1. Introduction
During the last few years, the amount of greenhouse gas emissions has increased, that resulted in increase of Earth's bulk temperature. To avoid this, “Net Zero” concept has been proposed, which focuses on greenhouse gas emission neutrality until 2050 [1]. The thermal power plants and the transportation sectors are among the sources of greenhouse gas emissions [2], [3]. In power systems, the integration of renewable energy resources, such as offshore wind farms or solar farms, is proposed as a solution. For instance, the capacity of wind farms in the UK was only 2.5 GW before 2012, and now it is approximately 11 GW [4]. Typically, offshore wind farms harvest 8 MW to 13 MW of electrical power per turbine.
Transformers play crucial role in uninterruptable delivery of harvested energy to the loads. To do this, large conventional copper-based transformers exhibit a high amount of loss, heavy weight, large footprint, vulnerability against transients and harmonics, and high cost [5], [6], [7]. To tackle these issues, High Temperature Superconducting (HTS) transformers were proposed which offer lower loss, lighter weight, and lower total ownership cost [8], [9], [10], [11]. Important challenges of HTS transformer implementation in power networks are AC loss and fault performance. AC loss-related analysis has been discussed in the literature [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]. The importance of fault performance of HTS transformers is that superconducting coated conductors are fragile against faults. Thus, by high amplitude short circuit currents, the heat generated in tapes abruptly increases, and consequently, the winding temperatures might burn out [29], [30]. This makes the fault performance analysis of HTS transformers as an important step towards their full commercialization [31].
In this regard, reference [32], the fault current limitation capability of a 64 MVA HTS transformer was discussed to show how HTS transformers could be used to limit the fault current imposed on the power system. In this reference [32], the impedance of the HTS transformer during fault is compared with the impedance of a copper-based transformer with the same ratings. Results showed that in the presence of the HTS transformer, 89% of the fault current is limited. However, a discussion on the thermal characteristics of the HTS transformer is missing. The fault performance of a 1 MVA HTS transformer was studied in [33] concerning the thermal characteristics of an HTS transformer. This study aimed to show how changes in the thermal mass of different layers in the HTS coated conductor would impact the fault performance of the HTS transformer. The results showed that the temperature of windings could reach to maximum of 600 K which results in their burnout, however; no solution was proposed for that. An Equivalent Circuit Model (ECM) is used in [34] which characterizes the fault performance of a 10 kVA, 230 V/115 V HTS transformer under a three-phase short circuit fault. The presented results showed that the ECM model has an excellent agreement with the numerical model. Also, it is shown that under the applied fault, the windings of the HTS transformer could burn out, especially low voltage windings. The impact of inrush currents was discussed in [35]. The properties of superconducting tapes such as the thickness of stabilizers and the substrates could have a direct impact on the fault performance of HTS tapes, which is analysed and discussed in [36], [37]. The impact of changing the structure of the HTS tapes and their effect on the Fault Current Limiting (FCL) capability of HTS transformers is discussed in [38], [39], [40], [41], [42]. For this purpose, the thermal mass and electric conductivity of substrate and stabilizer layers have been changed by increasing the thickness of these sublayers and changing their materials. The results have shown that FCL HTS transformers could suppress the fault current, however, their main problem is still the rapid temperature rise. To address the issue of temperature, increase in FCL HTS transformers, another type of HTS transformers has been proposed, known as Fault Tolerant Current Limiting (FTCL) HTS transformers in [43]. These transformers not only limit the fault current, but the temperature increase rate would be limited to avoid thermal runaway or burnouts by increasing the heat transfer from the tape surface to the coolant [44]. Usually, in this type, the heat transfer ratio is increased by using different types of dielectrics to cover the HTS tapes, also lowering the operating temperature of the coolant, and structural changes of the HTS tapes have a direct impact on the peak temperature of HTS transformers. Experimental tests have shown that FTCL HTS transformers could endure a massive fault current for 2 seconds without the possibility of burnout [43]. Experimentally validated models have shown that such HTS transformers could be recovered even when 225% of loading is applied to the HTS transformer after fault clearance [45]. The characterization of FTCL HTS transformers has been discussed in the literature, however, their system-level study is still missing. The system-level study allows a comprehensive understanding of the HTS transformer's behaviour when interacting with different components of the power system. It also shows the interdependencies in different components of power systems where these interdependencies could predict that how changes in the power system, could impact the characteristics of FTCL HTS transformer.
