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Superconducting magnetic energy storage (SMES) devices integrated with resistive type superconducting fault current limiter (SFCL) for fast recovery time
Journal of Energy Storage 13 (2017) 287–295
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Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Superconducting magnetic energy storage (SMES) devices integrated with resistive type superconducting fault current limiter (SFCL) for fast recovery time Raja Sekhar Dondapatia,* , Abhinav Kumara , Gadekula Rajesh Kumara , Preeti Rao Usurumartib , Sreekanth Dondapatic a
School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab 144 401, India PVK Institute of Technology Anantapur, Andhra Pradesh, India c School of Mechanical and Building Sciences, VIT University, Chennai, India b
A R T I C L E I N F O
Article history: Received 29 June 2017 Received in revised form 5 July 2017 Accepted 6 July 2017 Available online xxx Keywords: Energy storage Superconducting fault current limiter (SFCL) Superconducting magnetic energy storage (SMES) MATLAB/SIMULINK Recovery time
A B S T R A C T
Energy storage devices experience load fluctuations due to fault currents, lightening and non-uniform load distribution. Hence, Superconducting Magnetic Energy Storage (SMES) devices are incorporated to balance these fluctuations as well as to store the energy with larger current density. Further, Superconducting Fault Current Limiter (SFCL) are integrated with SMES for avoiding fault currents. In addition, SFCL are preferred in electrical utility networks due to their better technical performance during faults as compared to the conventional Circuit Breakers. Self-triggering from superconducting state to normal state during fault and very fast recovery to its original superconducting state after fault removal is the fundamental operation of Resistive type Superconducting Fault Current Limiter (R-SFCL). Moreover, commercial applications of SFCL in electrical power systems are enormously increasing due to the availability of long length High Temperature Superconducting (HTS) tapes. In the present work, an algorithm is developed to estimate the recovery time of R-SFCL with three phases to be used in SMES. Further, the electrical and thermal strategies to develop R-SFCL are also presented. In addition, the short circuit behaviour under fault currents is investigated considering 440 kV/1.2 kA capacity line. Finally, the percentage of fault compensation in all the three phases of SMES integrated with R-SFCL is calculated. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction The drastic increase in the power demand leads to higher short circuit faults in the power generation, energy storage, power transmission and distribution [1,2]. Hence, distributed generation systems are employed in smart grids to meet this demand. However, the fluctuations in the power generation cause instabilities in the power system [3] including storage systems. These instabilities increase with higher transmission voltages resulting in the damage of circuit breakers [4]. Hence, it is necessary to replace the entire smart grid with superconducting power grid consisting of superconducting power generators, superconducting cables, superconducting magnetic energy storage devices, superconducting transformers and superconducting
* Corresponding author. E-mail address: [email protected] (R.S. Dondapati). http://dx.doi.org/10.1016/j.est.2017.07.005 2352-152X/© 2017 Elsevier Ltd. All rights reserved.
motors as shown in Fig. 1. However, AC losses are reported to be increasing with the transport current [5] in superconducting power systems. One of the solutions to protect the entire power system is to incorporate the Superconducting Magnetic Energy Storage (SMES) system. A typical solenoidal type SMES with different subcomponents is shown in Fig. 2. This in turn creates the need for the effective cooling strategies to be adapted for current leads connected to the Superconducting Magnetic Energy storage Systems (SMES). Hence, it is essential to protect the entire power system from faults by means of resistive type Superconducting Fault Current Limiter (SFCL). These SFCLs are made of High Temperature Superconductors (HTS) due to their capacity to handle large current densities and self-triggering capabilities [6] which can compensate the faults within milliseconds and automatically recover [7] to their superconducting state in few milliseconds [8]. These advantages made R-SFCL to integrate with the electrical power system to limit the fault in the first cycle and prevent the power system from severe
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Fig. 1. Superconducting power grid with superconducting Generators, SMES, Cables, Transformers and Motors.
damage [9]. However, the fault current compensation depends on the material of the superconducting layer because of the index value [10]. In the past, BSCCO based 1st generation tapes are used (Bi-2212 [11] and Bi-2223) [12] because of the availability in long lengths. The index value for these tapes lies in between 8 and 12 [10] which is very low compared with the 2nd generation YBCO tapes [13,14] with the index value 20–40. These 2nd generation
superconductors offer high current density and faster recovery from the faults. Further, cooling strategies which could be adapted for superconducting magnets [15–19], current leads [20], power transmission cables [21–23] are already reported in the literature. Similarly, such cooling strategies for SMES devices are to be developed for energy efficient systems.
Fig. 2. Components of Typical Solenoidal HTS Superconducting Magnetic Energy Storage Device.
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Motivated by the importance of development of SMES devices and corresponding design of R-SFCL, the present work aims at developing a strategic design of R-SFCL. Further, the capability of compensating the fault current in the three phase is evaluated. Finally, the percentage of fault compensation in all the three phases of SMES integrated with R-SFCL is calculated.
Yazawa et al. [26]: AHTS ¼ wt
In the present section, electrical and thermal design strategies to be used for SMES devices are presented. The design is mainly based on the transient stability of the fault current by ElectroThermal interactions with Time-Current characteristics [1,24], and depends on the operating current.
