Analysis of the loss and thermal characteristics of a SMES (Superconducting Magnetic Energy Storage) magnet with three practical operating conditions

Accepted Manuscript Analysis of the loss and thermal characteristics of a SMES (Superconducting Magnetic Energy Storage) magnet with three practical operating conditions

Ying Xu, Li Ren, Zhongping Zhang, Yuejin Tang, Jing Shi, Chen Xu, Jingdong Li, Dongsheng Pu, Zhuang Wang, Huajun Liu, Lei Chen PII:

S0360-5442(17)31792-9

DOI:

10.1016/j.energy.2017.10.087

Reference:

EGY 11731

To appear in:

Energy

Received Date:

10 March 2017

Revised Date:

09 October 2017

Accepted Date:

19 October 2017

Please cite this article as: Ying Xu, Li Ren, Zhongping Zhang, Yuejin Tang, Jing Shi, Chen Xu, Jingdong Li, Dongsheng Pu, Zhuang Wang, Huajun Liu, Lei Chen, Analysis of the loss and thermal characteristics of a SMES (Superconducting Magnetic Energy Storage) magnet with three practical operating conditions, Energy (2017), doi: 10.1016/j.energy.2017.10.087

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ACCEPTED MANUSCRIPT

Highlights  The loss characteristics of a SMES magnet are studied.  Three kinds of power compensation experiments are carried out.  A thermal model of the magnet is developed.  The thermal characteristics of the magnet under three operating conditions are studied.

ACCEPTED MANUSCRIPT

Analysis of the loss and thermal characteristics of a SMES (Superconducting Magnetic Energy Storage) magnet with three practical operating conditions Ying Xua*, Li Rena, Zhongping Zhanga, Yuejin Tanga, Jing Shia, Chen Xub, Jingdong Lia, Dongsheng Pua, Zhuang Wanga, Huajun Liuc and Lei Chend a State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, 430074 Wuhan, China b Zhejiang Electric Power Corporation Research Institute, 310014 Hangzhou, China c Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China d School of Electrical Engineering, Wuhan University, 430072 Wuhan, China E-mail: [email protected] Abstract The losses of Superconducting Magnetic Energy Storage (SMES) magnet are not neglectable during the power exchange process with the grid. In order to prevent the thermal runaway of a SMES magnet, quantitative analysis of its thermal status is inevitable. In this paper, the loss characteristics of a self-developed 150 kJ SMES magnet are analyzed by means of experiments and simulations, including the loss of the joint resistance, the eddy current loss of the metal cooling structures and the AC loss of the superconducting magnet. A thermal model of the magnet was built to theoretically analyze the relationship between the current and magnet temperature variation. Three kinds of power compensation experiments were carried out to study the thermal characteristics of the SMES magnet. The temperature variation of the magnet under these three operating conditions was simulated. The simulation results and experimental results are compared and analyzed. Keywords: AC loss, eddy current, joint resistance, SMES, thermal analysis

1. Introduction The development of wind energy, solar energy and other renewable clean energies has grown rapidly in the last 20 years [1-6]. Different from the output power characteristics of the traditional coal-fired power and hydroelectric power, the power of these renewable energies is random and intermittent. Their large-scale grid connection will pose a threat to the stable operation of the power system. Researchers are trying to find solutions to deal with these threats [7-12]. Energy Storage Systems (ESS) has the ability of flexible charging and discharging, and recent development and advances in the ESS have made the application of energy storage technologies a viable solution for the above problems. Therefore, more and more attention has being paid to the energy storage technologies [13-20]. Currently, there are lots of technologies used for ESS, which include: Battery Energy Storage (BES) [21-26], Compressed Air Energy Storage (CAES) [27-36]. Flywheel Energy Storage (FES) [37-41], Supercapacitor Energy Storage (SES) [42-46], and SMES [47-53]. All these storage technologies have their own advantages and disadvantages [54,55]. For large-scale applications, key factors of the energy storage include: higher energy and power storage densities, greater cycling capabilities, higher reliability, and lower cost. So far, BES technologies are relatively mature, and have achieved commercial applications. More attention should be payed to its limited cycle life and recycling/disposal problems. CAES shows high power and energy capacity rating for power application, but it is limited by topographical conditions for large-scale applications. FES stores electrical energy in the form of rotational kinetic energy, which has the features of long life cycle, high efficiency, free from depth of discharge effects, environmentally friendly [56]. More effort should be made to reduce the friction losses to improve the self-discharge rate. SES is a fast energy storage device with a response time of tens to hundreds of milliseconds. However, SES has a self1

ACCEPTED MANUSCRIPT discharge rate of 5% per day, which need to be improved. SMES uses superconducting magnet to store electrical energy and discharge it back to the grid or other loads when necessary. They have very rapid response for either charge or discharge with a response time of a few milliseconds [57,58]. They almost have unlimited cycle life. It is endowed with a great development prospect. Although nowadays, the capital and operating cost of SMES is very high, its unique fast response speed and unlimited cycle life have attracted lots of attention. With the performance increase of the High Temperature Superconducting (HTS) material, HTS SMES has potential to be more economical and more efficient because HTS wires work at a higher operation temperature range, such as 15-30 K, than LTS wires. This will greatly accelerate the practical process of SMES.