In this paper, a 50 MVA 3-phase FTCL HTS transformer was considered for the system-level study of HTS transformers in a benchmark power system of the IEEE Standard 399-1997, presented in [46], [47]. This study aims to show how FTCL HTS transformers would behave under real fault scenarios. Three types of winding for FTCL HTS transformers were discussed in this paper, namely, HTS transformers with bare tapes, Kapton insulated tapes, and solid insulated tapes. The results have shown that by using insulations, the peak temperature of HTS windings is 34% to 72% reduced, compared to bare HTS windings. Also, an HTS transformer with solid insulated windings could tolerate 170% to 192% of overloading after fault clearance. This means that overloading could be tolerated by the HTS transformer, even when the temperature is higher than the operational temperature. As a result of this, exactly after fault clearance, the HTS transformer could deliver the power to the grid.
2. Modelling methodology
In this paper, studied HTS transformer is characterized through an ECM, where electrical components are used to determine the thermal, magnetic, and electric characteristics of HTS tapes, as well as the windings behaviour. The ECM of a 3-phase HTS transformer is illustrated in Fig. 1, where Fig. 1(a) shows the ECM of HTS tapes used in windings of the HTS transformer while Fig. 1(b) shows the ECM of the whole HTS transformer including the iron core. To develop such a model, one must first conceive the characterization performance of an HTS transformer, and then, translate the characteristic into the circuit-based components such as resistors, inductances, and capacitances. The procedure of characterization and modelling by ECM is shown in Fig. 2.
Fig. 1. The equivalent circuit model used for characterising the HTS transformer, referenced from the Primary Side. |
Fig. 2. Modelling procedure of HTS transformer using ECM. |
It should be noted that electrically, any HTS transformer could operate in three operational states, which are steady-state, transient-state, and recovery-state. The flowchart shown in Fig. 3 shows the modelling procedure of the HTS transformer. The first step is getting the design and operational properties of the HTS transformer, as well as the features of superconducting tape sub-layers. Then, the current at each time step is measured, if the current is higher than the critical current of the HTS winding, the HTS transformer is operating in a transient state without any need for measuring the temperature. However, if the current is lower than the critical current, it does not mean that the transformer is operating in a steady state. This is because the temperature could be higher than the critical temperature of HTS tapes which means the recovery state is going on. Finally, if both current and temperature are lower than their critical values, the HTS transformer is working in a steady-state.
Fig. 3. Flowchart of Modelling procedure by ECM in HTS transformer. |
Equation (1) calculates the equivalent resistance of the HTS tapes and equation (2) calculates the temperature and current dependent characteristic of the superconducting sublayer in HTS tape [48].
$\rho_{\text {tape }}=\left(\frac{1}{\rho_{s c}}+\frac{1}{\rho_{\text {stab }}}+\frac{1}{\rho_{s u b}}+\frac{1}{\rho_{a g}}\right)^{-1}$
$\rho_{s c}(J, T)=\left\{\begin{array}{cc} \rho_{0} & J<J_{c}(T) \\ \rho_{0}+\left(\frac{E_{0}}{J}\right)\left(\frac{J}{J_{c}(T)}-1\right)^{n} & J<J_{c}(T)<3 J_{c}(T) \\ \frac{\left(\rho_{\text {sat }}\right)\left(\left(\frac{E_{0}}{J}\right)\left(\frac{J}{J_{c}(T)}-1\right)^{n}\right)}{\left(\rho_{s a t}\right)+\left(\rho_{0}+\left(\frac{E_{0}}{J}\right)\left(\frac{J}{J_{c}(T)}-1\right)^{n}\right)} & J>3 J_{c}(T) \end{array}\right\}$
where, $\rho_{s c}$ is the resistivity of the superconducting sublayer, $\rho_{stab}$ is the resistivity of stabilizer, $\rho_{sub}$ is the resistivity of substrate, $\rho_{ag}$ is the resistivity of the silver layer in HTS tape, $\rho_{0}$ is the resistivity of Yttrium Barium Copper Oxide (YBCO) tapes in steady-state, $E_0$ is the electric field, J is the current density, $J_c$(T) is the critical current density, n is the index value, and $\rho_{sat}$ is the saturation resistance [49].
