10%, which is acceptable for further analysis. Therefore, the simplification can be adopted in model from the aspect of electric field equivalence. The converter 3D model is established according to [21] and depicted in Fig. 7, where the iron core and the pressboard barriers are built. The thickness of each pressboard between windings is given as 10 mm. In the simplified 3D model, the number of tetrahedral finite elements of the converter transformer model is 3.6 × 107 , and the number of nodes is 6.1 × 106 . Compared with the total number of tetrahedral finite elements in the 3D model when pressboard thickness is given as 5 mm, the computation of the simplified model has been greatly reduced.
Fig. 6. Comparison of the electric field distribution (a) AC withstand voltage (b) DC withstand voltage.
Fig. 7. Sections of converter transformer model.
4. Results and analysis 4.1. Electric field of the proposed model under withstand voltage test The simulation is conducted to calculate the electric field of the inner insulation structure under AC, DC, and polarity reversal voltages. The model is placed in a cubic zone, which is assigned as the mineral oil in simulation. In the simulation, the iron core, tap winding, line winding and the boundary of oil area are all grounded. Figs. 8 and 9 show the electric field of the simulation results under DC and AC withstand tests, respectively. As shown in Fig. 8, the insulation oil undertakes more electric stress than the pressboard. The highest electric field in oil is 7.58 kV/mm, which is within the limitation 8 kV/mm. In the DC voltage simulation, the pressboards undertake
Table 3 Parameters of materials in simulation. Materials
Relative permittivity [24]
Conductivity [23] (S/m)
Mineral oil (23 °C) Insulation paper (23 °C)
2.3 4.1
1.3337 × 10−14 1.77791 × 10−17
5
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Fig. 9. Electric field of inner insulation structure (a) Electric field of zone I (b) Electric field of top view.
Fig. 8. Electric field distribution of AC test (kV/mm) (a) Electric field of zone I (b) Electric field of zone II (c) Electric field of zone III. Fig. 10. Electric field in oil along the electrostatic rings in AC withstand test.
most of the electric stress. The highest electric field value near to the electrostatic ring is around 30 kV/mm. In this model, the highest electric field appears in the pressboard, which is near the bottom of the valve winding with the value of around 35.2 kV/mm. This difference can be traced to the simplification on the bottom of the winding in the modeling process. However, the highest electric field still within the designing limitation 40 kV/mm. which is introduced in the power transformer manual book published by Baoding Tianwei Baobian Electric Co., Ltd. Further illustration is depicted in Fig. 10, in which the electric field in oil around the electro-static rings is obtained. The lowest electric field of the outer ring is around 5 kV/mm, whereas the highest electric field is 6.5 kV/mm. The simulation results indicate that electric superposition is involved in this model. The electric field in oil around the winding of AC withstand test is asymmetric. The electric field between two windings is evidently smaller than those in other parts. The difference of electric field is nearly 30%, this result cannot be obtained in conventional 2D models. In the polarity reversal test, the time step for calculation is set to 3 s. The polarity reversal test involves four stages in accordance with the IEC 60076-57 standard. First, the voltage rises at time point 60 s from zero to −966 kV in 1 min and remains for 90 min. Then, it rises from the negative to the positive side with a voltage level of +966 kV in 1 min and remains for 90 min. Thereafter, the voltage starts to change from +966 kV to −966 kV in 1 min and remains for 45 min. Finally,
Fig. 11. Electric field in polarity reversal condition at zone III.
the voltage drops to zero in 1 min. The electric field distribution in the polarity test when voltage changes from −966 kV to +966 kV is shown in Fig. 11. First, the pressboards share the majority of the electric stress. When the voltage starts to change from the positive to the negative side, the electric field 6
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Fig. 12. Electric field under hybrid voltage at zone III.
in insulation oil increases first and then decreases. When the voltage reaches to the positive side and remains in steady state again, the pressboards will share most of the electric stress. The electric field in insulation paper and oil remains within the limitation. 4.2. Electric field of the proposed model with voltage harmonics The results above indicate that the maximum electric field of the proposed model under withstand voltages is all within the design limitation. In other words, the proposed model can guarantee the calculated electric field for further analysis. The voltage waveform of the converter transformer with both Y/Δ and Y/Y configuration is applied in simulation. To analyze the simulation results, several lines are depicted, which are shown in Fig. 12. The horizontal line A starts from the middle height of the outer electro-static ring and ends at the outermost pressboard. As for the line B, it links the points with maximum curvature in insulation structures from the electro-static ring to the outermost pressboard. Meanwhile, considering the inhomogeneity of electric field distribution, two circles are also given in Fig. 12. The circle C locates in maximum curvature of the pressboard, where the data around the pressboard will be obtained. Similarly, the circle D locates in the insulation paper of middle height of the electro-static ring. In Fig. 13, the surface maps show the electric field along the given lines in one period (0.02 s). According to the electric field along lines A and B, the pressboard withstands most of the electric field because of the DC voltage. Along the given line B, the electric field increases first and then decreases, and the highest electric field is 16.55 kV/mm. The electric field is also influenced by the AC component, the highest electric field of 16.55 kV/mm drops to 15.9 kV/mm with the changing rate of 6% in one period (0.02 s). Moreover, the electric field in the pressboard, which is the closest to the winding compared to other parts, the electric field fluctuates more than in other parts. For example, at the initial point of line A, the highest electric field is 13.33 kV/mm and the lowest value is 11.98 kV/mm. The fluctuation rate caused by AC voltage is around 10%. However, when it comes to the end of the line A, the highest value is 10.88 kV/mm and the lowest one is 10.41 kV/mm with the changing rate of 4.3%. This finding indicates that the electric field of the insulation materials close to the voltage source is more sensitive to the voltage change than those in the other parts. According to the inhomogeneous electric field distribution along the circle C, where the highest value is 16.33 kV/mm and the lowest value is 11.78 kV/mm with a difference of 27.8%. Meanwhile, the serrated outline clearly indicates the influence of the applied voltage waveform on the electric field. The lowest value is 15.32 kV/mm with a difference of 6.2%. However, according to circle D, the results are more evident. The highest electric field is 13.61 kV/mm, and the lowest value is 10.62 kV/mm. The difference of the electric filed caused by the structure is 22%. And the electric field changes from the maximum value 13.61 kV/mm to the minimum value 12.11 kV/mm in 0.02 s is also observed, where the difference caused by the applied voltage is 11.02%. It further helps to indicate that the electric in the insulation structure which are closer to the voltage source has higher fluctuation rate than other parts. Similarly, the electric field of Y/Y configuration acquired as Fig. 14.