1.1. The novelty of this paper Superconducting magnet (SC magnet) is one of the core components of the SMES system. Losses of superconducting magnet will reduce the efficiency of SMES system. Superconducting wire is free from loss when carrying DC current. But the wire is carrying alternating current or in a dynamically changing magnetic field, electromotive force and induced current will appear in the wire. This will lead to energy dissipation. Our laboratory has developed several sets of SMES systems [5860]. Through experiments found that, during the charging or discharging process, the operating current of the superconducting magnet is dynamically changing. As is known, dynamic current will lead to heat losses. The loss and heat of the magnets in this process can not be ignored. To prevent the thermal runaway of a HTS magnet, quantitative analysis of its loss and thermal characteristics is necessary. In addition, it is also necessary to study the eddy current loss of the cooling structures for the widely used cooling technology in the field of superconducting magnets. Conduction-cooled method is one of the options to achieve the temperature range and is now widely used in HTS magnet cryogenic system [61-63]. The cooling power is conducted through a complex cooling structure, so thermal analysis should be carried out to make sure that the conduction cooling system is valid. Since the general cooling structures are made of metal with high thermal conductivity, the metal cooling structures themselves will produce eddy currents when there is a dynamically changing current in the superconducting coil. This induced eddy currents also causes energy dissipation. These losses in SC magnet and cooling structures increase the burden on the cryogenic cooling system and reduce the efficiency of SMES system. The research content of this paper is based on the above background, we systematically and comprehensively study the loss and thermal characteristics of the conduction-cooled HTS SMES system. The research methods and results will further enhance the safety and reliability of SMES, which is very important for the popularization and application of HTS SMES system. Good representations of the research work on the dynamic electromagnetic, loss and thermal characteristics of HTS SMES are as analysed below. A. Ishiyama et al. [64] evaluated the electromagnetic and thermal characteristics in a conduction-cooled Bi2223 HTS coil under pulse current. Kenji Tasaki et al. [65] analysed the thermal stability and thermal runaway currents of a conductioncooled Bi2223 HTS coil at 15-30 K. Hiroki Kojima et al. [66,67] investigated the temporal evolutions of temperature of a HTS solenoidal coil for typical current patterns of load fluctuation compensation at different ambient temperatures. Hiroshi Miyazaki et al. [68] studied the degradation and thermal runaway properties of a four stacked YBCO pancake coils at 77 K. H. Yeom et al. [69] focused on the cool-down and thermal characteristics of a HTS SMES conduction cooling system, which consists of six dummy double pancake coils without charging current. Seong-Gyeom Kim et al. [70] reported the chargedischarge and thermal–electrical characteristics of GdBCO single-pancake coils with different types of insulation materials. Takahiro Ariyama et al. [71] studied the heat transfer characteristics of HTS wire in a small conduction-cooled HTS coil. The present work is different from the published work already in the literature in the following ways. Our study on the losses and thermal characteristics of SMES magnet is based on an actual SMES system and three practical operating conditions. Different from the HTS coils in the existing work, the analyzed SMES has a hybrid magnet consisting of 12 Bi2223 coils and 6 YBCO coils. The advanced H-formulation method is used to evaluate the AC loss of the magnet. Also, a three-dimensional thermal model considering the anisotropy and the temperature-dependent thermal properties of the superconducting magnet was established. This model contains the spiral current leads and cooling plates with actual 2

ACCEPTED MANUSCRIPT geometry. This is different from the published work in the use of small-scale HTS coils and assumed current profile. The research work of this paper is closer to the practical application of SMES, which is more reference for readers. As a previous work of this study, a numerical model to analyze the cooling process of a 150 kJ/100 kW SMES magnet has been cross-checked with experimental measurements, which is a preliminary check of the assumptions, boundary conditions, effective material properties in the numerical method [72]. In this paper, based on the 150 kJ / 100 kW HTS SMES system developed in authors’ laboratory [58], numbers of power compensation experiments have been conducted. The loss characteristics of the magnet were analyzed in detail by means of experiments and simulations, including the loss of the joint resistance, the eddy current loss of the metal cooling structures and the AC loss of the SC magnet. And thermal characteristics were also tested and simulated. The resistance of each joint in the magnet was measured. In order to get a better understanding of the contribution of various losses to the temperature rise of the magnet, finite element method was used to analyze the effect of the losses. The eddy current loss on these metal structures and the AC loss of the SC magnet were evaluated. The evaluation models of eddy current loss and AC loss are introduced. Based on the previously established thermal analysis model, the calculated and measured heat losses were loaded into the thermal model as heat sources to simulate the temperature characteristics of the magnet. The three power exchange experiments with the gird are the maximum power output experiment, the dynamic power compensation experiment in a simulated power system and the field test in a hydropower station. The comparison between the simulation results and the experimental results shows that the simulation results differ slightly from the experimental ones, which proves the validity of the loss calculation model and the thermal analysis model. The paper is organized as follows. In section 2, we describe the 150 kJ / 100 kW HTS SMES system, focusing on the HTS magnet and the conduction cooling cryogenic system. In section 3, we present the aforementioned three power compensation experiments briefly. In section 4, we introduce the loss and thermal evaluation model of SMES, and show the calculation results of joint resistance loss, eddy current loss and AC loss. In section 5, we show the results and discussion of the thermal analysis model under the three practical operating conditions. Finally, in section 6, we present our conclusions.

2. The 150 kJ/100 kW SMES The 150 kJ/100 kW SMES mainly consists of four parts, which are SC magnet, cryogenic system, Power Conversion System (PCS) and Monitoring and Control System (MCS). Considering the energy demand at different locations in the power system, the SMES vehicle system with high mobility is designed. It includes two standard containers, one container is placed with the superconducting magnet and the cryogenic system, the other is placed with the PCS and MCS.