ð2Þ
Further, cross-sectional area of the tape in terms of Critical current and Critical current density is given by: A¼
2. Electrical and thermal design of R-SFCL
289
Ic Jc ðTÞ
ð3Þ
3) Length of the superconducting Tape The length of the tape can be calculated from Eq. (5) using the parameters, first peak current (Irp) and resistance of the SFCL (RSFCL) as follows [27] pffiffiffi 2V rms ð4Þ LHTS ¼ Epeak
2.1. Development of algorithm The first step in developing an algorithm consists of selecting the type of the coated conductor (YBCO) and specifying the initial parameters such as the temperature of the cryogenic coolant (Ta), critical current at coolant temperature (Tc), critical temperature of the superconductor (Ta), width of the conductor (w), thickness of the conductor (t), critical current density (Jc), resistivity (r), index number of the conductor (n) and specific heat (CV). It is reported that the range of recovery time for maximum fault current compensation is between 80 ms to 120 ms [25]. Moreover, the behaviour of the superconductors can be studied from the J-B-T curve [2]. The basic parameters on which the R-SFCL design depends are 1) Transport Current in the HTS tape Using the relation between the RMS current and the peak current, the currents in different layers of the superconducting tapes are calculated using: pffiffiffi ð1Þ Ip ¼ 2Irms 2) Cross-Sectional Area of the superconductor The current carrying capacity of the superconducting tape increases if the thickness of the tape increases as reported by
lSC ¼
RSFCL IC n n1 EC Irp
ð5Þ
where, Vrms is transmission voltage and EC is the Critical Field 4) Number of turns over the mandrel Turns depends on the width of the tape, length of the tape, diameter of the mandrel and the sense of winding. 2.2. Electrical strategy for R-SFCL integrated with SMES devices When a fault occurs, the current transmitted through the coated conductors exceeds the critical current. Thereby, a transition from the superconducting state to the normal state occurs behaving as Ohmic conductor. In this scenario, the conductor offers resistance and the fault must be compensated. However, the non-uniformity in HTS tape material (ceramic in nature) as well as cooling of the conducting layers, hotspots are expected to occur [28,29]. In order to avoid the hotspots in the layers of the conductor, a resistor is connected in parallel to the superconductor. There are three states of transition in the superconducting tapes during the fault current in power systems. Based on the E-J
Fig. 3. E-J characteristic of Superconductors with three states of transition.
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where, n is index term, J is operating current density, JC is critical current density and E0 is electrical field at the initial condition of transport current. In order to find the time taken for the compensation of fault current, it is necessary to calculate the voltage to predict the state of transition and the E-J characteristic equations. 2.3. State-1 flux creep state (r = 0) The state where the conductor acts as a superconductor and do not allow any magnetic flux lines to flow through it, resistivity at operating temperature is zero and follow the power law is called Flux creep state. The first region in Fig. 3 is the flux creep state. The E-J characteristic equation of flux creep state is given as: aðT Þ J ð7Þ Eð1Þ ðJ; T Þ ¼ E0 JC
Fig. 4. Algorithm for developing the R-SFCL for SMES devices.
characteristics, one can describe the state of transition. The states of transition are Superconducting or flux creep state, flux flow state, normal state as shown in Fig. 3. The transition from the superconducting state to the normal state is based on the E-J power law because the state of the superconductor depends on the Critical current density (JC). The E-J power law in the superconducting state is shown in Eq. (6) [30]. n J E ¼ E0 ð6Þ JC
The index term a(T) is the maximum value of the index terms i.e., superconducting state index term (b) and index term at the operating temperature a0 (T). EC is critical electrical field, Ta is ambient temperature (77 K) and T is operating temperature
aðT Þ ¼ max½b; a0 ðT Þ where,
a ðT Þ ¼
log EEC0 11 að1T
0
log JJC ððTTaÞÞ C
b
E0 EC
ð8Þ aÞ
By calculating the E (J, T), one can predict the state of the conductor and the transport current.
Fig. 5. Simulated model of three phases fault and R-SFCL under three phase load.
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2.5. State-3 normal state (r = constant)
Table 1 Parameters used for simulating the model in MATLAB/SIMULINK. Component
Parameters
Nominal Values
Three Phase Source
Phase to phase RMS voltage (V) Frequency (Hz) 3-Phase short circuit level at base voltage (VA) Base voltage (Vrms ph-ph)
440 103
Nominal phase to phase voltage Vn (rms) Active power (W) Inductive reactive power QL (positive var) Capacitive reactive Power Qc (negative var)
440 103
Three Phase Load
R-SFCL
Resistance (Ohms)
The state at which conductor allows the magnetic flux lines completely, does not show the property of superconductivity with high resistivity compared to flux flow state and follow a linear relation due to its Ohmic behaviour is called normal state. The E-J characteristic in Ohmic state [8] is shown in Eq. (10)
50 1584 106
T Eð3Þ ðJ; T Þ ¼ rðT C Þ J TC
440 103
305 106 0
0
165
2.4. State-2 flux flow state, (r = r (J)) The state at which the flux line starts flowing through the superconductors due to the flux pinning is called flux flow state. The resistivity of the conductor depends on the current density due to transport current. The second region in Fig. 3 shows the behaviour of the conductor in the flux flow state. The E-J characteristic equation in flux flow state is given in Eq. (9). Eð2Þ ðJ; T Þ ¼ E0
EC E0
aðbT Þ b a JC ðT a Þ J J C ðT Þ JC ðT a Þ
1500
291
ð9Þ
ð10Þ
where, E = 1 * 106 V/cm @ 77 K, 1000 JC 10000 A/cm2, 5 a 15, 0.1 E0 10 mV/cm, 2 b 4, 100 r 2000 mW-cm. The transition from superconducting state to the normal state can also be described in terms of the change in temperature with respect to the time as the state of superconductivity also depends on the critical temperature (TC) of the conductor. The behaviour of the superconductor in the three states is given in Eq. (11). The variation of electrical field (E) with respect to temperature at that particular time is used for calculating the time required for the runoff of superconductivity [31]. 8 a JðtÞ > > E > C > > JC ðT ðtÞÞ > > > > f or EðT; tÞ < E0 and T ðtÞ < T C > > > > b > < EC a JC ðT a Þ JðtÞ b ð11Þ EðT; tÞ ¼ E0 > JC ðT ðtÞÞ JC ðT a Þ E0 > > > > f or EðT; tÞ > E0 and T ðtÞ < T > > > > T ðtÞ > > rðT C Þ J ðtÞ > > TC > : f or T ðtÞ > T C The algorithm developed to design the R-SFCL which can be integrated with SMES devices is shown in Fig. 4. As per the algorithm, the initial parameters at ambient temperature (Ta) must be specified. When the fault occurs and if the temperature and electrical field are less than the critical temperature and critical filed the conductor, the conductor is still at superconducting state.