$L_{i}=\frac{N_{i}^{2} \mu_{0} \mu_{r} A_{F}}{\ell}$
$M_{i j}=\frac{N_{i} N_{j} \lambda_{i}}{I_{j}}$
where, $N_i$ is the turn number, $μ_0$ is the permeability of free space equal to 4π × 10−7H/m, $μ_r$ is relative permeability of the core material, AF is the cross-section area of the flux path, l is the height of the windings, $λ_i$ is the flux linkage of layer i, and $I_j$ is the excitation current of winding j.
$B_{a x}=\frac{1}{\sqrt{2} \pi} \frac{\mu_{0} I(t) N}{\ell}\left|\tan ^{-1} \frac{z_{j}+\frac{\ell}{2}}{r_{i}}-\tan ^{-1} \frac{z_{j}-\frac{\ell}{2}}{r_{i}}\right|$
$B_{r}=\frac{1}{2 \sqrt{2} \pi}\left[\ln \left(\left(\frac{2 r_{i}}{\ell}\right)^{2}+\left(\frac{2 z_{j}}{\ell}-1\right)^{2}\right)-\ln \left(\left(\frac{2 r_{i}}{\ell}\right)^{2}+\left(\frac{2 z_{j}}{\ell}+1\right)^{2}\right)\right]$
where, I(t) is the RMS current passing through the HTS windings and l is the coil height.
The calculation method for perpendicular and parallel magnetic field in HTS transformer based on the axial magnetic and radial fields are shown in equations (7), (8) which are based on the winding angle Θ [52]:
$B_{\|}=B_{a x} \cos \Theta+B_{r} \sin \Theta$
$B_{\perp}=B_{a x} \sin \Theta+B_{r} \cos \Theta$
The losses in HTS transformers must be calculated for the sake of heat load determination and gaining the value of temperature change. For this purpose, equations (9), (10), (11), (12), (13), (14), (15) are used which show the losses resulted by self-magnetic field, parallel magnetic field, perpendicular magnetic field, current lead, cryostat, and the iron core, respectively [53].
$Q_{s f}=\frac{f I_{c}}{\pi} \mu_{0}\left(\ln F_{i}-F_{i} \ln F_{i}+F_{i}-\frac{1}{2} F_{i}^{2}\right)$
$F_{i}=\frac{I_{o p}}{I_{c}}$
$Q_{\|}=\left\{\begin{array}{cl} \frac{f C A_{c}}{\mu_{0}} \frac{2 B_{\|}^{3}}{3 B_{p}} & B_{\|}<B_{P} \\ \frac{f C A_{c}}{\mu_{0}}\left(2 B_{P} B_{\|}-\frac{4}{3} B_{P}^{2}\right) & B_{\|}>B_{P} \end{array}\right\}$
$Q_{\perp}=K f \omega^{2} \frac{\pi}{\mu_{0}} B_{C} B_{\perp}\left[\ln \left(\cosh \frac{B_{\perp}}{B_{C}}\right)^{\frac{2 B_{C}}{B_{\perp}}}-\tanh \frac{B_{\perp}}{B_{C}}\right]$
$Q_{C L}=6 q_{C L}\left(I_{L V}+I_{H V}\right)$
$Q_{c r y o}=\frac{A_{\text {cryo }} \Delta T}{\delta_{\text {ins }}} \lambda_{\text {ins }}$
$Q_{\text {core }}=1.2 \mathbb{C}_{P} G_{\text {core }}$
where, f is frequency, Ic is critical current, C is the ratio between the superconductor cross section and the total tape cross section, BP is the full penetration flux density, Ac is the total tape cross section, Bc is the critical field, K is a geometrical parameter, w is the tape width, qcl is the specific thermal income per unit current [15], $I_{LV}$ is current at low voltage side, $I_{HV}$ is the current at high voltage side (in kA), $λ_{ins}$ is thermal conductivity of cryostat, $δ_{ins}$ is the thermal insulation thickness, $A_{cryo}$ is the cryostat surface, Gcore is the weight of the core, and $ \mathbb{C}_{P} $ is the loss per unit weight of ferromagnetic material [53].