Fig. 13. Electric field distribution of Y/Δ configuration.
Due to the lower DC voltage component, the electric field level is lower than the one in Y/Δ configuration. The way of the electric field distribution along the lines A and B is nearly the same. Compare with the results in Fig. 13, the outline of the surface maps obtained by circles C and D is also serrated. As for the circle C, the highest value is 10.51 kV/ mm and the lowest value is 7.69 kV/mm with a difference of 26.8%. And from the results t circle D, the difference caused by the structure is 22.20%. And the fluctuation rate of the electric field caused by the applied voltage is around 11.7%.
4.3. Influence of voltage harmonics on dV/dt and partial discharge In HVDC systems, not only the voltage harmonics could cause commutation failures [5], but also play an important role in insulation degradation. The obtained electric field above also indicates the fast transient of the applied voltage. The insulation degradation rate will be promoted by the voltage waveform featured with high changing rate. And the behavior of the partial discharge is also different from the one 7
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Fig. 14. Electric field distribution of the Y/Y configuration.
Fig. 15. Voltage changing rate along given lines and circles of Y/Δ configuration.
under low frequency AC voltage [25]. High magnitude PD pulses with superimposed voltage harmonics are observed through experiments in [26]. Experiment has been conducted in research [27] to analyze the influence of voltage charging rate (dV/dt) on the partial discharge (PD) in motor insulation materials. It pointed out that the voltage rise time have a significant influence on PD in motor insulation, as the magnitude of the PD of short rise time voltage (2.5 kV/us) is nearly seven times of the one under AC voltage (50 Hz). Even though the frequency of the harmonics in HVDC systems is not as high as the one in the operation of adjustable speed drives. But due to the superposition of harmonics with different frequencies as well as various phase angles, causing the distorted voltage waveform is also characterized with this kind of feature. Therefore, the voltage changing rate (dV/dt) is obtained in simulation for analysis.
From the line A to the circle D, the voltage changing rate in one period (0.02 s) of the Y/Δ configuration is depicted in Fig. 15. Several voltage changing rate peaks occur at the given period. According to results acquired by lines A and B, the voltage changing rate varies considerably from the lowest value of −0.08 kV/μs to the highest value of 1.42 kV/μs as time progresses. The voltage changing rate in insulation structures decreases when the distance to the winding increases. The voltage changing rate of circles C and D is also very high, and the highest voltage changing rate (dV/dt) is already 1.430 kV/μs. It is nearly unchanged because the relative position to the voltage source is constant. However, when the relative distance to the voltage source increases, the voltage changing rate in circle C varies slightly but remains at a high level. 8
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Fig. 17. Schematic diagram of PD event (a) Before PD (b) After PD.
process, the electric field in the cavity will decreases, when Ecav is lower than the extinction field Eext , the discharge stops. After the PD, free charges will accumulate on the cavity surface, result in opposite electric field Es . Therefore, before the next PD, the electric field in the cavity can be written as:
Ecav = fc E0 + Es
(3)
When Ecav has the opposite direction of Es , free charges accumulated on the surface tend to move to the center of upper (lower) cavity surface. Under this circumstance, the charge decay is less likely to happen. Because of the free charges on the cavity surface, next PD is likely to occur. Under the AC voltage, the direction of the electric field fc E0 can change. In this way, free charges will tend to move towards the opposite direction and charge recombination will be accomplished, resulting in decrement of the surface charge. Then the electric field in the cavity will increase again until the next PD occurs [28]. However, as for the voltage in converter transformer, normally DC component voltage is also involved. The DC voltage strengthens the PD activity under the AC half cycle with same DC polarity and inhibits the PD under the AC half cycle with opposite DC polarity [29]. According to the results in Section 2, the DC component is higher than the AC voltage, and there is no negative half cycle for the hybrid voltage. Therefore, after each PD, free charges accumulated on the cavity surface are hard to be neutralized. Due to the high voltage changing rate, the voltage will rise rapidly and decrease sharply. More free charges will be generated during the voltage increment. However, the time duration is not enough for the propagation of an electron avalanche. Those free charges will further accumulate on the cavity surface until the next PD is triggered. In this way, because of the applied voltage waveform and the electric field Es , the density of the PD will be lowered. But once a PD is triggered, the magnitude of the PD will be enhanced because of the accumulated free charges. In a long-term operation, the insulation material at the defects will degrades faster because of the higher impact from each PD. Considering the higher dV/dt is observed at the insulation parts which are closer to the winding, the quality of the insulation material of those parts should be carefully treated to ensure the operation safety.
Fig. 16. Voltage changing rate along given lines and circles of Y/Y configuration.
The voltage changing rate of the Y/Y configuration is also acquired and shown in Fig. 16. According to the results in lines A and B, the highest value is 2.960 kV/μs, which is already twice times of the one in Fig. 15. Similarly, the voltage changing rate along circles C and D is still nearly unchanged. However, the density of high peaks is lower than the one in Y/Δ configuration. Generally, PD happens at defects of the insulation materials, such as voids, cavities, cracks and joints. In this paper, the PD that occurs in a cavity within the insulation materials is discussed. According to Fig. 17, when the electric field in a cavity Ecav exceeds the inception field (Einc ) as well as there are effective free electrons to initiate an electron avalanche, a PD will be triggered. Before the discharge, the electric field in the cavity Ecav is equal to fc E0 , where fc is a dimensionless factor of the applied field in the cavity. During the PD
5. Conclusion A ± 800 kV HVDC system is simulated, and the measurement in a real ± 800 kV HVDC system is also conducted. The voltage harmonics in the valve winding are analyzed, which are mainly characterized by components with frequencies of 6k, 12k, 12k ± 1, and 6k ± 1. A 3D converter transformer model is built, and the electric field of the inner insulation structure is simulated. The inhomogeneity of electric field distribution exists in the insulation materials as the difference of the electric field along the electrostatic rings is nearly 30%. This result cannot be obtained in conventional 2D models. Based on the 3D model, both the insulation coordination and insulation allowance 9
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can be better determined in transformer designing. The electric field of the proposed 3D model is calculated by introducing the simulated valve voltage. The inhomogeneity of electric field distribution of insulation structure is further enhanced by the voltage harmonics. The insulation parts which are closer to the winding will have higher voltage changing rate. Moreover, the highest voltage changing rate in both Y/Δ configuration and Y/Y configuration is obtained, which is 1.43 kV/μs and 2.96 kV/μs respectively. Especially the waveform of Y/Δ configuration is featured with higher density of large voltage changing rate. This kind of high changing rate will increase the magnitude of partial discharge and accelerate the degradation of insulation materials. The results indicate that the influence of the defects within the insulation materials are more obvious under the voltage harmonics. The work accomplished in this paper may provide the corresponding reference for the application of insulation materials in converter transformers. Experiment is also necessary to study the voltage changing rate on partial discharge in future.