Normal operation without fault and R-SFCL
Phase A Phase B Phase C
1000
500
0
-500
-1000
-1500 0.00
0.01
0.02
0.03
0.04
0.05
Fig. 6. Three phases under load without fault and R-SFCL (normal operation).
0.06
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5000
Phase A Phase B Phase C
Fault current zone
Normal operation
4000 3000 2000 1000 0 -1000 -2000 -3000 -4000 -5000 0.00
0.01
0.02
0.03
0.04
0.05
0.06
Fig. 7. Three phases under load with fault and without R-SFCL (Fault condition).
If the operating temperature is less than critical temperature, and electric filed is higher than critical filed, then the conductor is said to be in flux flow state. If both the cases are violated then the conductor is considered to be in normal state. The variation in the
time for the compensation of the fault is calculated and the total time is compared with the time specified in the initial parameters for further simulations.
Phase A Phase B Phase C 2000
Fault current compensated zone
Normal operation
1500 1000 500 0 -500 -1000 -1500 -2000 0.00
0.01
0.02
0.03
0.04
0.05
Fig. 8. Three phases under load with RSFCL and with R-SFCL (Fault clear condition).
0.06
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293
Table 2 Current limitation rate in three phase transmission system. Phase
Critical Peak During Normal Operation (A)
Critical Peak During Fault (A)
Critical Peak with RSFCL (A)
Percentage of Compensation
Phase A Phase B Phase C
1200 1200 1200
3500 5000 4000
1700 1900 1600
51.43% 62% 60%
The compensation time taken for clearing the fault due to electrical strategy is studied. However, due to the fault, there is rise in temperature in the cryogenic bath and boiling of the liquid nitrogen (LN2) takes place. Hence, it is necessary to calculate the heat transfer rate between the mandrel and LN2 to retain the superconductivity in the HTS tapes after the fault compensation. The thermal strategy for designing the R-SFCL to be used for SMES devices is explained in the later subsection.
Thermal resistance from the superconductor to cryogenic bath is convective. Hence, the equivalent thermal resistance is given by Rconv ¼ 1=hsccb Amandral ðK=WÞ
ð14Þ
where, hsc-cb = Coefficient of heat transfer from Superconductor to cryogenic bath (W/m2 K). Heat dissipated from the superconductor can be calculated as follows We know that, for Ohmic conductor
2.6. Thermal strategy for R-SFCL integrated with SMES devices
Q ¼ i2 R
ð15Þ
When the temperature rises above critical temperature, the superconductor becomes Ohmic conductor. Further, rise in the temperature will leads to run-off of the superconductivity. Hence, one needs to cool the coated conductor to regain its superconductivity after the compensation of fault current within milliseconds for effective energy storage. The heat transfer rate can be calculated as follows. Superconductor heat Capacity (J/K)
For the time rate change in heat generation, we have R Q SC ðtÞ ¼ iSC ðtÞ2 RSC ðtÞdt in Joules
ð16Þ
C SC ¼ C v V SC
ð12Þ
where, Cv = volumetric specific heat of superconductor (J/Km3)@Ta, VSC = Volume of the Superconductor, V SC ¼ lSC aSC
Resistance for the Ohmic conductor is R¼
El Ja
ð17Þ
The time rate change in the resistance of the Superconductor is given as follows [32]. RSC ¼
Eðt; TÞlSC JðtÞaSC
ð18Þ
ð13Þ
Normal Fault without R-SFCL Fault with R-SFCL
Normal operation 4000
Compensated Fault current
Fault current
3000 2000
Short circuit
1000 0 -1000 -2000 -3000 0.00
0.01
0.02
0.03
0.04
0.05
Fig. 9. Comparison of the three phases under load in different operations.
