Modeling of the Resistive Type Superconducting Fault Current Limiter for Power System Analysis and Optimization

Transcription

1 Modeling of the Resistive Type Superconducting Fault Current Limiter for Power System Analysis and Optimization Antono Morandi Massimo Fabbri, Babak Gholizad DEI Guglielmo Marconi Dep. of Electrical, Electronic and Information Engineering Università di Bologna May 12, 2014 Bratislava, Slovakia

2 Outline Resistive fault current limiters and the state of the art Motivations and case study Numerical model of the resistive SFCL Electromagnetic model Thermal model Coupling with power system Numerical results The exact reference solution Reduced equivalent circuit - a step by step approach Effect of the mesh Heat exchange condition Temperature homogenization Neglecting the thermal effects Conclusion

3 fault happens!

4 a poly-phase fault produces an overcurrent: Damage of components Outage or even black out voltage disturbance Network operators are required to ensure appropriate power quality and to provide information about the type and the number of expected dips

5 loads V2 S cc X cc normal condition fault short circuit power poor persistent voltage quality high persistent voltage quality short circuit power low vulnerability high transient voltage quality high vulnerability poor transient voltage quality impedance For obtaining high network s performance both in normal condition and during the fault a condition-based increase of the impedance is required Fault threshold current Fault current limiter (FCL): a device with a negligible impedance in normal operation which is able to switch to a high impedance state in case of extra current (fault)

6 Resistive Type Superconducting fault Current Limiters (R-SFCL) conventional shunt reactor Advantages Immediate and and fail safe operation Compact size mechanical switch non linear SC resistor bifilar helical windings (1GHTS/bulks) alternate pancakes (2G HTS) Critical aspects Recovery time AC loss Hot spots during light overcurrent By direct exploitation of the SC/Normal transition resistive fault current limiters offer an excellent solution to fault current limitation

7 Nexans R-SFCL 16.6 MVA (12 kv / 0.8 ka) BSCCO bulk material RSE-A2A R-SFCL 3.8 MVA (10 kv / 0.2 ka) 1G HTS tape (Bi2223) Two more units of similar rating have been ordered recently to be installed in UK Upgrade to 15.6 MVA (9 kv/1ka) is programmed ECCOFLOW R-SFCL 40.0 MVA (24 kv / 1 ka) 2G HTS tape (YBCO-CC) The device has bee built and successfully tested. Live grid installation is under discussion Distribution (MV) level resistive HTS-FCL is now a mature technology

8 Paris, October 13, 2011 Nexans, Siemens and American Superconductor Corporation (NASDAQ: AMSC) today announced the successful qualification of a transmission voltage resistive fault current limiter (FCL) that utilizes high temperature superconductor (HTS) wire. This marks the first time a resistive superconductor FCL has been developed and successfully tested for power levels suitable for application in the transmission grid (138 kv insulation class and nominal current of 900 A). 138 kv / 0.9 ka 2G HTS tape (YBCO-CC) Feasibility of industry grade resistive HTS-FCL technology for Transmission (HV) level is also proved

9 Motivation #* FCL p% ##+ ]]! *% $?]] pp^ç FCL superconducting community! distribution network operators Technology details are not of the first interest of the operators, who first want to know the benefits A model for the reliable evaluation of the effects of the device on real word (not too simplified) grids is needed

10 The case study 15 kv Subtramission 132 kv 40 MVA Xcc = MVA A A typical distribution grid supplying a mix of industrial, commercial, residential and rural loads B 4 km 2 MVA 1 km C 10 MVA 4 MVA D 0.5 km 1.5 km 0.5 km FCL Typical settings of the protections Nominal Voltage Nominal current Opening time of circuit breaker, tocb Time delay for opening command, tdcb Is1 = 630 Arms I Is2 = 1400 Arms Is2 = 1400 Arms I Reclosing time of circuit breaker, trcb 4 MVA F 12 km sensitive customers E G disturbing customers overhead 4 MVA 6 MVA rural feeder 20 kvrms 480 Arms (12.5 MVA) 120 ms 800 ms tdcb 0 ms tdcb = 0 ms 400 ms This is to take into account temporary overcurrents which routinely occurs in the grid

11 Device level System level Design Criteria for YBCO-CC based resistive SFCL The device must provide appropriate limiting effect The device must provide appropriate protection from voltage disturbances to costumers not directly affects by the fault The device must not affect existing protections No damage must occur to the device during the fault The temperature must not overcame 300 K at the end of the fault For typical CC tapes (AMSC and Superpower) and fault duration of 120 ms the during fault RMS electric field must not overcome the typical value of V/m Parameters of the device Critical current Ic Shunt reactance Xs Quenched resistance Rq of the SC coil The need to provide appropriate protection from voltage disturbance sets the actual limit on the minimum possible impedance of the device