2.1. HTS magnet The HTS magnet was wound with two types of HTS wires, BSCCO tape and YBCO tape. The magnet consists of 12 BSCCO double-pancake coils and 6 YBCO double-pancake coils. Experiments show that the critical current of commercial Bi2223 tape is high, which can reach 200 A at 77 K, while the shortcoming is that it decreases rapidly with the increasing magnetic field. The critical current of YBCO tape is lower than that of Bi2223 tape, but its magnetic field sensitivity is lower, so it is suitable for applications in high magnetic field. Through the magnetic field calculation of the solenoid magnet, the magnetic field is strong at the center, and weak at the ends. To take full advantages of the two tapes, 12 BSCCO coils were divided into two same groups, placed at the ends of the magnet, and 6 YBCO coils were placed in the middle of the magnet. Figure 1 shows the structure of the magnet. Table 1 shows the detailed parameters of the 150 kJ/100 kW SMES magnet. The current leads of SMES connect the superconducting magnet with the power conditioning system. It should not only be available to carry large current, but also prevent outside heat to be leaked to the magnet. The current leads of the magnet are hybrid type composed of a normal copper upper stage and an YBCO HTS lower stage. Since the dewar size is limited, the copper lead is wound into a helix to reduce the occupied volume. The detailed parameters of the hybrid current leads are shown in table 2. And the pictures of copper lead and the YBCO lead are shown in figure 2. 3

ACCEPTED MANUSCRIPT 2.2. Cryogenic system The cryogenic system of the SMES adopts the conduction-cooled method. Two GM cryocoolers and a set of metal cooling structures cool the magnet to the designed temperature. Two main conduction cooling plates made of copper (OFHC) are installed at the top and bottom of the magnet, respectively. Between every two double-pancakes inserts a 1 mm thick copper (OFHC) cooling plate. Two 20 mm stainless steel flanges and fourteen ø12 mm stainless steel rods are used to fasten the magnet. The outside and inside of the cooling plates are connected by twenty-two ø12 mm copper rods. The plates and flanges are cut to reduce the eddy current losses. Figure 3 shows the pictures of the main plate and cooling plate. The cold head of the cryocooler and the 22 copper rods are connected with copper braided wires, providing a flexible connection between the cryocooler and the magnet. The magnet is hanged by four stainless steel rods, and the rods are fixed below the upper cover plate of the dewar. The diagram of the magnet support structure is shown in figure 4.

3. Three power compensation experiments In order to test the power compensation performance of the 150 kJ/100 kW SMES system, three kinds of power compensation experiments were carried out. Experiment #1, maximum power output experiment; experiment #2, dynamic power compensation experiment in a simulated power system and experiment #3, field test in a hydropower station. These three SMES power compensation experiments are briefly introduced in this section. As the losses are mainly related to the instantaneous waveform and amplitude of the magnet current, the currents under the three operating conditions are presented.

3.1. Experiment #1 The maximum power output experiment was carried out by connecting the magnet to the converter. First, we set the converter to charge the magnet at the current rate of 1 A/s. When reaching the pre-setting current value, the current stayed still at the value. Then the converter sent a power exchange command. Figure 5 shows the power exchange waveform of the SMES and the magnet current waveform. According to the previous settings, the magnet current rose from zero to 170 A in 170 s and turned into the standby state. Then the power exchange of + 100 kW/-80 kW started. We assumed that the power absorbed by SMES is positive, and the power outputted is negative. Each power command is maintained for 10 ms, and three commands are issued. After the power conditioning system sent out the discharging command, the magnet current charged the DC bus capacitor through the chopper to release the energy. As the current dropped to a small level, the system was shut down and released the remaining energy to the resistor prepared for absorbing the leftover energy.

3.2. Experiment #2 The 150 kJ SMES is used to suppress the dynamic oscillation of a power system caused by generator terminal short-circuit fault. The circuit of experiment #2 is shown in figure 6. Before the fault the active power output of the generator is 3.2 kW, and reactive power output is 0.9 kVar. Short-circuit point D11 has a three-phase ground fault. The duration of the fault is 300 ms, and then the fault is removed. The SMES monitoring system recorded the generator power oscillation waveform. The output power of the SMES and current waveform of the SC magnet during the experiment are shown in figure 7. It can be seen that in the power exchange process between the SMES and the grid, the current underwent several changes. The results show that, without SMES, the first peak value of power fluctuation is 9.26 kW, and the oscillation lasts for 5 s. However, with SMES, the amplitude of the first oscillation of the system is reduced from near 10 kW to less than 6 kW, and the oscillation last time is reduced to about 2 s. The experiment confirms that SMES has a quick detection of fault removal time and can be applied quickly.

3.3. Experiment #3 After the laboratory experiments, the SMES was used to stabilize the output power fluctuation of a hydropower station, to verify its ability of dampening the power source output fluctuation. The SMES was applied to the Qiliwan hydropower station in Changyang, located in Hubei Province, for field experiment. In the station, there was one hydroelectric generator 4