0.06
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RSFCL ðtÞ ¼ Rm
t 1 exp T SC
ð19Þ
where, Rm = maximum resistance of the Superconductor. Heat removed by the cryogenic cooling bath is given by Q removed ¼ hsccb ðAÞmandrel ðTðtÞ T a Þ
ð20Þ
Time rate change in the heat removal is given by Z Q removed ðtÞ ¼ hsccb ðAÞmandrel ðTðtÞ T a Þdt
ð21Þ
The transient stability of the system can be determined as follows From the basics of the conduction heat transfer dT CðTÞ ¼ rðkðTÞrTÞ þ qðTÞ dt
ð22Þ
Solving the Eq. (22) for the change in the temperature with respect to change in time is given by
rC SC dT ¼ ðQ generated Q removed Þdt
TðtÞ ¼ T a þ
1 C SC r
ð23Þ
Zt ðQ generation Q removal Þdt
ð24Þ
0
The rise in the temperature due to fault can be calculated from Eq. (24) and the time required for the compensation of the fault is calculated by relating the temperature change with E-J relations as follows. The time taken for the compensation of fault can be calculated using Eq. (24) and integrating on both sides. Z Z dT h i ð25Þ dt ¼ T ðtÞT ðaÞ 1 C SC IEðT ÞlSC Rconv 3. Simulation of R-SFCL to be integrated with SMES The model used for simulating the compensation of fault current in the three phases under load with fault and R-SFCL is shown in Fig. 5. Three phase source is connected to the three phase current measurement (A, B and C terminals) for measuring the increment and decrement in the current with change in the time. For three phases, individual R-SFCL is connected for compensating the fault current in each phase. Three phase fault and three phase load are connected in order to apply the load and the fault to A, B and C terminals in the current measurement. The scope is connected to Current measurement (Iabc) to observe the variations in the current under load. The main aim of the simulation is to reduce the fault occurred due to three phase fault and three phase load. The simulation is carried out for 440 kV/1.2 kA capacity suitable for Indian scenario. The parameters are initialized at time t = 0 with the parameters shown in Table 1 and model shown in Fig. 5 is simulated. 4. Results and discussions The simulated model is parametrically initialized by three phase source connected to current measurement. The three phases under load without fault and R-SFCL is simulated. Since, there is no fault in the phases, normal transmission is observed as shown in Fig. 6. The model is simulated up to 60 ms of current and it is observed a peak of 1200 A in all phases. Similarly, Fig. 7 shows the current distribution when the fault is occurred in three phases
under load with three phase fault without R-SFCL. It is observed that the peak current is increased as compared with the normal operation due to faults. The maximum faults are seen in the Phase B at its negative half cycle, followed by Phase C and Phase A in the positive half cycles. Fig. 8 shows the compensation of the fault current due to three phase fault under load condition. R-SFCL is used to compensate the fault and it is observed that almost 57.8% of the fault current is suppressed. The percentage of the compensation with critical peaks is shown in Table 2. Fig. 9 shows the comparison between current distributions in three phases under load during normal, fault without R-SFCL and fault with R-SFCL. It is observed that at 18 ms, short circuit has occurred in all the three phases and fault current is increased drastically in the next cycle. By using R-SFCL the fault current is compensated up to 58% in the first half cycle and the short circuit is reduced. Higher the resistance offered during the normal state, higher the reduction in the peak value in the first half cycle within few milliseconds. 5. Conclusions It is concluded that, transient thermo-electrical analysis is necessary to design R-SFCL which can be integrated to SMES. The three phase 440 kV/1.2 kA capacity transmission and distribution under load with fault current of 3500 A is compensated to 1700 A in phase A, 5000 A in Phase B is compensated to 1900 A and in phase C, 4000 A is compensated to 1600 A. The average compensation of fault is 57.8% with a recovery time of 60 ms. References [1] W.T.B. De Sousa, A. Polasek, R. Dias, C.F.T. Matt, R. de Andrade Jr., Thermal –electrical analogy for simulations of superconducting fault current limiters, Cryogenics (Guildf.) 62 (2014) 97–109. [2] W. Paul, M. Chen, Superconducting control for surge currents, IEEE Spectr. 35 (May) (1998) 49–54. [3] S. Romphochai, W. Kanokbannakorn, K. Hongesombut, Transient stability and fault current reduction of SPP with Bi-2212 SFCL considering recovery time, Procedia Comput. Sci. 86 (2016) 297–300. [4] L. Chen, Y. Tang, J. Shi, Z. Sun, Simulations and experimental analyses of the active superconducting fault current limiter, Phys. C Supercond. 459 (2007) 27–32. [5] G. Vyas, R.S. Dondapati, P.R. Usurumarti, Parametric evaluation of AC losses in 500 MVA/1.1 kA high temperature superconducting (HTS) cable for efficient power transmission: self field analysis, Proceedings -– UKSim-AMSS 8th European Modelling Symposium on Computer Modelling and Simulation, EMS 2014, 2014. [6] W. Paul, T. Baumann, J. Rhyner, F. Platter, Tests of 100 kW high-Tc superconducting fault current limiter, IEEE Trans. Appl. Supercond. 5 (2) (1995) 1059–1062. [7] M. Noe, A. Kudymow, S. Fink, S. Elschner, F. Breuer, J. Bock, H. Walter, M. Kleimaier, K. Weck, C. Neumann, F. Merschel, B. Heyder, U. Schwing, C. Frohne, K. Schippl, M. Stemmle, Conceptual design of a 110 kV resistive superconducting fault current limiter using MCP-BSCCO 2212 bulk material, IEEE Trans. Appl. Supercond. 17 (2) (2007) 1784–1787. [8] W. Paul, M. Chen, M. Lakner, J. Rhyner, D. Braun, W. Lanz, Fault current limiter based on high temperature superconductors – different concepts, test results, simulations, applications, Phys. C Supercond. Appl. 354 (2001) 27–33. [9] J. Zhu, X. Zheng, M. Qiu, Z. Zhang, J. Li, W. Yuan, Application simulation of a resistive type superconducting fault current limiter (SFCL) in a transmission and wind power system, Energy Procedia 75 (2015) 716–721. [10] S. Kar, S. Kulkarni, M. Dixit, K.P. Singh, A. Gupta, P.V. Balasubramanyam, S.K. Sarangi, V.V. Rao, Study on recovery performance of high Tc superconducting tapes for resistive type superconducting fault current limiter applications, Phys. Procedia 36 (2012) 1231–1235. [11] S. Elschner, F. Breuer, A. Wolf, M. Noe, L. Cowey, J. Bock, Characterization of BSCCO 2212 bulk material for resistive current limiters, IEEE Trans. Appl. Supercond. 11 (I) (2001) 2507–2510. [12] K. Sasaki, C. Nishizawa, T. Onishi, Test results and analysis of current limiting characteristics in conduction cooled bi2223 fault current limiter, IEEE Trans. Appl. Supercond. 13 (2) (2003) 2048–2051. [13] W. Schmidt, B. Gamble, H. Kraemer, D. Madura, A. Otto, W. Romanosky, Design and test of current limiting modules using YBCO-coated conductors, Supercond. Sci. Technol. 014024 (23) (2010) 1–9.