By having the values of total heat load in each time step, the thermal characteristic of the HTS transformer could be determined based on equation (16) [54]:
$D(T) C_{p}(T) \frac{\partial T}{\partial t}=k(T) \frac{\partial^{2} T}{\partial x^{2}}+Q-\nabla q$
where, $ D(T) $ is the density of the material in (kg/m3), Cp(T) is the specific heat capacity in J/kg.K, k(T) is the thermal conductivity in W/m.K, Q is the total generated heat in windings of HTS transformer, and ∇q is the heat flux in bath cooling which could be translated as the amount of heat transferred from the surface of the superconductor to the coolant fluid, under pool boiling conditions. During steady state, Q is equal to the losses calculated in equations (9), (10), (11), (12), (13), (14), (15) while under transient states, Q equals to the amount of Joule loss generated in stabilizers of HTS tapes in transformer winding. For the determination of the heat flux, more equations and details have been discussed in [45].
3. Results and discussions
In this section, the configuration of the power system is introduced where the HTS transformer is implemented in. The characteristic of the HTS transformer, during normal conditions in this power system is analysed. The fault performance of the HTS transformer covered with different insulation materials as well as bare tapes is analysed. The best fault tolerability performance of an HTS transformer with insulated windings is discussed more in terms of recovery under load.
3.1. Power grid configuration, specifications, and fault scenarios
In this paper, a standard power system, i.e., IEEE Standard 399-1997 is considered to analyse the fault performance of the HTS transformer under power system conditions in the presence of the Distributed Generators (DGs). Here DGs are synchronous generators that supply part of power for the related loads in the microgrids (MG). This means that DG1 supplies part of the electric power required by Load 1 and Load 2 while DG2 is responsible for supplying Load 3 and Load 4, as shown in Fig. 4. The power system consists of three main parts, as shown in Fig. 4, the upper part which has two Points of Common Coupling (PCC), a capacitor bank, a load, and an HTS transformer. Other parts of the grid are two Microgrids, i.e., MG1, and MG2, each of which has two loads and a DG. The voltage of the HTS transformer is 132 kV/13.8 kV which makes the reference voltage of the understudied grid to be 13.8 kV. The MGs are connected to the main grid through a PCC which is a Circuit Breaker (CB), when MGs need to inject into/receive power from upper hand grid, the CB is closed. In the case of islanding opertional mode, CB would be open. In this concept, islanding refers to the operation condition of MGs where their generated power is equal to consumed power, thus, they do not need to inject/receive the power to/from the upper hand power system [55]. The details of the power system are tabulated in Table 1 and more information is discussed in [46], [47]. The aim of considering these two load scenarios is to investigate whether a fault occurring in one of the MGs would still allow the HTS transformer to provide the required power for another MG that experiences no faults. As seen in Fig. 4, when F1 happens, MG1 is still operating and power should be supplied, this is also the case with F2 fault and MG2.