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
Declaration of Competing Interest
[17]
The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
[18] [19]
Acknowledgment
[20]
This project was supported by National Key R&D Program of China (2016YFB09008040), and the State Grid Science & Technology Project (5204DY170010).
[21] [22]
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[1] Yuncai Lu, Wei Li. Study on condition assessment and fault diagnosis for converter transformers. In: High Voltage Engineering and Application (ICHVE), 2016 IESEE International Conference on. IEEE; 2016. [2] Liu Yaqing, et al. Calculation method of winding eddy-current losses for high-voltage direct current converter transformers. IET Electr Power Appl 2016;10(6):488–97. [3] Azizian Fard M, Reid AJ, Hepburn DM. Analysis of HVDC superimposed harmonic voltage effects on partial discharge behavior in solid dielectric media. IEEE Trans Dielectrics Electr Insulation 2017;24(1):7–16. [4] Azizian Fard M, et al. Influence of voltage harmonic phenomena on partial discharge behavior at HVDC. IEEE International Conference on Dielectrics (ICD). vol. 1. 2016. [5] Wang Feng, Liu Tian-qi, Li Xing-yuan. Decreasing the frequency of HVDC commutation failures caused by harmonics. IET Power Electron 2017;10(2):215–21. [6] Van Hertem D, Ghandhari M, Delimar M. Technical limitations towards a SuperGrid –A European Prospective. In: IEEE International Energy Conference and Exhibition (EnergyCon); Dec. 2010. p. 302–09. [7] Bartnikas R. Partial discharges: their mechanism, detection and measurement. IEEE Trans Dielectr Electr Insul 2002;9:763–808. [8] Florkowski M, Florkowska B. Distortion of partial-discharge images caused by high-
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voltage harmonics. In: IEE Proc. Generation, Transmission and Distribution, vol. 153; 2006. p. 171–80. Bastos GM, Brandao JC, Santelli J, Albuquerque R, Arenare S, Mendes JC, et al. HVDC converter transformer performance on ITAIPU system. In: Presented at the B4-201, CIGRE Paris Symp., Paris, France; 2006. Shayma'a M. Kamal, et al. Influence of a proposed converter transformer on harmonic suppression for HVDC systems. In: IEEE Power Systems Conference (MEPCON), 2017 Nineteenth International Middle East; 2017. Luo, Longfu, et al. A novel method of harmonic suppression in the AC/DC transmission system based on novel converter transformer. International Conference on Power System Technology; 2006. Gang Liu, et al. Quasi-static electric field computation of converter transformer by adaptive time step FEM. In: IEEE International Conference on Computational Problem-Solving (ICCP); 2010. Zhang Liang-xian, et al. Research on transient electric field distribution of converter transformer valve side winding under polarity reversal. In: IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP); 2013. Pu Zi-Heng, et al. Analysis of voltage distribution characteristics in UHVDC converter transformer winding based on the reduced-scale model. IEEE Trans Magn 2014;50(11):1–5. Yan Li, et al. The calculate of nonlinear and anisotropic electric field in valve side winding of converter transformer. In: International Conference on Electrical Machines and Systems (ICEMS); 2011. Yea Manje, et al. Design optimization for the insulation of HVDC converter transformers under composite electric stresses. IEEE Trans Dielectr Electr Insul 2018;25(1):253–62. Sood VK, Khatri V, Jin K. EMTP modelling of CIGRE benchmark based HVDC transmission system operating with weak AC systems. In: IEEE International Conference on Power Electronics, Drives and Energy Systems for Industrial Growth, vol.1; 1995. p. 426–432. Szechtman M, Wess T, Thio CV. A benchmark model for HVDC system studies. In: International Conference on Ac and Dc Power Transmission. IET; 2002. p. 374–78. Faruque MO, Zhang Y, Dinavahi V. Detailed modeling of CIGRE HVDC benchmark system using PSCAD/EMTDC and PSB/SIMULINK. IEEE Trans Power Delivery 2005;21(1):378–87. Louie KW, Wilson P, Wachal RW, et al. HVDC power system harmonic analysis in the time and frequency domains. In: IEEE International Conference on Power System Technology, Powercon; 2007. p. 1–8. Jin Zheng, Da Wan, et al. Converter transformer and manufacturing technology, 1st ed. State grid of China; 2016. p. 79–80. IEC 60641-3-1. Pressboard and presspaper for electrical purposes – Part 3: Specifications for individual materials – Sheet 1: Requirements for pressboard, types B.0.1, B.0.3, B.2.1, B.3.1, B.3.3, B.4.1, B.4.3, B.5.1, B.5.3 and B.6.1; 2008. GB/T 1410-2006. Methods of test for volume resistivity and surface resistivity of solid electrical insulating materials. [S]l 2006. GB 11297.11-1989 Test method for the dielectric constant of pyroelectric materials. [S]; 1989. Fabiani D, Cavallini A, Mazzanti G, Montanari GC. The effect of charge mobility on partial discharge characteristics of enamelled wires for PWM-controlled motors. In: Proceedings of the 2004 IEEE International Conference on Solid Dielectrics, 2004. ICSD 2004, Toulouse, France, Vol.2; 2004. p. 856–59. Florkowski M, Florkowska B, Furgal J, Zydron P. Impact of high voltage harmonics on interpretation of partial discharge patterns. IEEE Trans Dielectr Electr Insul December 2013;20(6):2009–16. Wang P, Cavallini A, Montanari GC, Wu G. Effect of rise time on PD pulse features under repetitive square wave voltages. IEEE Trans Dielectr Electr Insul 2013;20(1):245–54. Pan C, Chen G, Tang J, Wu K. Numerical modeling of partial discharges in a solid dielectric-bounded cavity: a review. IEEE Trans Dielectr Electr Insul 2019;26(3):981–1000. Li J, Han X, Liu Z, Yao X, Li Y. PD characteristics of oil-pressboard insulation under AC and DC mixed voltage. IEEE Trans Dielectr Electr Insul 2016;23(1):444–50.