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Contents lists available at ScienceDirect
Journal of Energy Storage journal homepage: www.elsevier.com/locate/est
Superconducting magnetic energy storage (SMES) devices integrated with resistive type superconducting fault current limiter (SFCL) for fast recovery time Raja Sekhar Dondapatia,* , Abhinav Kumara , Gadekula Rajesh Kumara , Preeti Rao Usurumartib , Sreekanth Dondapatic a
School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab 144 401, India PVK Institute of Technology Anantapur, Andhra Pradesh, India c School of Mechanical and Building Sciences, VIT University, Chennai, India b
A R T I C L E I N F O
Article history: Received 29 June 2017 Received in revised form 5 July 2017 Accepted 6 July 2017 Available online xxx Keywords: Energy storage Superconducting fault current limiter (SFCL) Superconducting magnetic energy storage (SMES) MATLAB/SIMULINK Recovery time
A B S T R A C T
Energy storage devices experience load fluctuations due to fault currents, lightening and non-uniform load distribution. Hence, Superconducting Magnetic Energy Storage (SMES) devices are incorporated to balance these fluctuations as well as to store the energy with larger current density. Further, Superconducting Fault Current Limiter (SFCL) are integrated with SMES for avoiding fault currents. In addition, SFCL are preferred in electrical utility networks due to their better technical performance during faults as compared to the conventional Circuit Breakers. Self-triggering from superconducting state to normal state during fault and very fast recovery to its original superconducting state after fault removal is the fundamental operation of Resistive type Superconducting Fault Current Limiter (R-SFCL). Moreover, commercial applications of SFCL in electrical power systems are enormously increasing due to the availability of long length High Temperature Superconducting (HTS) tapes. In the present work, an algorithm is developed to estimate the recovery time of R-SFCL with three phases to be used in SMES. Further, the electrical and thermal strategies to develop R-SFCL are also presented. In addition, the short circuit behaviour under fault currents is investigated considering 440 kV/1.2 kA capacity line. Finally, the percentage of fault compensation in all the three phases of SMES integrated with R-SFCL is calculated. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction The drastic increase in the power demand leads to higher short circuit faults in the power generation, energy storage, power transmission and distribution [1,2]. Hence, distributed generation systems are employed in smart grids to meet this demand. However, the fluctuations in the power generation cause instabilities in the power system [3] including storage systems. These instabilities increase with higher transmission voltages resulting in the damage of circuit breakers [4]. Hence, it is necessary to replace the entire smart grid with superconducting power grid consisting of superconducting power generators, superconducting cables, superconducting magnetic energy storage devices, superconducting transformers and superconducting
* Corresponding author. E-mail address: [email protected] (R.S. Dondapati). http://dx.doi.org/10.1016/j.est.2017.07.005 2352-152X/© 2017 Elsevier Ltd. All rights reserved.
motors as shown in Fig. 1. However, AC losses are reported to be increasing with the transport current [5] in superconducting power systems. One of the solutions to protect the entire power system is to incorporate the Superconducting Magnetic Energy Storage (SMES) system. A typical solenoidal type SMES with different subcomponents is shown in Fig. 2. This in turn creates the need for the effective cooling strategies to be adapted for current leads connected to the Superconducting Magnetic Energy storage Systems (SMES). Hence, it is essential to protect the entire power system from faults by means of resistive type Superconducting Fault Current Limiter (SFCL). These SFCLs are made of High Temperature Superconductors (HTS) due to their capacity to handle large current densities and self-triggering capabilities [6] which can compensate the faults within milliseconds and automatically recover [7] to their superconducting state in few milliseconds [8]. These advantages made R-SFCL to integrate with the electrical power system to limit the fault in the first cycle and prevent the power system from severe
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Fig. 1. Superconducting power grid with superconducting Generators, SMES, Cables, Transformers and Motors.
damage [9]. However, the fault current compensation depends on the material of the superconducting layer because of the index value [10]. In the past, BSCCO based 1st generation tapes are used (Bi-2212 [11] and Bi-2223) [12] because of the availability in long lengths. The index value for these tapes lies in between 8 and 12 [10] which is very low compared with the 2nd generation YBCO tapes [13,14] with the index value 20–40. These 2nd generation
superconductors offer high current density and faster recovery from the faults. Further, cooling strategies which could be adapted for superconducting magnets [15–19], current leads [20], power transmission cables [21–23] are already reported in the literature. Similarly, such cooling strategies for SMES devices are to be developed for energy efficient systems.
Fig. 2. Components of Typical Solenoidal HTS Superconducting Magnetic Energy Storage Device.
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Motivated by the importance of development of SMES devices and corresponding design of R-SFCL, the present work aims at developing a strategic design of R-SFCL. Further, the capability of compensating the fault current in the three phase is evaluated. Finally, the percentage of fault compensation in all the three phases of SMES integrated with R-SFCL is calculated.
Yazawa et al. [26]: AHTS ¼ wt
In the present section, electrical and thermal design strategies to be used for SMES devices are presented. The design is mainly based on the transient stability of the fault current by ElectroThermal interactions with Time-Current characteristics [1,24], and depends on the operating current.