Fig. 4. A schematic of a power system where two Micro Grids (MGs) have been considered and the power is delivered to the system through an HTS transformer. |
Table 1. The specifications of the power system consisting of an HTS transformer. |
| Parameter | Value | Unit |
|---|---|---|
| Voltage of DG2 | 13.8 | kV |
| Generated power by DG2 | 2.5 | MVA |
| Active power of load 4 | 0.9 | MW |
| Active power of load 3 | 0.9 | MW |
| Reactive power of load 3 | 0.6 | MVAr |
| Active power of load A | 3.2 | MW |
| Reactive power of load A | 1.9 | MVAr |
| Reactive power of capacitor bank | 1.5 | MVAr |
| Voltage of DG1 | 13.8 | kV |
| Generated power by DG1 | 5 | MVA |
| Active power of load 2 | 1.5 | MW |
| Reactive power of load 2 | 1.0 | MVAr |
| Active power of load 1 | 0.8 | MW |
| Reactive power of load 1 | 0.47 | MVAr |
| Fault timing 1 | 4 to 4.1 | s |
| Fault timing 2 | 4.5 to 4.6 | s |
The HTS transformer is a 50 MVA transformer with an X/R ratio approximately equal to 22, where YBCO-based coated conductors are used in its windings. This HTS transformer operates at 65 K base temperature which is cooled down by sub-cooled liquid nitrogen. The electrical properties of this HTS transformer are tabulated in Table 2, the design of transformer is shown in Table 3, and the properties of HTS tapes are listed in Table 4.
Table 2. The specifications of the 50 MVA HTS transformer [56]. |
| Parameter | Primary side | Secondary side | unit |
|---|---|---|---|
| Nominal voltage | 132 | 13.8 | kV |
| Number of strands | 8 | 17 | - |
| Nominal current | 480 | 2250 | A |
| Number of turns | 860 | 156 | - |
| Number of layers | 10 | 4 | - |
| Gap between layers | 0.05 | 0.025 | mm |
| Turns per layer | 86 | 39 | - |
| Windings critical current | 740 | 3400 | A |
| Maximum flux density in the core | 1.6 | T | |
| Loading safety factor of windings | 65% | ||
| Total leakage reactance | 0.067 | p.u. | |
| Magnetisation reactance | 105 | p.u. | |
Table 3. Design summary of 50 MVA HTS transformer [56]. |
| Description | Value (mm) |
|---|---|
| Core radius | 300 |
| High voltage winding details | |
| Radius to midpoint | 402.5 |
| Height | 516 |
| Radial build | 21.5 |
| Low voltage winding detail | |
| Radius to midpoint of inner winding | 364.5 |
| Radius to midpoint of outer winding | 440.5 |
| Height | 507 |
| Radial build | 8.7 |
| Gap between adjacent windings | 23 |
| Clearance between windings and Core | |
| Upper | 300 |
| Lower | 300 |
| Radial space between inner LV winding and core | 60 |
| Radial space between inner LV winding and outside of cryostat | 40 |
| Separation between adjacent phase cryostats | 30 |
| Gap between coils and core on top | 300 |
| Gap between coils and core on bottom | 300 |
| Gap between adjacent windings | 23 |
Table 4. The properties of YBCO coated conducted used in winding of HTS transformer [56]. |
| Parameter | Value/type | Unit |
|---|---|---|
| Critical current @65 K & 0 T | 260 | A |
| Index value @65 K & 0 T | 28 | - |
| Tape width | 4.4 | mm |
| Tape thickness | 100 | µm |
| Stabiliser thickness | 40 | µm |
| Stabiliser material | Copper | - |
| Shield thickness | 3.8 | µm |
| Shield material | Silver | - |
| Substrate thickness | 50 | µm |
| Substrate material | Hastelloy | - |
| Superconducting thickness | 1 | µm |
| Superconducting material | YBCO | - |
Fig. 5 shows the DG's start-up current and the steady-state operation of the grid, after the transients are damped, the shown current is measured on the secondary side of the HTS transformer. As seen in this figure, when the DGs start to work, a current, higher than the rated current, is injected into the power system as well as the HTS transformer, after 2 seconds the transient current is damped and the current finally enters its steady state. The HTS transformer is designed so that the starting current does not cause the thermal deterioration of the YBCO tapes. As shown in Fig. 6, the maximum temperature of phases A, B, and C regarding the starting current is about 65.8 K which is just about 1% higher than the maximum temperature of these phases at steady state.
