Characteristic Analysis of Electromagnetic Force in an HTS Field Coil Using a Performance Evaluation System

Abstract

A performance evaluation system (PES) can experimentally test the structural stability and magnetic field effects of HTS coils against high magnetic fields and electromagnetic forces before mounting the HTS coils on a large-capacity rotating machine. This paper deals with the characteristic analysis of electromagnetic force in an HTS field coil for a 10 MW Class HTS Wind Power Generator using PES. Based on the designed 10 MW class HTS wind power generator, the HTS coils are manufactured and installed in the PES by a support structure, which is designed considering the electromagnetic force (torque) and heat loads in the HTS coil. To check the stress and deformation in the support structure caused by the electromagnetic force generated from the coil, strain gauge sensors were attached to the support structure and measured under full-load conditions. As a result, the maximum magnetic field and electromagnetic force are 2.8 T and 71 kN, respectively. Compared to the analysis results, the magnetic field and generated electromagnetic force in the HTS coil were the same under no-load and full-load conditions. These results will be effectively used to study and fabricate high magnetic field coils for HTS applications, as well as the PES being fabricated.

1. Introduction

Wind power has recently been included as a renewable resource that uses key technologies to deliver energy to industry [1]. For a long time, wind power generation has been dominated by onshore wind power, but, recently, wind turbine generators have been installed offshore which use high-quality wind or air currents while minimizing interference with residents [2,3,4]. Offshore wind power systems have great development potential, but the energy costs of offshore wind power development significantly increase because the systems must be built in the sea. Huge development costs are an obstacle to offshore wind power generation [5,6,7].

Therefore, one of the biggest challenges the offshore wind energy sector faces is to reduce the cost of energy [8,9]. To solve that problem, the development of large wind turbines is a topic of great interest for the wind industry. To reduce wind power conversion costs, large wind turbines are preferred. Expanding the capacity of an individual turbine enhances its energy density, boosts the wind farm’s efficiency, and lowers the cost of supporting infrastructure [10,11,12,13,14].

High-temperature superconducting (HTS) generators, which utilize coils capable of high current and magnetic flux density, are well-suited for large-scale wind power systems and can considerably decrease both volume and weight compared to conventional generators [15,16,17,18]. While HTS generators have primarily been explored through design concepts and prototype testing in wind turbines, their effects on generator performance in practice remain uncertain due to the lack of detailed design and operational experience [19,20,21,22,23,24].

A performance evaluation system (PES) can experimentally test the structural stability and magnetic field effects of HTS coils against high magnetic fields and electromagnetic forces before mounting the HTS coils on a large-capacity rotating machine.

This paper deals with the characteristic analysis of electromagnetic force in an HTS field coil for a 10 MW Class HTS Wind Power Generator using PES. A 10 MW class HTS generator was developed, and the PES was designed in accordance with its specifications. This design process utilized electromagnetic analysis conducted with the 3D finite element method (FEM). The PES incorporates three HTS field coils arranged to form a pole pair, considering the effects of mutual inductance and magnetic field distribution among the coils [25]. During operation at maximum torque, specific field current and three-phase current values were applied to both the HTS field coil and the armature coil [26]. The HTS field coil structure is subjected to mechanical stress and strain due to the Lorentz force and torque [27]. Following the design of the 10 MW HTS wind power generator, the HTS coils were manufactured and installed into the PES, supported by a structure designed to accommodate the electromagnetic forces and thermal loads affecting the HTS coil. To check the stress and deformation in the support structure caused by the electromagnetic force generated from the coil, strain gauge sensors were attached to the support structure and measured under full-load conditions. As a result, the operating current and maximum magnetic flux density applied to the field coil were 221 A and 2.8 T, respectively. To simulate load conditions, when a three-phase current was applied to the armature coil while the operating current was passing through the field coil, forces were generated in the field coil and armature coil, and the vertical and horizontal forces were 70.6 kN and 3 kN, respectively. Compared to the analysis results, the magnetic field and generated electromagnetic forces in the HTS coil were the same under no-load and full-load conditions. These results will be instrumental in advancing the study and development of high magnetic field coils for HTS applications, in addition to supporting the fabrication of the PES.

2. Design of the PES Based on the 10 MW HTS Generator

2.1. Specifications of the 10 MW Class HTS Generator

The design of the 10 MW class HTS generator was carried out using a FEM program.

Table 1. Specifications of the 10 MW class HTS generator.

Items	Value
Rated output power	10.5 MW
Rotating speed	9.6 rpm
Rated torque	10.57 MN·m
Rated Line to Line voltage	6.6 kV
Rated armature current	918 A
Number of poles	40
Rated frequency	3.2 Hz
Effective length	700 mm
Air gap	18 mm
Weight of generator	124.8 ton

represents the specifications of this generator, including a rotating speed of 9.6 rpm and a rated torque of 10.57 MN·m [27].