ð2Þ
Further, cross-sectional area of the tape in terms of Critical current and Critical current density is given by: A¼
2. Electrical and thermal design of R-SFCL
289
Ic Jc ðTÞ
ð3Þ
3) Length of the superconducting Tape The length of the tape can be calculated from Eq. (5) using the parameters, first peak current (Irp) and resistance of the SFCL (RSFCL) as follows [27] pffiffiffi 2V rms ð4Þ LHTS ¼ Epeak
2.1. Development of algorithm The first step in developing an algorithm consists of selecting the type of the coated conductor (YBCO) and specifying the initial parameters such as the temperature of the cryogenic coolant (Ta), critical current at coolant temperature (Tc), critical temperature of the superconductor (Ta), width of the conductor (w), thickness of the conductor (t), critical current density (Jc), resistivity (r), index number of the conductor (n) and specific heat (CV). It is reported that the range of recovery time for maximum fault current compensation is between 80 ms to 120 ms [25]. Moreover, the behaviour of the superconductors can be studied from the J-B-T curve [2]. The basic parameters on which the R-SFCL design depends are 1) Transport Current in the HTS tape Using the relation between the RMS current and the peak current, the currents in different layers of the superconducting tapes are calculated using: pffiffiffi ð1Þ Ip ¼ 2Irms 2) Cross-Sectional Area of the superconductor The current carrying capacity of the superconducting tape increases if the thickness of the tape increases as reported by
lSC ¼
RSFCL IC n n1 EC Irp
ð5Þ
where, Vrms is transmission voltage and EC is the Critical Field 4) Number of turns over the mandrel Turns depends on the width of the tape, length of the tape, diameter of the mandrel and the sense of winding. 2.2. Electrical strategy for R-SFCL integrated with SMES devices When a fault occurs, the current transmitted through the coated conductors exceeds the critical current. Thereby, a transition from the superconducting state to the normal state occurs behaving as Ohmic conductor. In this scenario, the conductor offers resistance and the fault must be compensated. However, the non-uniformity in HTS tape material (ceramic in nature) as well as cooling of the conducting layers, hotspots are expected to occur [28,29]. In order to avoid the hotspots in the layers of the conductor, a resistor is connected in parallel to the superconductor. There are three states of transition in the superconducting tapes during the fault current in power systems. Based on the E-J
Fig. 3. E-J characteristic of Superconductors with three states of transition.
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where, n is index term, J is operating current density, JC is critical current density and E0 is electrical field at the initial condition of transport current. In order to find the time taken for the compensation of fault current, it is necessary to calculate the voltage to predict the state of transition and the E-J characteristic equations. 2.3. State-1 flux creep state (r = 0) The state where the conductor acts as a superconductor and do not allow any magnetic flux lines to flow through it, resistivity at operating temperature is zero and follow the power law is called Flux creep state. The first region in Fig. 3 is the flux creep state. The E-J characteristic equation of flux creep state is given as: aðT Þ J ð7Þ Eð1Þ ðJ; T Þ ¼ E0 JC
Fig. 4. Algorithm for developing the R-SFCL for SMES devices.
characteristics, one can describe the state of transition. The states of transition are Superconducting or flux creep state, flux flow state, normal state as shown in Fig. 3. The transition from the superconducting state to the normal state is based on the E-J power law because the state of the superconductor depends on the Critical current density (JC). The E-J power law in the superconducting state is shown in Eq. (6) [30]. n J E ¼ E0 ð6Þ JC
The index term a(T) is the maximum value of the index terms i.e., superconducting state index term (b) and index term at the operating temperature a0 (T). EC is critical electrical field, Ta is ambient temperature (77 K) and T is operating temperature
aðT Þ ¼ max½b; a0 ðT Þ where,
a ðT Þ ¼
log EEC0 11 að1T
0
log JJC ððTTaÞÞ C
b
E0 EC
ð8Þ aÞ
By calculating the E (J, T), one can predict the state of the conductor and the transport current.
Fig. 5. Simulated model of three phases fault and R-SFCL under three phase load.
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2.5. State-3 normal state (r = constant)
Table 1 Parameters used for simulating the model in MATLAB/SIMULINK. Component
Parameters
Nominal Values
Three Phase Source
Phase to phase RMS voltage (V) Frequency (Hz) 3-Phase short circuit level at base voltage (VA) Base voltage (Vrms ph-ph)
440 103
Nominal phase to phase voltage Vn (rms) Active power (W) Inductive reactive power QL (positive var) Capacitive reactive Power Qc (negative var)
440 103
Three Phase Load
R-SFCL
Resistance (Ohms)
The state at which conductor allows the magnetic flux lines completely, does not show the property of superconductivity with high resistivity compared to flux flow state and follow a linear relation due to its Ohmic behaviour is called normal state. The E-J characteristic in Ohmic state [8] is shown in Eq. (10)
50 1584 106
T Eð3Þ ðJ; T Þ ¼ rðT C Þ J TC
440 103
305 106 0
0
165
2.4. State-2 flux flow state, (r = r (J)) The state at which the flux line starts flowing through the superconductors due to the flux pinning is called flux flow state. The resistivity of the conductor depends on the current density due to transport current. The second region in Fig. 3 shows the behaviour of the conductor in the flux flow state. The E-J characteristic equation in flux flow state is given in Eq. (9). Eð2Þ ðJ; T Þ ¼ E0
EC E0
aðbT Þ b a JC ðT a Þ J J C ðT Þ JC ðT a Þ
1500
291
ð9Þ
ð10Þ
where, E = 1 * 106 V/cm @ 77 K, 1000 JC 10000 A/cm2, 5 a 15, 0.1 E0 10 mV/cm, 2 b 4, 100 r 2000 mW-cm. The transition from superconducting state to the normal state can also be described in terms of the change in temperature with respect to the time as the state of superconductivity also depends on the critical temperature (TC) of the conductor. The behaviour of the superconductor in the three states is given in Eq. (11). The variation of electrical field (E) with respect to temperature at that particular time is used for calculating the time required for the runoff of superconductivity [31]. 8 a JðtÞ > > E > C > > JC ðT ðtÞÞ > > > > f or EðT; tÞ < E0 and T ðtÞ < T C > > > > b > < EC a JC ðT a Þ JðtÞ b ð11Þ EðT; tÞ ¼ E0 > JC ðT ðtÞÞ JC ðT a Þ E0 > > > > f or EðT; tÞ > E0 and T ðtÞ < T > > > > T ðtÞ > > rðT C Þ J ðtÞ > > TC > : f or T ðtÞ > T C The algorithm developed to design the R-SFCL which can be integrated with SMES devices is shown in Fig. 4. As per the algorithm, the initial parameters at ambient temperature (Ta) must be specified. When the fault occurs and if the temperature and electrical field are less than the critical temperature and critical filed the conductor, the conductor is still at superconducting state.