Fig. 5. The current of the power system under steady state and start-up current of the DGs. |
Fig. 6. Temperature characteristic of the HTS transformer with bare windings, under DG start-up current and steady state of the grid. |
Fault scenarios are imposed in MGs where the fault resistance is 0.01 Ω, and their impact on the HTS transformer is going to be discussed. As shown in Fig. 7, fault scenario 1, imposes approximately 40 kA fault current to the grid while scenario 2 imposes 50 kA fault current to the grid.
Fig. 7. Fault current characteristic for different fault scenarios in studied power system. |
This investigation aims to see how different fault scenarios would increase the windings temperature of the HTS transformer. If the HTS transformer does not face burnouts in two fault scenarios, it can supply the required power of healthy MG when the other one is experiencing a short circuit fault. In this regard, burnout happens when the temperature of superconducting tapes/windings surpasses the 300 K limit [44]. Under such condition, superconducting properties of the tapes/windings are compromised, or they are deformed due to exposure to excessive harsh thermal conditions. In other words, the HTS material essentially loses its ability to superconduct effectively and may even undergo irreversible changes [44].
3.2. Fault tolerability concept for HTS transformer
In this section, the thermal characteristic of the HTS transformer affected by different fault currents at different locations of the power system is analysed. In this regard, three different scenarios are considered for the insulation method of the HTS windings on both the HV and LV sides. These scenarios include HTS windings with bare tapes, with Kapton insulated tapes, and with Acrylated Urethane solid insulation. Heat transfer regimes for HTS tapes with different insulations are shown in Fig. 8, based on the results presented in [44]. As shown in this figure, using insulated tapes in HTS windings increases the heat flux value during the nucleate boiling regime. The maximum heat flux value in the nucleate boiling regime for bare tape is 30 kW/m2 while this value for Kapton insulated tape is about 80 kW/m2 (166% increase). By using solid insulated tapes, this value is even further increased, and reaches 170 kW/m2 which means a 112% increase compared to Kapton insulated tapes and a 460% increase compared to bare tapes. The data shown in Fig. 8 are experimentally measured and published in [44].
Fig. 8. Heat transfer regimes for HTS tape of transformer with different insulations. |
Fig. 9 displays the temperature profile of secondary windings of the HTS transformer, in phase A under the F1 fault scenario. When a fault happens, the temperature starts to rapidly increase, until the fault is cleared. After that, the temperature reduces until it gets back to the base temperature, i.e., 65 K. Due to the lower heat flux value of bare tapes, the windings temperature approaches to near 350 K which could increase the risk of HTS tape burnout. By using Kapton insulated tapes, the peak temperature of the HTS winding is 34% reduced while using solid insulated tapes could even further reduce the peak temperature of HTS winding. Using Acrylated Urethane as insulation of HTS windings could 72% reduce the peak temperature. Since, insulations increase the heat flux value of the nucleate boiling regime, during a fault, more heat is transferred from the windings surface to cryogenic coolant fluid.
Fig. 9. Temperature characteristic of HTS transformer with different types of insulations, under F1 fault. |
As shown in Fig. 10, F2 has more fault current than F1, the peak temperature of the secondary windings under this fault increases. Compared to F1 scenario, bare HTS windings experience a 35% temperature increase under the F2 fault scenario, which is 460 K, while this number for Kapton insulated windings and solid insulated windings is approximately equal to 28% and 20%, respectively. Bare tapes experience a 35% peak temperature increase while this value for Kapton insulated and solid insulated windings is about 27% and 21, respectively. However, even after the fault current increase imposed on HTS windings, the peak temperature of solid insulated HTS windings is about 150% and 310% lower than the peak temperature of Kapton insulated and bare windings, respectively. As a result of this, even under a higher fault current amplitude of F2, the HTS with solid insulated windings is still capable of providing the load for the MG2.
Fig. 10. Temperature characteristic of HTS transformer with different types of insulations, under F2 fault. |
As shown in the above figures, solid insulated windings could tolerate fault current without any risk of burnouts and deformation. Based on this, the next step is investigating how loading after fault clearance could be tolerated by an HTS transformer.