Further details on the HTS field coil for this generator are provided in

Table 2. Specifications of the HTS field coil for 10 MW class HTS generator.

Items	Value
Operating temperature	35 K
Number of turns per layer	310
Number of layers per coil	4
Operating current	221 A
Safety margin	35%
Total length of the HTS wire (40 pole)	115.64 km
Width of HTS field coil	405 mm
Height of HTS field coil	62 mm
Effective length of HTS field coil	700 mm
Material of bobbins	Aluminum
Material of supports	GFRP
Material of salient pole	50PN470
Material of back iron	50PN470

, which specifies an operating temperature of 35 K and a current of 221 A. The generator requires 115.64 km of HTS wire, which is coated with 0.15 mm thick and 12 mm wide flat conductive tape. The bobbin, supporter, and salient pole materials are aluminum, GFRP, and 50PN470, respectively.

Figure 1 shows the configuration and magnetic field distribution through FEM analysis of a designed 10 MW class HTS wind power generator. As shown in Figure 1, the maximum magnetic field of the generator is 2.8 T at the HTS coil. The highest magnetic field occurs at the curved point of the HTS field coil. The magnetic flux density in the gap between the rotor and the armature is 0.8 T, and the magnetic flux density at the salient pole is 3.5 T.

Figure 1 shows the configuration and magnetic field distribution of the designed 10 MW class HTS wind power generator, as analyzed by FEM. The figure shows that the maximum magnetic field of 2.8 T occurs at the HTS coil, with the highest magnetic field observed at the coil’s curved section. The magnetic flux density is 0.8 T in the gap between the rotor and the armature, and 3.5 T at the salient pole.

The operating field current of the designed HTS field coil was selected by confirming the critical current according to the specifications of the superconducting wire. When considering the angle of the wire and the vertical magnetic field, the value of the operating current was selected as 221 A with a margin of 35%. In addition, the axial length of the HTS field coil is 700 mm, the number of turns is 310 turns, and the number of layers of the HTS coil per pole is four layers. The gap from the HTS field coil to the cryostat was designed to be 40 mm.

$$F_{tan}={\displaystyle \frac{T}{r\times p}}$$

(1)

where F_tan is the tangential force of the HTS field coil, T is the torque of the generator, r is the radius of the generator, and p is the number of poles of the generator.

The torque, radius, and number of poles of the designed 10 MW class HTS generator are 10.34 MN·m, 3.6 m, and 40 poles, respectively. According to Equation (1), the calculated tangential force of the HTS field coil of the designed HTS generator is 70.6 kN.

Figure 2 shows the amplitude and direction of the tangential and radial forces acting on the HTS coil under both no-load and full-load conditions. The Lorentz force, which acts perpendicular to the directions of the magnetic field and current in the HTS field coil, is evident. In a no-load condition, the armature current is zero, meaning the magnetic field remains unchanged. Conversely, in a full-load condition, the armature current influences the magnetic field, leading to variations.

Under the full-load condition, the HTS field coil experiences maximum radial and tangential forces of 70.6 kN and 3 kN, respectively. Consequently, the tangential force exceeds the radial force due to the high magnetic field and substantial torque of the large-capacity HTS generator. The forces observed in the stator section mirror those in the rotor section but in opposite directions for both radial and tangential forces.

2.2. Design of the PES

Figure 3 illustrates the concept and benefits of the PES, which is tailored to the specifications of the 10 MW class HTS generator. The PES features three HTS coils arranged to form a pole-pair, taking into account the mutual inductance and magnetic field distribution among the coils. By employing three HTS coils, the force characteristics and magnetic distribution of the central HTS coil closely resemble those of the complete generator. Consequently, the HTS field coil’s characteristics can be accurately replicated in simulations using the PES.

The PES has the advantage of being able to check problems with the torque of a wind power generator, as well as the basic output characteristics and magnetic pattern of the superconducting coil. In addition, evaluation methods that can be applied in the armature section include armature output characteristics and measurement of armature torque and support force according to the armature winding method, armature material, air gap, and wind speed.

Evaluation items for the field coil include magnetic flux density, maximum cooling temperature and cooling distribution, cooling load, superconducting magnet critical current, depending on temperature, de-lamination characteristics of the superconducting magnet, impregnation method, and winding method. Through these various tests and tests, there are various advantages that can prevent generator accidents and economic losses and increase the reliability of large-capacity wind power generators.