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
3D modeling of an HVDC converter transformer and its application on the electrical field of windings subject to voltage harmonics
T
⁎
Weidong Suna, Lijun Yanga, , Firuz Zareb, YanWei Xiac, Li Chenga, Kuiyu Zhoua a
State Key Laboratory of Power Equipment & System Security and New Technology, College of Electrical Engineering, Chongqing University, Chongqing 400044, China School of Information Technology and Electrical Engineering, The University of Queensland, St Lucia, Qld 4072, Australia c Hebei Electric Power Research Institute, Shijiazhuang 050000, Hebei, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Converter transformer Voltage harmonics HVDC Voltage changing rate Partial discharge
Converter transformers are key facilities in HVDC systems. The operation condition of converter transformers is more complex than that of conventional AC transformers. Because of the superposition of the voltage harmonics, the valve voltage wave is more serrated than a pure AC voltage. As a result, the insulation system withstands severe stress. Several tasks are accomplished in this study to obtain a better understanding of the electrical field distribution in converter transformers as well as analyze the effects of voltage harmonics on the main insulation of converter transformers. First, an HVDC system with a voltage of ± 800 kV is simulated and the voltage harmonics at the valve side are obtained. The simulation is verified based on the measurement in a real ± 800 kV HVDC substation. The harmonics in valve winding are mainly characterized by components with frequencies of 6k, 12k, 12k ± 1, and 6k ± 1. Then, a full-scaled 3D converter transformer model is proposed. The electric field of the proposed model is calculated under AC, DC, and polarity reversal voltages. Compared with conventional 2D models, the inhomogeneity of the electric field distribution is obtained, and the difference can reach 30%. Finally, the valve voltage waveform is applied on the 3D model to calculate the electric field using finite element method. Results show that the voltage harmonics in valve side further deepen the inhomogeneity of electric field in insulation structures. Moreover, a high value of voltage changing rate (dV / dt ) with value 2.96 kV/ μs is observed in simulation. The influence of defects on partial discharge within insulation materials under the voltage harmonics is also analyzed.
1. Introduction The converter transformer is an important facility in a HVDC system. Since the first HVDC system in China Southern Power Grid was constructed in 2003 [1], an increasing number of DC transmission lines have been applied in Chinese power systems. Compared with the conventional condition of AC systems, the converter transformers in HVDC systems need to withstand not only the AC and DC voltages but also the voltage harmonics. Thus, manufacturers and researchers have increasing concerns over the insulation safety of converter transformers. Harmonics in AC power systems increase because of the increasing of the non-linear loads. However, in HVDC systems, the harmonic pollution is much more severe due to the operation of rectifiers or inverters. The voltage waveform, especially at the valve side of the converter transformers, is mostly different from that in traditional AC transformers. Not only harmonics will cause high losses in converter transformers, but also the distorted valve voltage may increase the danger of
⁎
insulation fault [2–4]. They also lead to commutation failures for the entire system [5]. Thirty faults have occurred in operational converter transformers in the State Grid and China South Power Grid by 2016 due to the severe operation condition [6–8]. Meanwhile, a report made by CIGRE stated that 14 out of 22 failures happened in the valve windings of converter transformers [9]. Much effort has been conducted by now to investigate the voltage harmonics in HVDC systems for guaranteeing the safety of power systems. In field conditions, various methods are adopted to eliminate or suppress harmonics by applying filters or developing novel configurations of the converter transformer winding [10,11]. As for the analysis of the converter transformer insulation system, the finite element method (FEM) is widely adopted to calculate the electric field distribution of the inner structures. Simulations based on 2D models have been established to calculate the electric field of converter transformers in recent years [12–14]. In these studies, the 2D models are usually applied to calculate the electric field distribution in
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.ijepes.2019.105581 Received 13 November 2018; Received in revised form 20 June 2019; Accepted 26 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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pressboard and oil under AC, DC, and polarity reversal voltages. The anisotropic characteristic of insulation materials is also considered to obtain more reliable results [15]. Genetic algorithms are applied in simulation as well to optimize the insulation structure designing [16]. However, the influence of the voltage harmonics on converter transformer insulation system is rarely researched. Meanwhile, in those 2D models, the inner insulation structures are partly given to guarantee computation feasibility of the models in simulation. In real conditions, the inner structure of converter transformers is asymmetric, and the voltage superposition exists between insulation parts. Moreover, the 2D models provide only a section of the insulation structure, in which the electric field cannot be fully represented. The electric field analysis of converter transformers based on 3D models is rarely presented. As for the converter transformer manufacturers, 3D models may have been proposed and analyzed, but the models are confidential and are unavailable to researchers. Thus, for a better understanding of the converter transformers under voltage harmonics condition, it is necessary to build a 3D model for analysis. Several works are essential in this study to conduct the analysis of the influence of voltage harmonics on inner insulation in converter transformers. First, a ± 800 kV HVDC system will be simulated to obtain the valve voltage waves in converter transformers. Experiment will be conducted in a real ± 800kV HVDC system to obtain the valve voltage waves to verify the validation and rationality of the simulated results. The voltage harmonics in both simulation and experiment will be compared and analyzed. Then, a 3D converter transformer model will be established to conduct electric field analysis with harmonics. The electric field under AC, DC, and polarity reversal voltages will be calculated using the finite element method to ensure that the electric field is within the designing limitation. Finally, the simulated valve voltage is applied on the valve winding in the 3D model, to calculate the electric field of this model for estimating the influence of voltage harmonics on the insulation system.
Fig. 1. Simulation model of a ± 800 kV HVDC system.
Y/Δ configuration and two with Y/Y configuration). Furthermore, every two different transformers and two valve bridges form into a 12pulse voltage conversion system with a voltage level of ± 400 kV. Thus, a voltage of ± 800 kV can be reached by connecting two 12-pulse converters in series. The capacities and other parameters of converter transformers of inverter sides are shown in Table 1. The rated voltage of AC1 system is 525 kV. Converter transformers with rated voltages of line winding of 520 kV and valve winding of 165.65 kV are placed at the inverter side. The line voltage at the inverter side is 520 kV. In this paper, to analyze the voltage harmonics generated from the operation of converters, no external harmonic source is introduced. The AC system is simulated by connecting the voltage source and impedance in series according to Thevenin’s theorem. The control system is also the key component for the voltage conversion. The control flow of the HVDC system simulation is based on the benchmark model published by CIGRE in the 1990s [17–20]. The current margin control is adopted in this system. A current controller and given reference value are involved in the voltage conversion of rectifier. First, DC current measured from transmission line is compared with the current reference output of voltage-dependent current limit unit. The PI controller generates the alpha-order with an angle between 1° and 170°. The alpha-order signal is sent to the six-pulse converters of rectifier. Under normal condition, this control adjusts DC current in a short time to guarantee that the current is within the limits. As for the inverter side, a current controller and a gamma controller are applied for voltage conversion from DC to AC. The basic rules of the current controller of inverter are similar to those in rectifier control. The measured DC current is compared with the reference current with a current margin of 0.1 pu. Then, the inverter PI controller generates the alpha-order signal with a limitation between 110° and 150°. Meanwhile, the implementation of a gamma controller is introduced into this system. The measured value of gamma is compared with the reference value. Then, the error signal is sent to the PI controller to
2. Modeling of a ± 800 kV HVDC system 2.1. Basic definition of harmonics in power systems The voltage harmonic components are mainly produced by the switching of electronic facilities. High-frequency harmonic components can affect the grid current and the voltage. Harmonics are periodic nonsinusoidal signals with a frequency that is an integral multiple of the fundamental frequency in power systems. To evaluate the electric quality of the voltage in power systems, indexes such as harmonic distortion (HD) and total harmonic distortion (THD) are introduced to depict the influence of harmonics and given by the following equations: N = 50
THDU =
HDh =
∑h = 2 Uh2 U1
× 100%
Uh × 100% U1
(1)
(2)
where h is the harmonic order of the fundamental wave, U1 is the root mean square value of the fundamental wave, and Uh is the effective value of the h-order voltage harmonic. In an HVDC system, harmonics are determined by various factors and not only injected from the AC system but also generated by the application of six-pulse converters [6].