3.3. Post-fault recovery of the HTS transformer
In this section, the impact of transformer loading after fault clearance is investigated to see how much energy could result in burnout or thermal runaway of HTS windings, after fault clearance. For this purpose, different loadings have been applied to the HTS transformer during its recovery state. These loadings are representative of healthy MG supply by HTS transformer, after fault clearance. In this regard, Fig. 11 shows the under-fault and post-fault performances of the HTS transformer caused by the F1 fault scenario. When there is no loading after fault clearance, HTS windings rapidly recover to base operational temperature. This state is known as full recovery where the temperature of HTS windings is equal to the base temperature of the cryogenic coolant, here, 65 K. There is also another stat known as partial recovery where the temperature of HTS windings is lower than critical temperature but still higher than base coolant temperature. As seen in Fig. 11, when loading after fault clearance is considered, HTS windings are not able to enter the full recovery zone, instead, they operate in a partial recovery state. Here the temperature quickly drops from peak temperature due to nucleate boiling but when reaches to natural conduction regime, it will drastically slow down [43]. By the increase of the post-fault loading, more electrical energy would be injected into HTS windings, and this results in increasing the full recovery time of windings. However, HTS windings have a maximum capacity where any further increase in the input energy results in the thermal runaway of HTS windings. In the case of the F1 fault scenario, this maximum capacity is 192% of rated loading which means that by imposing a current 1.92 times higher than the rated current, HTS windings would never recover, face thermal runaway, and their temperature would increase until their full burnout.
Fig. 11. Recovery under load characteristic of HTS transformer with solid insulation under F1 fault scenario. |
Fig. 12 shows the post-fault performance of the HTS transformer, under the F2 fault scenario where different loadings have been applied to the HTS transformer after fault is cleared. The previous trend could be seen in this figure with one difference where the maximum tolerable post-fault loading of the HTS transformer is approximately 11.5% reduced. This reduction originated in the higher fault current of the F2 scenario compared to the F1 scenario.
Fig. 12. Recovery under load characteristic of HTS transformer with solid insulation, fault 2. |
After investigating on the impact of the post-fault loading, a mathematical exponential fitting is used here to estimate the full recovery time of the HTS windings, under F1 and F2 fault scenarios. In this regard, the fitting parameters are shown in Table 5 and Table 6 of the paper, based on different scenarios of faults and their post-fault loading before thermal runaway.
Table 5. The Fitting parameters of recovery time for the F2 fault scenario. |
| Loading % after fault | Fit Equation $ T(t)=a \exp (b \times t)+c \exp (d \times t) $ | |||
|---|---|---|---|---|
| a | b | c | d | |
| 0 | 0 | −18.5256 | 65.0709 | 0.0021 |
| 50 | 0.0003 | −6.4355 | 70.5509 | −0.0077 |
| 75 | 0.0013 | −5.5195 | 71.1775 | −0.0062 |
| 100 | 0.0032 | −4.9786 | 71.7508 | −0.0050 |
| 150 | 0.0108 | −4.2908 | 72.7753 | −0.0031 |
| 180 | 0.0192 | −3.9795 | 73.3245 | −0.0019 |
| 190 | 0.0362 | −3.6547 | 73.4095 | −0.0001 |
Table 6. The Fitting parameters of recovery time for the F2 fault scenario. |
| Loading % after fault | Fit Equation $ T(t)=a \exp (b \times t)+c \exp (d \times t) $ | |||
|---|---|---|---|---|
| a | b | c | d | |
| 0 | 0.0001 | −18.5783 | 65.0228 | 0.0033 |
| 50 | 0.0002 | −13.5252 | 71.0423 | −0.0171 |
| 75 | 0.0004 | −10.8429 | 71.6874 | −0.0155 |
| 100 | 0.0004 | −8.1846 | 72.1846 | −0.0125 |
| 150 | 0.0024 | −5.4080 | 73.0522 | −0.0074 |
| 160 | 0.0072 | −4.7501 | 73.1528 | −0.0055 |
| 165 | 0.0119 | −4.4606 | 73.1323 | −0.0045 |
Fig. 13 shows the estimated full recovery time of HTS windings under different fault scenarios concerning the variations of the loading. As can be seen, when loading increases from 0% to 50%, an abrupt change is observable while after that increasing the post-fault loading, increases the recovery time of the HTS windings. Finally, before the thermal runaway of the HTS windings, the full recovery time is increased abruptly again to around half an hour. This again shows why any further increase in post-fault loading results in the thermal runaway of the HTS windings.