Normal operation without fault and R-SFCL
Phase A Phase B Phase C
1000
500
0
-500
-1000
-1500 0.00
0.01
0.02
0.03
0.04
0.05
Fig. 6. Three phases under load without fault and R-SFCL (normal operation).
0.06
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5000
Phase A Phase B Phase C
Fault current zone
Normal operation
4000 3000 2000 1000 0 -1000 -2000 -3000 -4000 -5000 0.00
0.01
0.02
0.03
0.04
0.05
0.06
Fig. 7. Three phases under load with fault and without R-SFCL (Fault condition).
If the operating temperature is less than critical temperature, and electric filed is higher than critical filed, then the conductor is said to be in flux flow state. If both the cases are violated then the conductor is considered to be in normal state. The variation in the
time for the compensation of the fault is calculated and the total time is compared with the time specified in the initial parameters for further simulations.
Phase A Phase B Phase C 2000
Fault current compensated zone
Normal operation
1500 1000 500 0 -500 -1000 -1500 -2000 0.00
0.01
0.02
0.03
0.04
0.05
Fig. 8. Three phases under load with RSFCL and with R-SFCL (Fault clear condition).
0.06
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293
Table 2 Current limitation rate in three phase transmission system. Phase
Critical Peak During Normal Operation (A)
Critical Peak During Fault (A)
Critical Peak with RSFCL (A)
Percentage of Compensation
Phase A Phase B Phase C
1200 1200 1200
3500 5000 4000
1700 1900 1600
51.43% 62% 60%
The compensation time taken for clearing the fault due to electrical strategy is studied. However, due to the fault, there is rise in temperature in the cryogenic bath and boiling of the liquid nitrogen (LN2) takes place. Hence, it is necessary to calculate the heat transfer rate between the mandrel and LN2 to retain the superconductivity in the HTS tapes after the fault compensation. The thermal strategy for designing the R-SFCL to be used for SMES devices is explained in the later subsection.
Thermal resistance from the superconductor to cryogenic bath is convective. Hence, the equivalent thermal resistance is given by Rconv ¼ 1=hsccb Amandral ðK=WÞ
ð14Þ
where, hsc-cb = Coefficient of heat transfer from Superconductor to cryogenic bath (W/m2 K). Heat dissipated from the superconductor can be calculated as follows We know that, for Ohmic conductor
2.6. Thermal strategy for R-SFCL integrated with SMES devices
Q ¼ i2 R
ð15Þ
When the temperature rises above critical temperature, the superconductor becomes Ohmic conductor. Further, rise in the temperature will leads to run-off of the superconductivity. Hence, one needs to cool the coated conductor to regain its superconductivity after the compensation of fault current within milliseconds for effective energy storage. The heat transfer rate can be calculated as follows. Superconductor heat Capacity (J/K)
For the time rate change in heat generation, we have R Q SC ðtÞ ¼ iSC ðtÞ2 RSC ðtÞdt in Joules
ð16Þ
C SC ¼ C v V SC
ð12Þ
where, Cv = volumetric specific heat of superconductor (J/Km3)@Ta, VSC = Volume of the Superconductor, V SC ¼ lSC aSC
Resistance for the Ohmic conductor is R¼
El Ja
ð17Þ
The time rate change in the resistance of the Superconductor is given as follows [32]. RSC ¼
Eðt; TÞlSC JðtÞaSC
ð18Þ
ð13Þ
Normal Fault without R-SFCL Fault with R-SFCL
Normal operation 4000
Compensated Fault current
Fault current
3000 2000
Short circuit
1000 0 -1000 -2000 -3000 0.00
0.01
0.02
0.03
0.04
0.05
Fig. 9. Comparison of the three phases under load in different operations.