Table1 Parameters of converter transformer at inverter side in simulation and measurement.
2.2. General introduction of the HVDC simulation In this study, a bipolar DC transmission system with a rated capacity of 5000 MW and a voltage level of ± 800 kV is simulated to obtain the valve voltage of converter transformers. The rated DC current of each polarity is 3.125 kA. Fig. 1 shows that, at the rectifier side, each polarity is equipped with four converter transformers for each phase (two with 2
Voltage level
Simulation
Measurement
Rated voltage line winding Rated voltage valve winding Rated capacity impedance
520 kV 165.65 kV 750.63 MVA 0.18 pu
520 kV 165.65 kV 390.43 MVA 0.18 pu
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results indicate that the AC voltage is no longer the standard sinusoidal wave, and various harmonics are involved in the valve side. Measurements have been conducted in a real ± 800 kV HVDC substation to verify the rationality and validity of simulation results of harmonics in valve winding. The substation is called Huainan Converter Station, which is in Jiangsu Province and is one of the West to East Power Transmission Projects of China. The substation, located at the end of transmission terminal in the HVDC system, works as an inverter to convert the DC voltage to the AC one. The rated capacity of this converter station is 6400 MW. As for the inverter side, the rated voltage of AC system is 520 kV, and the rated voltages of both line windings are 520 and 165.65 kV, respectively. The AC part of the valve voltage has been measured from the first two converter transformers (with Y/Y and Y/Δ configurations, respectively) at negative polarity. The measured and simulated voltages are at the same voltage level even if the shape of the simulated curves is slightly different from the measured ones. Harmonics of the waveforms above are extracted by fast Fourier transform and depicted in Fig. 2. The harmonic order is considered to be fifty times the fundamental frequency of 50 Hz. The voltage harmonics in valve winding are made of two parts: one is the result of current harmonics in line winding, and the other is from the operation of converters. First, with the operation of converters, voltage harmonics with orders of 6k and 12k are generated (k is an integer that represents a multiple of the harmonic frequency relative to the fundamental frequency). Second, harmonics with orders 12k ± 1 and 6k ± 1 are mainly originated from the current harmonics of line winding. Other harmonics with orders 5, 7, 17, 19… will be balanced in the output of each 12-pulse converter due to the parallel connection of Y/Y and Y/Δ configurations between converter transformers. However, in each phase, harmonics still exist in the valve winding of the converter transformer. The voltage harmonics in the valve winding shown in Table 2 are divided into five major categories with orders of 12k ± 1, 6k ± 1, 12k, 6k, and 3k (k = 1, 2, …). In each category, the HD of each frequency is calculated using Eq. (2), and the THD is also presented. Evidently, the voltage harmonics with lower frequencies have higher magnitude. The THD of the simulation is higher than that in the measurement. According to the results of Y/Δ configuration, in the simulation, the highest harmonic distortion of 6k and 12k are 9.19% and 5.62%, respectively. In the measurement, these two values are 10.64% and 10.35%. As for categories 6k ± 1, 12k ± 1, the highest harmonic distortions in simulation are higher than the measurement. As for the Y/Y configuration, the highest harmonic distortion of 12k in simulation is 10.43%, which is higher than the value 3.52% obtained in measurement. Compared with the serrated voltage in Y/Δ configuration, the voltage waveform in Y/Y configuration is also featured with rippled wave. Considering the similar harmonic content in both two configurations, this kind of difference is caused by the various phase in voltage superposition. Overall, the calculation in Table 2 shows an excellent agreement between the simulation and the measurement, even if the harmonics distortion obtained in the simulation is slightly higher than the measurement. This disparity may be explained by the following reasons: First, the harmonics are strictly restrained by the application of filters in a real HVDC system. Second, in the real system, various loads are linked to the real AC system, wherein harmonics may be generated by other factors. The voltage harmonics originate from different sources. As for the harmonics with orders of 6k are generated by the 6-pulse converters. When two 6-pulse bridges are connected in series to form into a 12pulse converter, the harmonics with orders 12k will be generated. But as for the output, the DC voltage will not contain the harmonics with an order of 6k due to the offset of the voltage superposition. However, harmonics with orders of 6k and 12k still exist in the valve windings of each phase of the transformers. As for the voltage harmonics with
Fig. 2. Valve voltage comparison between simulation and measurement (a) Y/Δ configuration (b) Y/Y configuration.
generate another alpha-order signal, which is also within the limitation from 110° to 150°. The minimum value will be chosen from the two alpha signals as the firing-pulse signal for the inverters. The time step of the simulation is 50 μs, and the entire simulation duration is 5 s. Both the DC voltage and current in outputs at the positive polarity of rectifier side are 796 kV and 3.1 kA, respectively. The power output of two polarities is 4935 MW. The angle of alpha order in rectifier is 5.00°–5.040°, and the gamma order in inverter is within 16.580°–16.620°.