ACCEPTED MANUSCRIPT with installed capacity of 500 kW and rated output voltage of 6.3 kV. The circuit of the field experiment is shown in figure 8. In the power generation process of grid-connected renewable energies, stabilizing the power output fluctuation is of great significance. In the field experiment, the water diversion pipe of the hydropower station was relatively short, so the generator output power fluctuation caused by the random factors (such as the change of input mechanical power due to the short-term impact on the generator by the instability of the water head) was wildly. When the generator were running at 395 kW and 100 kVar, the SC magnet was charged to 60 A, which was in standby mode. Then it stepped into the operation mode. The active power output of the generator, the active power flowing into the grid and the output power of the 150 kJ SMES are all shown in figure 9. In figure 9 (a), the white line is the active power from the generator and the yellow curve is the line power. Figure 9 (a) demonstrates that the fluctuation amplitude of the active power flowing into the grid is significantly reduced with the operation of the SMES system. Figure 9 (b) shows the output power of the SMES system. When the output power of the generator is higher than the set value, SMES will quickly absorb the excess energy. When the output power is lower than the set value, SMES quickly releases its energy to the gird to keep the generator output power stable. Comparing figure 9 (b) with figure 9 (a), it can be seen that the output of SMES can follow the power fluctuations of the generator with a fast response speed. Without SMES system, the power fluctuation amplitude changes among 5 kW to 10 kW. With SMES system, the fluctuation amplitude of the line power is limited to about 1 kW. In total, the application of the SMES system compensated for more than 80% of the grid power fluctuation. Figure 10 shows the magnet current waveform in experiment #3.

4. Losses and thermal model of the magnet The objective of this section is the evaluation of heat sources. When SMES exchanges power with the power grid, losses in the magnet are very substantial. Thus, heat losses should also be taken into account to analyze the impact of all the main losses on the final temperature field. Heat sources of the analysis consists of AC loss in the superconducting tapes Qac, eddy current loss in the metal cooling structures Qec and joint resistance loss QJ. The calculation of the magnet temperature is divided into two steps. The first step is calculating the losses of the SC magnet, including the AC loss of the HTS coils, the eddy current loss of the metal structures and the resistance loss of the joints. The 17 joint resistances were measured with volt-ampere method. The calculation of the joint resistance loss is relatively simple. After obtaining the joint resistance and current profile of the SC magnet, the resistance loss could be calculated by formula (1). The evaluation of AC loss and eddy current loss is carried out with finite element method. Since the current waveforms of the magnet in the three experiments are quite irregular, there is no suitable empirical formulas to calculate these two types of losses. After obtaining the losses of the magnet, the second step is to transfer these losses to the thermal model as heat sources. Commercial FEM software is used to carry out the calculation. The eddy current loss evaluation model of the SC magnet was established using the FEM with the ANSYS software [73]. ANSYS provides good solutions for eddy current calculation and thermal analysis. AC loss was evaluated with the Partial Differential Equation (PDE) module of the commercial software Comsol [74]. The detailed experimental and calculation results of these losses are as follows.

4.1. Joint resistance loss First, the magnet was cooled to 20 K, and then excited by a linear increasing current. The V-I curve for each of the joints in the magnet was measured and recorded. A V-I curve of a joint is shown in figure 11. The value of each joint resistance was calculated using Ohm's law according to these V-I curves, and the results are listed in table 3. The maximal resistance of the joints is 1.735×10-7 Ω. The resistance of the joints are mostly less than 1×10-7 Ω. The sum of the joint resistance is 8.66×10-7 Ω. The joint resistance loss is determined with formula (1). t1

2 QJ   I mag rJ dt t0

(1)

Where Imag is the current of the SMES magnet; rJ, the joint resistance; t0 and t1 are the start time and the end time, respectively. Figure 12 shows the joint resistance loss power with the aforementioned three kinds of practical current. In regard to 5

ACCEPTED MANUSCRIPT experiment #1, the total loss energy in the process of charging, power exchange and discharging is 3.16 J according to formula (1), and the maximum instantaneous loss power is 2.9×10-2 W. For experiment #2, the total loss energy of the whole process is 1.68×10-1 J. The maximum instantaneous loss power is 3.43×10-3 W. In experiment #3, the total loss energy in the whole process is 2.01×10-1 J, and the maximum instantaneous loss power is 3.12×10-3 W.

4.2. Eddy current loss in cooling structures Eddy current loss analysis adopts transient solver of ANSYS. The three kinds of practical current were applied to the SC magnet. The model is based on the actual geometric parameters of metal cooling structures, taking into account the slits and cuts of the cooling plate, main plate and flange, as shown in figure 3. The eddy current loss is computed using the vector potential method as follows.

Qec  

t1

t0

1 n     J  J  dt N i 1

(2)

Where Qec is the eddy current loss per unit volume; [ρ] is the resistivity matrix; N is the number of integration points; J is the total current density in the element at integration point i. The resistivity of the copper (OFHC) at 20 K is 1.69×10-9 Ω·m, and the resistivity of the stainless steel at 20 K is 7.13×10-8Ω·m. The eddy current loss power of the metal structures with the three currents are shown in figure 13. The figure shows the eddy current losses of several typical cooling structures, where plate 1 is the cooling plate at the end of the magnet and plate 9 is the cooling plate at the middle of the magnet. The eddy current losses of the metal cooling structures are about 0.1 W because of the low charging/discharging rate of the magnet current, which is negligible compared to the losses in the power compensation process. Figure 13 demonstrates that the eddy current loss of the plates increase rapidly with the change of the magnet current after the start of the power exchange process, and the peak values of the losses vary depending on the change rate of the current. In experiment #2, the change rate of the magnet current is the lowest, so the peak loss power of plate 9 is the smallest, less than 50 W. In regard to experiment #1, the change rate of the current is the largest, and the peak loss power of plate 9 is as high as 1400 W. The peak loss power of plate 9 is about 600 W in experiment #3. After the end of power exchange, eddy current losses drop rapidly. In the above three experiments, the eddy current loss of the cooling plate in the middle of the magnet is greater than that of the plate at the end of the magnet. The main cooling plate has a relatively large thickness and located at the end of the magnet, its eddy current loss is much related to the magnet current profile. The change rate of the magnet current affects the magnetic field distribution and induced eddy current on the main cooling plate. Therefore, the loss of the main cooling plate is not necessarily greater than the loss of the cooling plate 9. In experiment #1, the loss of the main cooling plate is much less than that of the plate 9. In experiment #2, the loss of the main plate is greater than that of the plate 9, but in experiment #3, the loss of the main cooling plate is nearly the same as that of the plate 9.