0.06
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RSFCL ðtÞ ¼ Rm
t 1 exp T SC
ð19Þ
where, Rm = maximum resistance of the Superconductor. Heat removed by the cryogenic cooling bath is given by Q removed ¼ hsccb ðAÞmandrel ðTðtÞ T a Þ
ð20Þ
Time rate change in the heat removal is given by Z Q removed ðtÞ ¼ hsccb ðAÞmandrel ðTðtÞ T a Þdt
ð21Þ
The transient stability of the system can be determined as follows From the basics of the conduction heat transfer dT CðTÞ ¼ rðkðTÞrTÞ þ qðTÞ dt
ð22Þ
Solving the Eq. (22) for the change in the temperature with respect to change in time is given by
rC SC dT ¼ ðQ generated Q removed Þdt
TðtÞ ¼ T a þ
1 C SC r
ð23Þ
Zt ðQ generation Q removal Þdt
ð24Þ
0
The rise in the temperature due to fault can be calculated from Eq. (24) and the time required for the compensation of the fault is calculated by relating the temperature change with E-J relations as follows. The time taken for the compensation of fault can be calculated using Eq. (24) and integrating on both sides. Z Z dT h i ð25Þ dt ¼ T ðtÞT ðaÞ 1 C SC IEðT ÞlSC Rconv 3. Simulation of R-SFCL to be integrated with SMES The model used for simulating the compensation of fault current in the three phases under load with fault and R-SFCL is shown in Fig. 5. Three phase source is connected to the three phase current measurement (A, B and C terminals) for measuring the increment and decrement in the current with change in the time. For three phases, individual R-SFCL is connected for compensating the fault current in each phase. Three phase fault and three phase load are connected in order to apply the load and the fault to A, B and C terminals in the current measurement. The scope is connected to Current measurement (Iabc) to observe the variations in the current under load. The main aim of the simulation is to reduce the fault occurred due to three phase fault and three phase load. The simulation is carried out for 440 kV/1.2 kA capacity suitable for Indian scenario. The parameters are initialized at time t = 0 with the parameters shown in Table 1 and model shown in Fig. 5 is simulated. 4. Results and discussions The simulated model is parametrically initialized by three phase source connected to current measurement. The three phases under load without fault and R-SFCL is simulated. Since, there is no fault in the phases, normal transmission is observed as shown in Fig. 6. The model is simulated up to 60 ms of current and it is observed a peak of 1200 A in all phases. Similarly, Fig. 7 shows the current distribution when the fault is occurred in three phases
under load with three phase fault without R-SFCL. It is observed that the peak current is increased as compared with the normal operation due to faults. The maximum faults are seen in the Phase B at its negative half cycle, followed by Phase C and Phase A in the positive half cycles. Fig. 8 shows the compensation of the fault current due to three phase fault under load condition. R-SFCL is used to compensate the fault and it is observed that almost 57.8% of the fault current is suppressed. The percentage of the compensation with critical peaks is shown in Table 2. Fig. 9 shows the comparison between current distributions in three phases under load during normal, fault without R-SFCL and fault with R-SFCL. It is observed that at 18 ms, short circuit has occurred in all the three phases and fault current is increased drastically in the next cycle. By using R-SFCL the fault current is compensated up to 58% in the first half cycle and the short circuit is reduced. Higher the resistance offered during the normal state, higher the reduction in the peak value in the first half cycle within few milliseconds. 5. Conclusions It is concluded that, transient thermo-electrical analysis is necessary to design R-SFCL which can be integrated to SMES. The three phase 440 kV/1.2 kA capacity transmission and distribution under load with fault current of 3500 A is compensated to 1700 A in phase A, 5000 A in Phase B is compensated to 1900 A and in phase C, 4000 A is compensated to 1600 A. The average compensation of fault is 57.8% with a recovery time of 60 ms. References [1] W.T.B. De Sousa, A. Polasek, R. Dias, C.F.T. Matt, R. de Andrade Jr., Thermal –electrical analogy for simulations of superconducting fault current limiters, Cryogenics (Guildf.) 62 (2014) 97–109. [2] W. Paul, M. Chen, Superconducting control for surge currents, IEEE Spectr. 35 (May) (1998) 49–54. [3] S. Romphochai, W. Kanokbannakorn, K. Hongesombut, Transient stability and fault current reduction of SPP with Bi-2212 SFCL considering recovery time, Procedia Comput. Sci. 86 (2016) 297–300. [4] L. Chen, Y. Tang, J. Shi, Z. Sun, Simulations and experimental analyses of the active superconducting fault current limiter, Phys. C Supercond. 459 (2007) 27–32. [5] G. Vyas, R.S. Dondapati, P.R. Usurumarti, Parametric evaluation of AC losses in 500 MVA/1.1 kA high temperature superconducting (HTS) cable for efficient power transmission: self field analysis, Proceedings -– UKSim-AMSS 8th European Modelling Symposium on Computer Modelling and Simulation, EMS 2014, 2014. [6] W. Paul, T. Baumann, J. Rhyner, F. Platter, Tests of 100 kW high-Tc superconducting fault current limiter, IEEE Trans. Appl. Supercond. 5 (2) (1995) 1059–1062. [7] M. Noe, A. Kudymow, S. Fink, S. Elschner, F. Breuer, J. Bock, H. Walter, M. Kleimaier, K. Weck, C. Neumann, F. Merschel, B. Heyder, U. Schwing, C. Frohne, K. Schippl, M. Stemmle, Conceptual design of a 110 kV resistive superconducting fault current limiter using MCP-BSCCO 2212 bulk material, IEEE Trans. Appl. Supercond. 17 (2) (2007) 1784–1787. [8] W. Paul, M. Chen, M. Lakner, J. Rhyner, D. Braun, W. Lanz, Fault current limiter based on high temperature superconductors – different concepts, test results, simulations, applications, Phys. C Supercond. Appl. 354 (2001) 27–33. [9] J. Zhu, X. Zheng, M. Qiu, Z. Zhang, J. Li, W. Yuan, Application simulation of a resistive type superconducting fault current limiter (SFCL) in a transmission and wind power system, Energy Procedia 75 (2015) 716–721. [10] S. Kar, S. Kulkarni, M. Dixit, K.P. Singh, A. Gupta, P.V. Balasubramanyam, S.K. Sarangi, V.V. Rao, Study on recovery performance of high Tc superconducting tapes for resistive type superconducting fault current limiter applications, Phys. Procedia 36 (2012) 1231–1235. [11] S. Elschner, F. Breuer, A. Wolf, M. Noe, L. Cowey, J. Bock, Characterization of BSCCO 2212 bulk material for resistive current limiters, IEEE Trans. Appl. Supercond. 11 (I) (2001) 2507–2510. [12] K. Sasaki, C. Nishizawa, T. Onishi, Test results and analysis of current limiting characteristics in conduction cooled bi2223 fault current limiter, IEEE Trans. Appl. Supercond. 13 (2) (2003) 2048–2051. [13] W. Schmidt, B. Gamble, H. Kraemer, D. Madura, A. Otto, W. Romanosky, Design and test of current limiting modules using YBCO-coated conductors, Supercond. Sci. Technol. 014024 (23) (2010) 1–9.
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