Figure 4a shows the results of the FEM analysis for the electromagnetic forces in both the HTS generator and the PES. The PES was modeled to evaluate the maximum output torque and electromagnetic forces under both no-load and load conditions.

To replicate the electromagnetic forces of a 10 MW HTS generator using the HTS field coil of the PES, it is crucial to determine the input current required for the armature coil. In order to check the current and force of the PES, the input current of the armature coil in the FEM model of the PES is passed through the rated AC armature current of a 10 MW class HTS generator to check the forces of the coil according to the AC current. After evaluating these forces, the operating field current and the three-phase armature current corresponding to maximum torque were identified.

The FEM simulation confirmed that the electromagnetic forces generated with these current values were consistent with those of the designed 10 MW HTS generator under load conditions.

Figure 4b shows the three-phase armature current at the maximum output torque. The red color graph shows the radial force of the HTS field coil, that is, the attractive and repulsive force that occurs between the HTS coils and the armature module coil, and the blue color graph is the tangential force of the HTS field coil, that is, the force in the vertical direction of the coil, which is the value of the force generated by the torque. The selected three-phase output current at the maximum output torque was 1585 A, −601 A, and −984 A, respectively. The current values are supplied by a DC power supply to the three-phase coils of the stator part to generate torque between the HTS field coil and the stator coil.

Figure 4b illustrates the three-phase armature currents at maximum output torque. The red graph represents the radial force of the HTS field coil, reflecting the attractive and repulsive forces between the HTS coils and the armature module coil, while the blue graph indicates the tangential force, which is the vertical force generated by the torque. The three-phase output currents at maximum torque were 1585 A, −601 A, and −984 A, respectively. These current values are provided by a DC power supply to the three-phase stator coils to generate the torque between the HTS field coil and the stator coil.

Figure 5 presents the results of the FEM simulation for the electromagnetic forces of the PES. Initially, an operating current of 221 A was applied to the field coil at a ramping rate of 5 A/s to assess the forces under no-load conditions.

Subsequently, the simulation evaluated the electromagnetic forces generated under load conditions with a DC current applied to the three-phase armature coil. The FEM simulation indicated that the tangential and radial forces under load were 70.6 kN and 3 kN, respectively, matching the forces observed in the designed 10 MW-class HTS generator model.

Based on these electromagnetic force analysis results, a detailed configuration diagram of the PES was developed. The designed schematic diagram of the PES, including the HTS field coil and stator coil, is shown in Figure 6a. The configuration diagram of the entire designed PES and the direction and magnitude of forces are shown in Figure 6b.

3. Fabrication of the PES

3.1. Fabrication of the HTS Field Coils and Armature Coil

Figure 7 shows the fabricated HTS field coils of the designed 10 MW class HTS generator for PES. The HTS field coil was assembled with a salient pole after winding and impregnation based on the designed specification of the coil. The armature module coil for the PES was partially modularized based on the same overall dimensions based on the designed HTS generator. Figure 8 shows the fabrication process and armature winding method of the armature module coil for PES. In the case of the armature core, the blue part is the support part made of MC nylon material, and the middle part is the iron core made of silicon steel plate. The armature coil is made of square-type copper wire considering the winding method, and the end of the coil consists of a total of six terminals.

3.2. Experimental Setup of the PES for Testing the Electromagnetic Forces

Figure 9a shows the fabricated and assembled HTS field coils with the supporter. The positions of the strain gauges for measuring the electromagnetic force of the HTS field coil are shown in Figure 9b.

A strain gauge was used to measure the Lorentz force generated in the superconducting coil. Strain gauges are attached to the GFRP support to measure strain value, and the Lorentz force is calculated by converting the value. The deformation that occurs in the GFRP support when Lorentz force occurs is confirmed analytically. To increase reliability, structural analysis was performed using a FEM analysis model. The supporter is made of GFRP material, and, when a safety factor of 3 is applied, it can be said to be safe if a stress of 80 MPa or less is applied. As shown in Figure 10, the maximum stress of the coil support was designed to not exceed 80 MPa.

Figure 11 shows the strain gauge test method. The GFRP support used has the same size and shape as the support applied to the HTS field coil. In the figure below, the fix constraint part and load condition part are applied to both ends of the tensile tester. In addition, the test-jig was designed so that the supporter receives a force in a direction and magnitude similar to the actual Lorentz force of the HTS field coil. The attachment location of the strain gauge is the arm of the support with a plat area. Based on the load received by one support in the HTS field coil, the load is applied step by step using a tensile tester. The load was increased and decreased at 1 kN intervals from 0 to 40 kN. The test was repeated more than five times for each support using a total of two supports.