2.3. Voltage harmonics in the valve winding The valve voltage waves for Y/Δ and Y/Y configurations are shown in Fig. 2(a) and (b), respectively. The DC voltage is 695 kV for Y/Δ connection and that is 496 kV for Y/Y connection. The simulation 3
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Table 2 Harmonic content in simulation and experiment. Harmonic orders
Harmonics distortion (HD) % Simulation
Measurement
Y/Y
Y/Δ
Y/Y
Y/Δ
5 7 17 19 29 31 41 43
14.91 13.03 1.83 2.21 2.74 1.94 1.99 2.06
14.91 13.24 1.68 2.43 2.46 1.93 1.86 2.25
5.22 5.14 3.42 3.55 2.08 1.88 0.53 0.09
3.57 3.68 3.6 3.39 2.64 2.34 1.06 0.89
11 13 23 25 35 37 47 49
7.44 6.49 3.86 3.58 1.17 1.08 1.18 1.15
7.23 6.46 3.77 3.72 1.17 1.25 0.93 1.15
4.5 3.82 2.89 2.85 1.4 1.06 0.39 0.89
4.56 3.56 3.25 2.81 1.96 1.59 0.12 0.1
6k
6 18 30 42
9.17 4.76 2.07 0.73
9.19 4.76 2.056 0.74
11.06 2.61 2.92 0.94
10.64 2.34 2.59 1.03
12k
12 24 36 48
10.43 4.13 5.56 3.14
5.62 2.23 3.02 1.70
3.52 0.75 0.33 0.81
10.35 1.46 2.58 3.66
3k
3 9 15 21 27 33 39 45
34.50 3.03 5.09 3.31 1.18 2.40 1.58 0.78
34.58 3.19 5.27 3.18 1.34 2.55 1.36 1.08
31.07 5.92 2.88 1.11 3.83 1.04 1.41 0.86
29.81 7.21 3.63 1.92 3.28 1.62 0.74 1.6
45.57
44.36
36.79
36.37
6k ± 1
12k ± 1
THD %
Fig. 3. Two basic arrangements of converter transformer T – Tap winding L – Line winding V – Valve winding.
converter transformers, namely the type of single-phase with three windings and the type of single-phase with dual windings. The choice of the converter transformer is mainly determined by the total capacity of the HVDC system, that is, the capacity of each converter transformer. When the capacity of each converter transformer is less than 300 MVA, the single-phase transformer with three windings is generally adopted, the winding arrangement is shown as Fig. 3(a). However, when the voltage level of the HVDC system is higher than ± 500 kV, the capacity of the HVDC system will be promoted to 3000 MW. Under this circumstance, once the converter transformer with three windings is adopted, the capacity of each transformer will be around 600 MVA, causing the transformer too big for transportation. Thus, the singlephase converter transformer with dual windings, is commonly selected when voltage level is higher than ± 500 kV. In Fig. 3(b), the valve winding is placed at the outermost circle to ensure the insulation strength [21]. 3.2. Theoretical analysis for model simplification As for the composition of main insulation of converter transformers, the pressboards are adopted to form the surrounding barriers in the insulation system between windings. In transformer designing and manufacturing, the thickness of each pressboard generally ranges from 1.6 mm to 6 mm [22]. The thickness 5 mm is generally adopted in 2D models to calculate the electric field [16]. When the thickness of each pressboard is given as 5 mm in a full-scale 3D model, the difficulty of the grid meshing will be increased. Meanwhile, the number of tetrahedral finite elements will exceed 200 million after the grid meshing. To improve the computing efficiency, an appropriate simplification is necessary before the simulation. In a transformer tank, cylinder pressboards are placed between windings at certain distance to form into the main insulation system. Insulation oil are filled between pressboards. Theoretically, the pressboard barriers of the main insulation are similar with the plate capacitance, which is illustrated in Fig. 4(a). The pressboard is represented by the shadow area with thickness d1 and the thickness of insulation oil is d2. When the distance between the electrodes remain unchanged, as the thickness of both pressboards is doubled, the number of pressboards is halved. In ideal condition, when the two structures are applied with
orders of 12k ± 1 and 6k ± 1, are mainly derived from the current harmonics of the line winding. When the current harmonics flow through the line winding, voltage harmonics are generated because of the impedance of the line winding. Thus, voltage harmonics will be injected into valve winding from the line winding. Harmonics with an order of 3k mainly come from the power system of line side. Because various voltage harmonics are involved in the valve voltage, thereby causing the voltage curve serrated. Moreover, not only the frequencies of the harmonics are different from the fundamental wave, but also phase varies among the voltage harmonics. Although the valve voltage is obtained in measurement, the measurement step is 100 μs. In the simulation, the data size of the voltage wave is doubled by the finer step 50 μs. Considering the simulated wave can provide more information as well as the difference between simulation and measurement is acceptable. Therefore, in the subsequent finite element simulation, the simulated waveform will be used to calculate the electric field for analysis. 3. 3D converter transformer model After obtaining the valve voltage curve in the simulated HVDC system, a 3D converter transformer model is discussed and proposed in this section. 3.1. Winding arrangement of converter transformers
Fig. 4. Equivalent plate electrode of pressboard-oil system (a) Thinner insulation layers (b) Thicker insulation layers.
In general, there are two types of winding arrangement for 4
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Fig. 5. Electric field comparison between two different thickness settings (a) Each pressboard 5 mm. (b) Each pressboard 10 mm.
the same voltage, the electric field strength in pressboard or oil of Fig. 4(b) will be the same with that in Fig. 4(a). Simulation is conducted to verify the validation of the simplification. A 2D model is established in Fig. 5(a), there are 22 pressboards in total between the valve and line windings, the thickness of each pressboard is 5 mm. Then based on the same dimension, the model is simplified to 11 pressboards, the thickness of each pressboard is increased to 10 mm. The width of oil duct between pressboards is also doubled. The conductivity and relative permittivity of mineral oil and pressboard are shown in Table 3. By giving the same material settings, both the original and simplified models are calculated under the same AC and DC voltages. The AC and DC voltages are 902 kV and 1246 kV, respectively, which are calculated in accordance with the standard IEC 60076-57. The outcomes in Fig. 5 indicate the electric field distribution in these two models are similar with each other regardless AC or DC voltage. The electric field distribution along the red arrow lines in Fig. 5 is acquired. In AC withstand voltage simulation, the electric field in the insulation oil area between pressboards is shown in Fig. 6(a). The dash curve shows that results of the simplified model is highly in consistent with the former one. As for the DC withstand voltage simulation, the electric field in pressboard is slightly changed after the simplification. However, the deviation is within 10%, which is acceptable for further analysis. Therefore, the simplification can be adopted in model from the aspect of electric field equivalence. The converter 3D model is established according to [21] and depicted in Fig. 7, where the iron core and the pressboard barriers are built. The thickness of each pressboard between windings is given as 10 mm. In the simplified 3D model, the number of tetrahedral finite elements of the converter transformer model is 3.6 × 107 , and the number of nodes is 6.1 × 106 . Compared with the total number of tetrahedral finite elements in the 3D model when pressboard thickness is given as 5 mm, the computation of the simplified model has been greatly reduced.