4.3. AC loss in the SC magnet The AC loss of the SC solenoid magnet is evaluated by H-formulation method with a 2D model [75,76]. Finite element method has been widely used in the calculation of the current density, AC loss and magnetic field distribution and other characteristics of superconducting tapes and coils. The non-linear E-J characteristic is introduced into Maxwell's equation as the property of superconducting material, and the AC loss of the magnet can be obtained by directly solving the magnetic component Hr and Hz. Equation (3) and (4) are the converted equations of Faraday’s law and Ampere's law,

respectively.

  H    (  H )  0 r 0 t

J

H r H z  z r

(3) (4)

Where ρ is the resistivity; t, the time; H, magnetic field; μ0 and μr are the vacuum permeability and relative permeability, respectively. J is the current density, and Hr and Hz are the components of the magnetic field in the r and z directions. 6

ACCEPTED MANUSCRIPT Equation (5) is derived by substituting equation (4) into equation (3) for cylindrical coordinates. With appropriate boundary conditions, equation (5) can be solved by general-form PDE equations. Equations (6) and (7) are used to describe the magnetic field-dependent critical current density Jc(B) of BSCCO tape and YBCO tape, respectively. H H z  r  ( r  )  H r z r  0  0 r  r  t z   H H z  r  ( r  ) H z  z r  0  r   0 r  t r J c ( B)  J c0  (0.9756  e( 5.28 B )  2.05  e( 0.1106 B ) )

J c ( B) 

J c0



2

1  k 2 B/ /  B

2





B0

(5)

(6) (7)

Here, Jc0 is the self-field critical current density at 20 K. B⊥ and B|| are, respectively, the perpendicular and parallel components of magnetic flux density with respect to the tape’s surface. Equation (6) is a fitted curve from the experiment data, where Jc0 = 6.051 × 108 A/m2. Equation (7) is a Kim-like model from [77] that describes the anisotropy of the critical current density of YBCO tape, where Jc0 = 7.545 × 108 A/m2, B0 = 0.536 T, k = 0.162, and α = 0.912. Only half the pancake coils were modeled by applying boundary condition Hr = 0 at the bottom edge of the model. The axis-symmetric H-formulation has been applied to the model with magnetic field H = [Hr, Hz]T. In regard to the

mathematical equation of Qac (J/cycle), it is expressed as: N

Qac   [ 2 r  E  Jds ]dt t

s

1

(8)

For the superconducting domains, a nonlinear resistivity ρ = (E0/Jc(B))|(J/Jc(B))|n-1 is used, where E and J are the electrical field and current density respectively. For a single or multiple HTS tapes, the electromagnetic field distribution is relatively simple, the degree of freedom using of finite element method is less. For HTS magnets, the electromagnetic field characteristics are extremely complex. Formula (3) - (5) can’t be solved for large scale magnet with numerous turns because of too large number of degrees of freedom. In order to reduce the solved degrees of freedom and speed up the calculation, a homogenization method was adopted [78]. Several adjacent turns of a coil are combined into a new turn, assuming these adjacent turns have the similar current density distributions. A new current constraint should be applied to ensure that the transport current in the new turn equals the total current of the corresponding turns. Sn (9) n J (t ) ds = S i(t ) where i(t) is the transport current in each turn; Jφ, current density within area Ωn; S, cross-sectional area of a HTS tape; and Sn is the size of area Ωn. The detail of the AC loss model can be found in [79]. In all the three experiments, the magnet was charged at a speed of about 1 A / s. In experiment #1, the magnet was charged to 170 A, and maximum AC loss power was about 10 W appearing at the end of charging. As for experiment #2 and #3, the magnet was charged to 60 A, and maximum AC loss power in the process of charging was about 7 W also appearing at the end of charging. After the charging was finished, the current kept stable and the AC loss of the magnet decreases and stabilizes. After the start of power exchange, the AC loss of the magnet increased rapidly. The three power exchange conditions corresponds to the different change rate of the current, the AC losses of the three conditions are totally different. For experiment #1, the maximum AC loss power is 2576 W during power exchange process. With regard to experiment #2, the maximum AC loss power is only 7.6 W. In experiment #3, the maximum AC loss power is only 94 W. Comparing these three kinds of losses, the joint resistance loss is much lower than the AC loss and the eddy current loss. Obviously, the temperature rise of the magnet during the power exchange process is mainly determined by the AC loss and the eddy current 7

ACCEPTED MANUSCRIPT loss.

4.4. Thermal model of the magnet A 3D heat transfer model was built by FEM with ANSYS®, in which the anisotropy and the temperature dependent thermal properties of the materials used in the SC magnet were considered. For the thermal model, the temperature of the magnet is evaluated by solving the equation (10). dc

T ( x, y, z , t )  T  T  T  (K x )  (K y )  (K z )  Psum t x x y y z z

(10)

where d is the density; c, the specific heat capacity; T stands for temperature, Psum is the internal heat generation rate. x, y and z are the coordinates in the reference system. Kx, Ky and Kz are the thermal conductivity of x, y and z directions in the element, respectively. The detail description about the thermal model is in [72]. The losses were transferred to the thermal analysis model as heat sources. The mesh generated within the HTS magnet is shown in figure 17. A Dell Precision T7610 Tower Workstation, which has two six-core 2.60-GHz Intel Xeon E5-2630 v2 processors and 64GB 1866-MHz DDR3 ECC RDIMM main memory, is used to conduct the simulation. The CPU time is mainly determined by the size of magnet model and the complexity of the current waveform. The more irregular the waveform, the longer the CPU time required. For these three experiments, the CPU time for the losses and thermal analysis of the magnet is different. For this magnet model, the AC loss calculation time is about 15 to 22 hours, the eddy current loss calculation time is about 8 to 12 hours and the magnet temperature simulation takes about 20 to 36 hours.