Fig. 13. Estimated full recovery time of HTS transformer winding using exponential fitting, under two fault scenarios. |
The next step in the system analysis of the FTCL HTS transformer is to investigate the impact of long-duration faults on the thermal characteristics of the HTS windings. For this purpose, four fault durations have been considered for each fault scenario which include, 100 ms, 500 ms, 1000 ms, and 2000 ms, as shown in Fig. 14(a). The amount of fault energy imposed on the HTS windings during and after the fault is shown in Fig. 14(b).
Fig. 14. Faults with different durations, a) fault current, b) fault energy. |
Fig. 15 shows the temperature profile of the secondary windings of phase A, under different fault durations. As seen in this figure, by increasing the duration of the fault current, the peak temperature does not change. Because, after the first peak of the fault current, the amount of energy injected into the HTS windings is reduced so the temperature of HTS windings reduces. In case of 2 second fault, the fault energy is accumulated again and causes the temperature increase of the HTS windings, after reduction.
Fig. 15. Temperature characteristic of the solid insulated HTS transformer, under different lengths of fault. |
It should be mentioned that our proposed model for HTS transformer, as indicated in reference [45], demonstrates effective coping with experimental results. However, challenges exist, particularly in the context of system-level analysis for electric grids. While the proposed model exhibits speed advantages when compared to Finite Element Method (FEM)-based approaches, its computational time is depending on the chosen time step. For system-level analysis, scenarios may exist where transients with time steps less than a microsecond. Addressing such transients becomes imperative, as the computational time even for fast methods, like the proposed one, experiences a significant increase. A challenge lies in the fact that transformer models establish by primarily focusing on heat transfer experimental data extracted from component level testing, that is because of absence of experimental heat transfer results for MW-level winding heat transfer. To surmount these challenges, Artificial Intelligence (AI)-based surrogate models [30], [57], [58] come into play. These surrogate models establish a logical relationship between inputs (system variables) and outputs (system characteristics), bypassing the need to solve complex electromagnetic and thermomechanical equations. Generally characterized by their speed, these models offer faster computational times, with their accuracy tied to the precision of the underlying model.
4. Conclusion
High Temperature Superconducting (HTS) transformers will play a promising role in future power grids where most of the electrical power is generated by clean energy sources, such as wind farms and solar farms. HTS transformers offer 50% lower weight and size, lower energy losses, massive overloading capacity, and fault-tolerant characteristics. Indeed, Fault Tolerant Current Limiting HTS (FTCL HTS) transformers are novel types of HTS transformers that could endure fault currents. However, the system-level study of FTCL HTS transformers was never investigated. In this paper, a 132/13.8 kV, 50 MVA FTCL HTS transformer was implemented into a standard IEEE power system in the presence of distributed generation units. Then, the fault performance of the FTCL HTS transformer is studied, where the most important findings of this paper are:
•By using the bare tapes in HTS windings, the peak temperature of these windings increases, in the range of 340 K to 450 K, under different fault scenarios.
•Covering the HTS tapes with Kapton insulation papers, causes the peak temperature reduction of HTS windings in the range of 220 K to 270 K, under different fault scenarios.
•Substantial reduction in peak temperature of HTS windings is achieved when Acrylated Urethane insulations are used where the peak temperature ranges between 95 K to 110 K, for different fault scenarios.
•The Acrylated Urethane-insulated HTS transformer could also endure 170% to 192% post-fault overloading, without any risk of HTS tape burnout.
•Imposing the loading and overloading, after fault clearance, increases the full recovery time of HTS windings while the partial recovery time is still low.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
For open access, the author(s) has applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising from this submission.