Fig. 6. Comparison of the electric field distribution (a) AC withstand voltage (b) DC withstand voltage.
Fig. 7. Sections of converter transformer model.
4. Results and analysis 4.1. Electric field of the proposed model under withstand voltage test The simulation is conducted to calculate the electric field of the inner insulation structure under AC, DC, and polarity reversal voltages. The model is placed in a cubic zone, which is assigned as the mineral oil in simulation. In the simulation, the iron core, tap winding, line winding and the boundary of oil area are all grounded. Figs. 8 and 9 show the electric field of the simulation results under DC and AC withstand tests, respectively. As shown in Fig. 8, the insulation oil undertakes more electric stress than the pressboard. The highest electric field in oil is 7.58 kV/mm, which is within the limitation 8 kV/mm. In the DC voltage simulation, the pressboards undertake
Table 3 Parameters of materials in simulation. Materials
Relative permittivity [24]
Conductivity [23] (S/m)
Mineral oil (23 °C) Insulation paper (23 °C)
2.3 4.1
1.3337 × 10−14 1.77791 × 10−17
5
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Fig. 9. Electric field of inner insulation structure (a) Electric field of zone I (b) Electric field of top view.
Fig. 8. Electric field distribution of AC test (kV/mm) (a) Electric field of zone I (b) Electric field of zone II (c) Electric field of zone III. Fig. 10. Electric field in oil along the electrostatic rings in AC withstand test.
most of the electric stress. The highest electric field value near to the electrostatic ring is around 30 kV/mm. In this model, the highest electric field appears in the pressboard, which is near the bottom of the valve winding with the value of around 35.2 kV/mm. This difference can be traced to the simplification on the bottom of the winding in the modeling process. However, the highest electric field still within the designing limitation 40 kV/mm. which is introduced in the power transformer manual book published by Baoding Tianwei Baobian Electric Co., Ltd. Further illustration is depicted in Fig. 10, in which the electric field in oil around the electro-static rings is obtained. The lowest electric field of the outer ring is around 5 kV/mm, whereas the highest electric field is 6.5 kV/mm. The simulation results indicate that electric superposition is involved in this model. The electric field in oil around the winding of AC withstand test is asymmetric. The electric field between two windings is evidently smaller than those in other parts. The difference of electric field is nearly 30%, this result cannot be obtained in conventional 2D models. In the polarity reversal test, the time step for calculation is set to 3 s. The polarity reversal test involves four stages in accordance with the IEC 60076-57 standard. First, the voltage rises at time point 60 s from zero to −966 kV in 1 min and remains for 90 min. Then, it rises from the negative to the positive side with a voltage level of +966 kV in 1 min and remains for 90 min. Thereafter, the voltage starts to change from +966 kV to −966 kV in 1 min and remains for 45 min. Finally,
Fig. 11. Electric field in polarity reversal condition at zone III.
the voltage drops to zero in 1 min. The electric field distribution in the polarity test when voltage changes from −966 kV to +966 kV is shown in Fig. 11. First, the pressboards share the majority of the electric stress. When the voltage starts to change from the positive to the negative side, the electric field 6
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Fig. 12. Electric field under hybrid voltage at zone III.
in insulation oil increases first and then decreases. When the voltage reaches to the positive side and remains in steady state again, the pressboards will share most of the electric stress. The electric field in insulation paper and oil remains within the limitation. 4.2. Electric field of the proposed model with voltage harmonics The results above indicate that the maximum electric field of the proposed model under withstand voltages is all within the design limitation. In other words, the proposed model can guarantee the calculated electric field for further analysis. The voltage waveform of the converter transformer with both Y/Δ and Y/Y configuration is applied in simulation. To analyze the simulation results, several lines are depicted, which are shown in Fig. 12. The horizontal line A starts from the middle height of the outer electro-static ring and ends at the outermost pressboard. As for the line B, it links the points with maximum curvature in insulation structures from the electro-static ring to the outermost pressboard. Meanwhile, considering the inhomogeneity of electric field distribution, two circles are also given in Fig. 12. The circle C locates in maximum curvature of the pressboard, where the data around the pressboard will be obtained. Similarly, the circle D locates in the insulation paper of middle height of the electro-static ring. In Fig. 13, the surface maps show the electric field along the given lines in one period (0.02 s). According to the electric field along lines A and B, the pressboard withstands most of the electric field because of the DC voltage. Along the given line B, the electric field increases first and then decreases, and the highest electric field is 16.55 kV/mm. The electric field is also influenced by the AC component, the highest electric field of 16.55 kV/mm drops to 15.9 kV/mm with the changing rate of 6% in one period (0.02 s). Moreover, the electric field in the pressboard, which is the closest to the winding compared to other parts, the electric field fluctuates more than in other parts. For example, at the initial point of line A, the highest electric field is 13.33 kV/mm and the lowest value is 11.98 kV/mm. The fluctuation rate caused by AC voltage is around 10%. However, when it comes to the end of the line A, the highest value is 10.88 kV/mm and the lowest one is 10.41 kV/mm with the changing rate of 4.3%. This finding indicates that the electric field of the insulation materials close to the voltage source is more sensitive to the voltage change than those in the other parts. According to the inhomogeneous electric field distribution along the circle C, where the highest value is 16.33 kV/mm and the lowest value is 11.78 kV/mm with a difference of 27.8%. Meanwhile, the serrated outline clearly indicates the influence of the applied voltage waveform on the electric field. The lowest value is 15.32 kV/mm with a difference of 6.2%. However, according to circle D, the results are more evident. The highest electric field is 13.61 kV/mm, and the lowest value is 10.62 kV/mm. The difference of the electric filed caused by the structure is 22%. And the electric field changes from the maximum value 13.61 kV/mm to the minimum value 12.11 kV/mm in 0.02 s is also observed, where the difference caused by the applied voltage is 11.02%. It further helps to indicate that the electric in the insulation structure which are closer to the voltage source has higher fluctuation rate than other parts. Similarly, the electric field of Y/Y configuration acquired as Fig. 14.
Fig. 13. Electric field distribution of Y/Δ configuration.
Due to the lower DC voltage component, the electric field level is lower than the one in Y/Δ configuration. The way of the electric field distribution along the lines A and B is nearly the same. Compare with the results in Fig. 13, the outline of the surface maps obtained by circles C and D is also serrated. As for the circle C, the highest value is 10.51 kV/ mm and the lowest value is 7.69 kV/mm with a difference of 26.8%. And from the results t circle D, the difference caused by the structure is 22.20%. And the fluctuation rate of the electric field caused by the applied voltage is around 11.7%.