5. Results and discussion The temperature variation of the magnet with time in experiment #1, #2 and #3 is shown in figure 18. The curves contain the temperatures at the top, middle and bottom of the magnet both in simulation and experiment. The accuracy of the temperature data collection system is not very high. The measured temperature data has certain fluctuation, but it does not affect the temperature variation trend. In figure 18 (a), the measured temperature data shows that the temperature rise at the middle of the magnet is the largest, and the minimum temperature rise appears at the top of the magnet. The loss calculation results in section 4 show that the AC loss of the pancakes in the middle of the magnet is smaller than that at the end of the magnet. However, the eddy current loss of the cooling plate located in the middle of the magnet is much larger than that at the end of the magnet. From the considerations of cooling efficiency and heat capacity, because of the thick main cooling plate and the stainlesssteel flange, the heat capacity at the both ends of the magnet is large. The main plate is directly connected with the cold head of the GM cryocooler, so the upper region of the magnet can be cooled better. On the contrary, the heat capacity of the middle region of the magnet is small, and the cooling effect of the middle region is not very good. All these reasons eventually lead to a higher temperature rise in the middle of the magnet. The simulation results show that the temperature variation trend is consistent with the experimental ones. The temperature rise in the middle region is higher and the temperature in the upper region is lower. The temperature characteristics of the magnet in the experiment were well simulated. Nonetheless, the temperature rise in simulation is smaller than the experimental results. The simulation error may come from the approximation of magnet current. Since the converter is connected to the magnet through a Pulse Width Modulation (PWM) chopper, the chopping voltage will produce a high frequency, although small amplitude, current ripple on the magnet. The current ripple is not taken into account in the simulation, which could be one of the main sources of the error. At the beginning of experiment #2, as shown in figure 18 (b), the temperature of the top of the magnet was 19 K, and the temperature of the middle part and the lower part of the magnet was 20 K. Due to the existence of measurement error and fluctuation, the starting temperature difference of the magnet between experiment and simulation is less than 1K, which is considered to be acceptable. Our main concern is the temperature rise and temperature variation trend in the simulation. In the experiment, the temperature rise of the magnet is about 0.5 ~ 1 K, the temperature rise in the simulation is smaller, rising 8

ACCEPTED MANUSCRIPT about 0.5 K. In addition to the error caused by the approximation of the current, it may be related to the assumption that the cooling plate is in good contact with the superconducting double-pancakes. In an actual magnet, there may be areas where the double-pancake is not in good contact with the cooling plate, which can weaken the cooling effect of these areas. This is also one of the reasons why the temperature rise in the experiment are higher than that in the simulation. In experiment #3, although the loss power of the magnet is smaller than that of experiment #1, the loss energy of the magnet is relatively large because of its longer power exchange time. In figure 18 (c), the magnet temperature has undergone dramatic changes, especially in the middle region of the magnet where the cooling effect is poor, and its temperature rise is most obvious. After the end of the power exchange, the magnet current was only 55 A. The loss power declined rapidly. The temperature in the middle of the magnet also returned to the average temperature of the magnet in a short time. The sharp temperature change in experiment #3 did not appear in experiment #1. The main reason is as follow. After the end of the maximum power exchange test, the magnet current in experiment #1 was still 170 A. In the discharge process, the loss was still high, so the temperature at the middle of the magnet didn’t appear a short-term rapid drop. In summary, the results of thermal analysis are largely consistent with the experimental results, and it clearly reflects the temperature characteristics of the magnet in the three practical operating conditions. At the same time, loss calculation results in section 4 are also validated.

6. Summary We have carried out three kinds of compensation experiments of the 150 kJ HTS SMES with the power grid. The current and temperature data have been measured experimentally. The resistances of the magnet joints were measured and the joint resistance loss was calculated. The thermal analysis model and the loss calculation model (including eddy current model and AC loss model) of the 150 kJ SMES were established. The eddy current loss and AC loss were evaluated under three practical currents. The calculated and measured losses were transferred into the thermal analysis model as heat sources. The temperature variations of the magnet under three operating conditions were simulated. The simulation results are compared with the experimental results, and the error analysis is done. Based on the experiment and simulation results, the following conclusions were arrived at: 1) The results of the three experiments show that SMES has a fast response speed. The response time from receiving the command to power output is only a few milliseconds. Due to its fast response, SMES lays a positive effect on suppressing the dynamic oscillation of the power system, stabilizing the output power fluctuation of power station, etc. 2) For the conduction-cooled SC magnet with the metal cooling structures, the eddy current loss and the AC loss dominate the losses during the power compensation process, and eddy current loss accounts for more. From the point of view of reducing the losses of a magnet, measures should be taken to reduce the eddy current loss when designing the SC magnet. However, from the perspective of magnet protection, the heat generated by the eddy current loss could initiate additional normal zones during a quench, which could decrease the temperature of the hot-spot. This protection method is known as quench back. The larger the eddy current loss, the faster quench back is activated. Therefore, the design of the cooling structures is a compromise between dynamic losses and magnet protection. 3) In this paper, the improved H-formulation method is used to evaluate the AC loss of the SC magnet. The unique properties of superconductors, such as the magnetic field dependence of the critical current density Jc-B and the non-linear E-J characteristic, are taken into account in this method. The comparison between the simulated temperature rise and the test results shows that the loss calculation method and the thermal model are effective. For axisymmetrical magnets, 2D modeling could effectively reduce the degree of freedoms and speed up the calculation. However, this method is difficult to deal with 3D models with huge amount of freedoms. Large scale magnets often adapt multiple solenoids or toroidal geometry, which are non-axisymmetrical. For further work, it is suggested to investigate the method for the AC loss calculation of non-axisymmetrical magnets. The work in this paper can help to understand the temperature characteristics of HTS magnet under different operating conditions, and it provides a reference for the quantitative analysis of loss and thermal characteristics of HTS magnets.