12 Parameters of the FCL for the case study Main characteristics of the Reference Coated Conductor Substrate, Hastelloy 100 m YBCO 1 m Stabilizer, Silver 2 m Reinforcement, stainless steel 127 m Critical current, 77 K, self field 330 A Quenched resistance at 91 K 77.8 m Design constrains I c 2 I s1 X sv 3 V 3 I s 2 and V X cc X s X cc Xs Ic > 890 A 3 Rq X s Main characteristics of the device Number of tapes in parallel of the conductor Critical current Total resistance of the conductor per unit length Total length of conductor Total quenched resistance Shunt reactance 2 < Xs < 3.5 Rq >Xs < A 25.9 m 400 m

13 Outline Resistive fault current limiters and the state of the art Motivations and case study Numerical model of the resistive SFCL Electromagnetic model Thermal model Coupling with power system Numerical results The exact reference solution Reduced equivalent circuit - a step by step approach Effect of the mesh Heat exchange condition Temperature homogenization Neglecting the thermal effects Conclusion

14 Mathematical formulation The basic assumption is that the behavior is homogeneous along the full length of the HTS conductor Commercial HTS tapes have good longitudinal uniformity of the critical current which assures homogenous transition of the whole conductor length A 2D approach is used form modeling the device Hobl et al., IEEE TASC, 2013

15 Electromagnetic model Power system The FCL interacts with the power system by meas of two terminals FCL Circuit model of the complete system dl IFCL + z x A 2D composite (multi-material) domain is considered y vfcl dl S A Cartesian reference frame is introduced Geometrical model of the FCL The A- formulation is used for expressing the electric field Ex Ax x t

16 The domain is connected to a two terminals component (bipole) which represents the power system. An electric scalar potential exists within the domain not due to charge accumulation but to satisfy the boundary condition The problem involving can be solved autonomously in terms of applied voltage v per unit length of conductor 2 0 vfcl x 0 n vfcl eˆ x x eˆ x dx vfcl dl x dl The vector potential can be expressed in terms of local current density J as A y, z 0 J y ', z ' dy ' dz ' 2 S with ln 1 y y ' 2 z z ' 2 Since in fault current limiters a non inducting configuration is used to allocate the required conductor length no external sources exists for the vector potential

17 A constitutive relation able to link the superconducting and the normal conducting state is required since high current (above Ic) operation is to be dealt with Brandt, 1999 Duron et. al., 2004 The bounded E-J power law is assumed for modeling the superconductor E eq J, T J eq J, T NS (T ) SC J, T NS (T ) SC J, T E0 J SC J, T J c T J c T normal state n 1 Merely a phenomenological relation. No current sharing between a normal and a SC path is assumed creep Due to the non inducting layout no dependence of Jc on B is assumed A linear (though temperature dependent) relation is assumed for the normal conducting constituents of the tape (buffer layer, stabilizer, reinforcement) E T J

18 The following equation is finally obtained which links the distribution of current within the cross section to the total voltage across the FCL (T, J ) J VFCL 0 J y ', z ' dy ' dz ' t 2 S L total voltage across the FCL total length of conductor This equation can be discretized and solved numerically provided that 1. The temperature is known at any point of the domain A thermal model is needed 2. The total voltage across the FCL is known Coupling with the power system is needed

19 Thermal model T ( y, z ) z x c(t ) y d T q (T, J ) J 2 0 dt q y ( y, z ), q z ( y, z ) Energy conservation n q h(t T0 ) T T0 Non linear convection is assumed at the boundary T0 is the equilibrium temperature of the coolant q k (T ) T Fourier s Law relates the heat flux to the temperature Temperature dependence of specific heat c, thermal conductivity k and heat exchange coefficient h is assumed

20 Finite dimensional model electromagnetic 1. A subdivision of the composite domain in finite number NE of rectangular elements is introduced 2. A uniform current density is assumed within each element Jh Ih Sh discontinuity of J is naturally allowed at the interface between different materials 3. A solution is looked for in the weak form bye means of the weighted residuals approach 1 S Sh h L L 0 Ih Sh k S k 2 di k S ds ' dt VFCL ds k h 1,..., N E k 1,..., N E

21 Each of the discretized equation of the weak form corresponds to the voltage balance (Kirchhoff s voltage law) of a circuit branch Mh,k Ih Rh Rh T, I h L Sh M hk 0 L 2 S h S k ds ' ds k 1,..., N E Sh Sk VFCL I1 I2 VFCL IFCL INE The whole conductor is subdivided in a number NE of independent current elements (branches) in parallel which are mutually coupled. All branches are subject to the voltage across the FCL. The total current through all branches is the current of the FCL The electromagnetic finite element model is stated in the form of an equivalent circuit d M I R (T, I ) I 1VFCL dt Solving system

22 Structured rectangular meshes are very well suited to cope with domain with high aspect ratio Tape 1 Tape 2 Tape 3 A mix of elements with very different aspect ratio is introduced to discretize the different layers of the HTS tape. This allows to deal with the geometrical complexity of the domain without introducing a too large number of elements. M hk 0 L 2 S h S k ds ' ds Sh Sk Thanks to the logarithmic kernel no troubles arise with the calculation of the coupling coefficients provided that a different order of integration is used for the inner and the outer integral in order to avoid overlapping of the field ant e source point As a limit the second dimension of very thin elements can be neglected and the line integrals can be used instead of the surface ones