4.3. Influence of voltage harmonics on dV/dt and partial discharge In HVDC systems, not only the voltage harmonics could cause commutation failures [5], but also play an important role in insulation degradation. The obtained electric field above also indicates the fast transient of the applied voltage. The insulation degradation rate will be promoted by the voltage waveform featured with high changing rate. And the behavior of the partial discharge is also different from the one 7
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Fig. 14. Electric field distribution of the Y/Y configuration.
Fig. 15. Voltage changing rate along given lines and circles of Y/Δ configuration.
under low frequency AC voltage [25]. High magnitude PD pulses with superimposed voltage harmonics are observed through experiments in [26]. Experiment has been conducted in research [27] to analyze the influence of voltage charging rate (dV/dt) on the partial discharge (PD) in motor insulation materials. It pointed out that the voltage rise time have a significant influence on PD in motor insulation, as the magnitude of the PD of short rise time voltage (2.5 kV/us) is nearly seven times of the one under AC voltage (50 Hz). Even though the frequency of the harmonics in HVDC systems is not as high as the one in the operation of adjustable speed drives. But due to the superposition of harmonics with different frequencies as well as various phase angles, causing the distorted voltage waveform is also characterized with this kind of feature. Therefore, the voltage changing rate (dV/dt) is obtained in simulation for analysis.
From the line A to the circle D, the voltage changing rate in one period (0.02 s) of the Y/Δ configuration is depicted in Fig. 15. Several voltage changing rate peaks occur at the given period. According to results acquired by lines A and B, the voltage changing rate varies considerably from the lowest value of −0.08 kV/μs to the highest value of 1.42 kV/μs as time progresses. The voltage changing rate in insulation structures decreases when the distance to the winding increases. The voltage changing rate of circles C and D is also very high, and the highest voltage changing rate (dV/dt) is already 1.430 kV/μs. It is nearly unchanged because the relative position to the voltage source is constant. However, when the relative distance to the voltage source increases, the voltage changing rate in circle C varies slightly but remains at a high level. 8
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Fig. 17. Schematic diagram of PD event (a) Before PD (b) After PD.
process, the electric field in the cavity will decreases, when Ecav is lower than the extinction field Eext , the discharge stops. After the PD, free charges will accumulate on the cavity surface, result in opposite electric field Es . Therefore, before the next PD, the electric field in the cavity can be written as:
Ecav = fc E0 + Es
(3)
When Ecav has the opposite direction of Es , free charges accumulated on the surface tend to move to the center of upper (lower) cavity surface. Under this circumstance, the charge decay is less likely to happen. Because of the free charges on the cavity surface, next PD is likely to occur. Under the AC voltage, the direction of the electric field fc E0 can change. In this way, free charges will tend to move towards the opposite direction and charge recombination will be accomplished, resulting in decrement of the surface charge. Then the electric field in the cavity will increase again until the next PD occurs [28]. However, as for the voltage in converter transformer, normally DC component voltage is also involved. The DC voltage strengthens the PD activity under the AC half cycle with same DC polarity and inhibits the PD under the AC half cycle with opposite DC polarity [29]. According to the results in Section 2, the DC component is higher than the AC voltage, and there is no negative half cycle for the hybrid voltage. Therefore, after each PD, free charges accumulated on the cavity surface are hard to be neutralized. Due to the high voltage changing rate, the voltage will rise rapidly and decrease sharply. More free charges will be generated during the voltage increment. However, the time duration is not enough for the propagation of an electron avalanche. Those free charges will further accumulate on the cavity surface until the next PD is triggered. In this way, because of the applied voltage waveform and the electric field Es , the density of the PD will be lowered. But once a PD is triggered, the magnitude of the PD will be enhanced because of the accumulated free charges. In a long-term operation, the insulation material at the defects will degrades faster because of the higher impact from each PD. Considering the higher dV/dt is observed at the insulation parts which are closer to the winding, the quality of the insulation material of those parts should be carefully treated to ensure the operation safety.
Fig. 16. Voltage changing rate along given lines and circles of Y/Y configuration.
The voltage changing rate of the Y/Y configuration is also acquired and shown in Fig. 16. According to the results in lines A and B, the highest value is 2.960 kV/μs, which is already twice times of the one in Fig. 15. Similarly, the voltage changing rate along circles C and D is still nearly unchanged. However, the density of high peaks is lower than the one in Y/Δ configuration. Generally, PD happens at defects of the insulation materials, such as voids, cavities, cracks and joints. In this paper, the PD that occurs in a cavity within the insulation materials is discussed. According to Fig. 17, when the electric field in a cavity Ecav exceeds the inception field (Einc ) as well as there are effective free electrons to initiate an electron avalanche, a PD will be triggered. Before the discharge, the electric field in the cavity Ecav is equal to fc E0 , where fc is a dimensionless factor of the applied field in the cavity. During the PD
5. Conclusion A ± 800 kV HVDC system is simulated, and the measurement in a real ± 800 kV HVDC system is also conducted. The voltage harmonics in the valve winding are analyzed, which are mainly characterized by components with frequencies of 6k, 12k, 12k ± 1, and 6k ± 1. A 3D converter transformer model is built, and the electric field of the inner insulation structure is simulated. The inhomogeneity of electric field distribution exists in the insulation materials as the difference of the electric field along the electrostatic rings is nearly 30%. This result cannot be obtained in conventional 2D models. Based on the 3D model, both the insulation coordination and insulation allowance 9
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can be better determined in transformer designing. The electric field of the proposed 3D model is calculated by introducing the simulated valve voltage. The inhomogeneity of electric field distribution of insulation structure is further enhanced by the voltage harmonics. The insulation parts which are closer to the winding will have higher voltage changing rate. Moreover, the highest voltage changing rate in both Y/Δ configuration and Y/Y configuration is obtained, which is 1.43 kV/μs and 2.96 kV/μs respectively. Especially the waveform of Y/Δ configuration is featured with higher density of large voltage changing rate. This kind of high changing rate will increase the magnitude of partial discharge and accelerate the degradation of insulation materials. The results indicate that the influence of the defects within the insulation materials are more obvious under the voltage harmonics. The work accomplished in this paper may provide the corresponding reference for the application of insulation materials in converter transformers. Experiment is also necessary to study the voltage changing rate on partial discharge in future.
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
Declaration of Competing Interest
[17]
The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
[18] [19]
Acknowledgment
[20]
This project was supported by National Key R&D Program of China (2016YFB09008040), and the State Grid Science & Technology Project (5204DY170010).
[21] [22]
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