Acknowledgements 9

ACCEPTED MANUSCRIPT This work was supported by National Science Foundation for Post-doctoral Scientists of China under Grant 2016M602297 and National Natural Science Foundation of China under Grant 51707074.

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ACCEPTED MANUSCRIPT Tables and Figures:

Nomenclature Qac

AC loss (J)

B⊥

Qec

eddy current loss (J)

B||

QJ

joint resistance loss (J)

E0

Imag

current of the SMES magnet (A)

i (t)

perpendicular components of magnetic flux density with respect to the tape’s surface (T) parallel components of magnetic flux density with respect to the tape’s surface (T) characteristic electric field (which is usually set equal to 10-4) (V/m) transport current in each turn of the coil (A)

rJ

joint resistance (Ω)

Jφ

current density within area Ωn (A/m2)

t0

start time of the current-carrying process (s)

S

cross-sectional area of a HTS tape (m2)

[ρ]

resistivity matrix (Ω·m)

TDown

temperature at the bottom of the magnet (K)

t1

end time of the current-carrying process (s)

Sn

size of area Ωn (m2)

N

number of integration points

TUp

temperature at the top of the magnet (K)

TMiddle

the temperature at the middle of the magnet (K)

(A/m2)

Jt

total current density

ρ

index for resistivity (Ω·m)

J

current density (A/m2)

t

index for time (s)

Hr

magnetic field in the r direction (A/m)

H

magnetic field (A/m)

Hz

μ0

vacuum permeability (H/m)

Jc(B)

μr

relative permeability (H/m)

Jc0

magnetic field in the z direction (A/m) magnetic field dependence of the critical current density (A/m2) self-field critical current density (A/m2)

n

n value of the superconductor

Kx, y, z

thermal conductivity (W/(m·K))

d T

density (kg/m³) Temperature (K)

c Psum

specific heat capacity (J/(kg·K)) internal heat generation rate (W/s)

Table 1. Specifications of the SC magnet. Number of double-pancakes (YBCO/BSCCO) Inner radius of coil (YBCO/BSCCO) Outer radius of coil (YBCO/BSCCO) Height of coil (YBCO/BSCCO) Total length of the conductor DC link voltage Critical current Stored energy Maximum parallel magnetic field to tape Maximum perpendicular magnetic field to tape Measured inductance

13

18 (6/12) 120 mm/ 132 mm 198 mm/198 mm 11.5 mm/12 mm 4800 m (BSCCO) 2400 m (YBCO) 800 V 180 A 157 kJ 4.73 T 2.66 T 9.7 H

ACCEPTED MANUSCRIPT Table 2. Parameters of the hybrid current leads. Length of the copper lead

700 mm

Radius of the copper lead Length of the YBCO lead

4 mm 270 mm

Width of the YBCO lead Maximum current

35 mm 250 A

Table 3. Resistance of the joints. Joint No. #1 #2 #3 #4 #5 #6 #7

Resistance/Ω） 8.82×10-9 1.085×10-7 3.744×10-8 5.446×10-8 2.075×10-8 6.704×10-8 4.755×10-8

#8

2.875×10-8

Joint No. #9 #10 #11 #12 #13 #14 #15 #16 #17

Resistance/Ω） 2.916×10-8 2.806×10-8 4.416×10-8 1.763×10-8 3.572×10-8 2.271×10-8 3.932×10-8 1.028×10-7 1.735×10-7

BSCCO coils YBCO coils BSCCO coils

(a)

(b)

Figure 1. Structure of the SC magnet. (a) shows a picture of the SC magnet and (b) shows the relative position of the BSCCO coils and YBCO coils.

Figure 2. Pictures of copper lead (left) and the YBCO lead (right).

14

ACCEPTED MANUSCRIPT

Figure 3. Pictures of the main plate (left) and the cooling plate (right).

Figure 4. Diagram of the magnet support structure with (left) and without thermal radiation shield cylinder (right).

120

200

(a)

180

(b)

174

80

168

Current/A

Power/kW

150

40 0

100

50

-40 -80 7.40

184.04 184.08 184.12 Power exchange process

0

7.44

7.48 Time/s

7.52

0

50

100

150

200

250

300

350

400

Time/s

Figure 5. (a) shows the power waveform during the power exchange process between the SMES and the grid and (b) shows the current waveform of the magnet in experiment #1.

15

ACCEPTED MANUSCRIPT T1 230/800V 6kVA

G

01QF 32QF

TA

76XL

75XL

ZL2=17.5Ω

ZL1=5.32Ω

T2 800/380V 100kVA



41QF 21QF

D11

01#G

21#W

Δ

DT 220/110V 10kVA

SMES

Figure 6. Circuit of the experiment #2.