Figure 12 shows the fabrication of the frame for PES based on the structural analysis results of the stainless-steel frame. In order to manufacture a frame for installing the HTS field coil and armature module coil for PES, it is necessary to check the safety of whether the three HTS field coils can be sufficiently supported when this force is applied to the frame. When stainless steel, a non-magnetic material, is used, the maximum displacement is about 1 mm. In the case of mechanical stress, it can be seen that a maximum of 70 MPa occurs, and the maximum stress occurs at the corner of the square pipe joint depending on the left and right forces. In the case of stainless steel, the minimum yield stress is 245 MPa, and when comparing the yield stress of the material, it has a safety factor of about 3.5. Considering the fatigue caused by continuous testing of the evaluation device, it is designed to have a safety factor of over 3.

Figure 13 shows the overall experimental setup condition of the PES. The system consists of a HTS field coil, armature coil, cryo-cooling system, DC power supply, DAQ measurement device, and so on.

4. Experiment Results of HTS Coil Using the PES

To evaluate PES performance, first, the magnetic field characteristics were confirmed when the field current and armature current were applied.

Figure 14 shows the magnetic field of the HTS field coils according to the input field current. A field current was applied to the superconducting coils up to the target current value of 155 A, and it was confirmed that the electromagnetic field increased accordingly.

Figure 15 shows the magnetic field of the HTS field coils according to input armature currents. The armature current was applied to the armature coils with each ramping rate up to the target value, and it was confirmed that the magnetic field increased accordingly. As a result of the experiment, the magnetic field value was 82 mT, which was confirmed to be the same as the simulation value of 82.8 mT at the target armature current.

After confirming the electromagnetic characteristics according to the field current and armature current, a strain gauge was used to check the force generated in the coil to check the strain in the supporter at the target current value. Then, the value was compared and analyzed with the simulation results to calculate the force generated from the coil.

Figure 16 shows the position of the strain gauge sensor. The strain gauge was installed where stress is most concentrated on the supporter that supports the superconducting coil. When a tangential force of 71 kN was generated under load conditions, the displacement value at that location was checked in the simulation and compared with the experimental results to calculate the generated force.

To evaluate PES performance, first, the magnetic field characteristics were confirmed when the field current and armature current were applied.

Figure 17 shows data analysis to confirm the force according to the strain value by comparing the force and strain voltage value and strain value in experiments and simulations.

Figure 18 shows the radial and tangential forces under no-load and load conditions. When a field current of 155 A was applied, a radial force of 53 kN was generated under no-load conditions, and then under a load condition where each of the three-phase armature currents was applied, and radial and tangential forces were generated simultaneously.

As a result of the experiment, 72.2 kN of tangential force and 44 kN of radial force was generated. In the case of tangential force, the force was similar to that of the designed 10 MW HTS generator, and the error rate was 0.98%. The comparative analysis results of the tangential force and output power of the HTS generator and PES are shown in

Table 3. Comparative analysis results of the force and output power of the HTS generator and PES.

Part	HTS Generator	PES	Error
Tangential force of the HTS field coil	71.5 kN	72.2 kN	0.98%
Total output power	10.5 MW	10.6 MW	0.98%

.

5. Conclusions

This paper deals with the electromagnetic force characteristics in an HTS field coil for a 10 MW class HTS Wind Power Generator employing a PES. This study involved designing a 10 MW HTS generator and defining the PES structure according to the generator’s specifications. The PES design, based on FEM electromagnetic analysis, incorporates three HTS field coils arranged to form a pole pair, addressing mutual inductance and magnetic field distribution effects. Based on the designed 10 MW class HTS wind power generator, the HTS coils are manufactured and installed in the PES by a support structure, which is designed considering the electromagnetic force and heat loads in the HTS coil. To check the stress and deformation in the support structure caused by the electromagnetic force generated from the coil, strain gauge sensors were attached to the support structure and measured under full load conditions. As a result, the operating current and maximum magnetic flux density applied to the field coil were 221 A and 2.8 T, respectively. As a result of the experiment, 72.2 kN of tangential force, and 44 kN of radial force was generated. In the case of tangential force, the force was similar to that of the designed 10 MW HTS generator, and the error rate was 0.98%. The experiment revealed that the operating current and maximum magnetic flux density in the field coil were 221 A and 2.8 T, respectively, with tangential and radial forces measured at 72.2 kN and 44 kN. The tangential force closely matched the design specifications with a 0.98% error rate. Both the magnetic field and electromagnetic forces in the HTS coil were consistent under no-load and full-load conditions. These results will be instrumental in advancing the study and development of high magnetic field coils for HTS applications, in addition to supporting the fabrication of the PES.