1

(a)

60

(b)

60

54

Current/A

Power/kW

0 -1 -2

48

40

86

88

90

92

Power exchange process

20

-3

0

8

9

10 Time/s

11

12

0

50

100

150

Time/s

Figure 7. (a) shows the output power of the SMES and (b) shows the current waveform of the magnet in experiment #2.

T1

G1

101

111

6.3kV line

121 10kV line substation

T2 CT1

D1

PT1

MCS

G3 D2 T4

T3

CT2

T5 magnet PCS

contactor

Figure 8. Circuit of the field experiment.

16

resistor

200

ACCEPTED MANUSCRIPT (a)

41

9

With SMES

(b)

Power/kW

Power/kW

6 40

39

3 0 -3 -6

38

4

6

8

10

12

Time/s

6

14

7

8

9

10

Tmie/s

11

12

13

Figure 9. Output power of the generator and SMES. (a) shows the output power of the generator and line power and (b) shows the output power of the SMES.

70 60

60

Current/A

50 40

40

76

78

80

Power exchange process

20

0 0

50

Time/s

100

150

Figure 10. Current waveform of the SC magnet in experiment #3.

-6

×10

Test curve Fitted curve

1.3

Voltage/V

1.2 1.1 1.0 0.9 0.8 0

2

4

6

8 10 12 Current/A

Figure 11. The V-I curve of the 10th joint.

17

14

16

18

ACCEPTED MANUSCRIPT -3

×10

(a)

0.028 0.026 0.024

0.02

(b)

0.003 Joint resistance loss/W

Joint resistance loss/W

0.03

184.04

184.08

184.12

0.01

0.00

32

28 24 20

0.002

88

92

96

100

0.001

0.000

-50

0

50 100 150 200 250 300 350 400 Time/s

0

20

40

60

80 100 120 140 160 Time/s

-3

×10

(c)

3

Joint resistance loss/W

0.003 2

0.002

76

78

80

0.001 0.000 0

20

40

60

80 100 120 140 160 Time/s

Figure 12. The joint resistance loss power. (a), (b) and (c) show loss power in experiment #1, #2 and #3, respectively.

Eddy current loss/W

1600 1200 800 400

184.04

(b)

plate 1 plate 9 main plate

80 60 40 20 0

0 184.06

184.08 Time/s

184.10

600 Eddy current loss/W

Eddy current loss/W

100

plate 1 plate 9 main plate

(a)

184.12

86

(c)

87

plate 1 plate 9 main plate

400

200

0 76

77

Time/s

18

78

79

88 Time/s

89

90

ACCEPTED MANUSCRIPT Figure 13. Instantaneous eddy current loss power during the power exchange process. (a), (b) and (c) show eddy current loss power in experiment #1, #2 and #3, respectively.

(a)

1000 100

100

10

AC loss/W

1000

1

10

184.08

184.16

1

Coil #1 Coil #2 Coil #3 Coil #4 Coil #5 Coil #6 Coil #7 Coil #8 Coil #9

(b)

900

AC loss/W

10000

600

300

0.1 0.01

0

0

50

100 150 200 250 300 350 400 Time/s

184.04

184.06

184.08 Time/s

184.10

184.12

Figure 14. Instantaneous AC loss power in experiment #1. (a) shows the total AC loss of the magnet and (b) shows the AC loss of each double-pancake coil. 8

3

4

6

AC loss/W

Coil #1 Coil #2 Coil #3 Coil #4 Coil #5 Coil #6 Coil #7 Coil #8 Coil #9

(b)

(a)

0 86

87

88

89

AC loss/W

8

4 2 0

2

1

0 0

40

80 Time/s

120

160

86.0

86.5

87.0 87.5 Time/s

88.0

Figure 15. Instantaneous AC loss power in experiment #2. (a) shows the total AC loss of the magnet and (b) shows the AC loss of each double-pancake coil.

80

(a)

100

40

30

0 76

60

78

AC loss/W

AC loss/W

80

Coil #1 Coil #2 Coil #3 Coil #4 Coil #5 Coil #6 Coil #7 Coil #8 Coil #9

(b)

80

40

20

10

20 0

0

0

20

40

60

80 100 120 140 160 Time/s

76

77

Time/s

78

79

Figure 16. Instantaneous AC loss power in experiment #3. (a) shows the total AC loss of the magnet and (b) shows the AC loss of each double-pancake coil.

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ACCEPTED MANUSCRIPT (a)

(b)

(c)

(d)

Figure 17. Mesh generated within the HTS magnet. (a) shows the connection between the cryocooler and the magnet, (b) shows the view of the two current leads, (c) shows side view of the magnet and (d) shows the view of the cold rod, cooling plates and their connections.

TDown(FEM) 22

TUp(FEM)

21

TDown(Test)

20

TUp(Test)

TMiddle(Test)

Temperature/K

Temperature/K

22

TDown(FEM)

TMiddle(FEM)

(a)

19 18

TMiddle(FEM)

(b)

TUp(FEM) TDown(Test)

21

TMiddle(Test) TUp(Test)

20

19

17 0

500

1000 1500 Time/s

2000

2500

3000

0

400

Time/s

800

1200

TDown(FEM) 22

TMiddle(FEM)

(c)

TUp(FEM)

Temperature/K

TDown(Test) TMiddle(Test)

21

TUp(Test) 20 19 0

300

600 900 Time/s

1200

Figure 18. Temperature variation of the magnet with time in experiment #1: (a), #2: (b) and #3: (c). TDown, temperature at the bottom of the magnet; TUp, temperature at the top of the magnet, and TMiddle is the temperature at the middle of the magnet.

20