23 Comparison between circuit and edge elements models Both models use piecewise uniform approximation of the current density within the elements on the y-z plane Both models introduce the same number of unknowns (the number of rectangles is equal to the number of cotree branches) It can be shown that Two equivalent solving systems are assembled Circuit method formulates one voltage balance equation for each of the rectangles composing the mesh Edge elements method formulates a set of collective voltage balance equation applying to the clusters of rectangles enclosed in the fundamental loops The same solution in terms of current distribution is arrived at

24 Finite dimensional model Thermal 1. The same subdivision introduced for the electric problem is used 2. A uniform temperature is assumed within each element T (r) Th if r S h 3. The line integral of the Fourier law along the (horizontal or vertical) path connecting each pair of neighbouring elements is taken. It is assumed the heat flux is oriented perpendicular to the shared face rh Qhk Ghk Th Tk with rk Ghk k h Th k k Tk 2 k h Th k k Tk nˆ rk rh 4. The heat flux through boundary faces Is expressed as rh Qh 0 h(th T far ) Th T far

25 3. A solution is looked for in the weak form bye means of the weighted residuals approach Ih 1 d c T Q S S h h dt h k hk h S h h 2 ds 0 h 1,..., N E k 0,1,..., N E Each of the discretized equation of the weak form formally corresponds to the current balance (Kirchhoff s currents law) of a circuit node Ch T0 Gh0 T0 Tm C h ch Ghm 2 kh kk k k r r Ghk h k k h 0 Th Ghl Ghk T0 ph Tk Tl if elemets h and k share a face otherwise h if elemets h has a face onn the boundary Gh 0 0 otherwise I ph h h Sh 2

26 T1 Tn T2 Tn+1 The whole conductor is subdivided in a number NE of nodes connected through thermal conductances All nods are connected to a reference one by means of a capacitance. A NE -order dynamic circuit is obtained A current is forced in each node to take into account of the power dissipation The thermal finite element model is stated in the form of an equivalent circuit C(T) d T 1T0 G (T) T I t R (I, T) I dt

27 Power system The coupled electromagnetic- thermal behaviour of the FCL is modelled by means of two coupled circuits VFCL IFCL I1 I2 d M dt I R (T, I ) I 1VFCL C(T) d T 1 T G (T) T I t R (I, T) I 0 dt INE T1 Tn T2 Tn+1 FCL The state variables are I1, I2,, INFE T1, T2,, TNFE + state variables of the power system

28 Outline Resistive fault current limiters and the state of the art Motivations and case study Numerical model of the resistive SFCL Electromagnetic model Thermal model Coupling with power system Numerical results The exact reference solution Reduced equivalent circuit - a step by step approach Effect of the mesh Heat exchange condition Temperature homogenization Neglecting the thermal effects Conclusion

29 Coupling with the power system The equivalent circuit of each of the components of the power system is introduced switch feeder feeder B load C feeder feeder switch shunt feeder load FCL F load load E D A feeder switch transformer feeder feeder G switch feeder load A global equivalent circuit is obtained switch load

30 A tree-cotree decomposition of the global equivalent circuit is introduced The shunt is placed within the tree. Cotree currents include the state variable of the FCL Tree currents are expressed as a function of the cotree ones Voltage of all branches is expressed as function of the tree currents and the derivatives VPS M PS 1VFCL 0 0 d I c R PS M dt I 0 I c Vg R (I, T) I 0 0 This equation incorporates the electromagnetic model of the FCL

31 The state equation is obtained by means of the Kirchhoff s current law M L PS 0 0 d Ic R L PS M dt I 0 0 I c V L g R (I, T) I 0 L : matrix of the fundamental loops The solving system of the thermal network must be added due to the temperature dependence of the resistive terms of the FCL M PS 0 d I c 0 I c R PS Vg L L L 0 R (I, T) I M dt I 0 0 d T 1T0 G (T) T I t R (I, T) I C ( T ) dt Complete electromagnetic and thermal model of the FCL and the power system The state variables are I1, I2,, INFE T1, T2,, TNFE + cotree currents of the power system The voltage impressed by the generator is the forcing term of the system

32 Solving procedures A zero order coupling exists between the electric and the thermal model Time constants of the thermal problem are much longer than those of the electric one A week coupling can be assumed for solving the electric amd the thermla state equation t0 t Ic0, I0, T0 Temperature is assumed constant during the electric step The average power during the electric step is assumed as input of the thermal problem t0+ t Ic, I, T M L PS 0 C 0 d Ic R L PS M dt I 0 d T 1T0 G T Pav dt Pav 1 t I 0 R (I 0, T0 ) I 0 I t R (I, T0 ) I 2 0 I c V L g R (T) I 0

33 An implicit Euler scheme is used for solving the two differential systems M PS 0 1 I c I c0 L M t I I I c R V L g L PS 0 R (I, T) I 0 C 1 T T0 G T Pav t Ih Th M h,k Ih Th t + Mh,k j h M h, j t Ij C + j M h, j t Tk I j,0 C t C (Th 0 Tg 0 ) t Tk Inductors and capacitors are transformed in static components A non dynamic circuit is solved during thee time step

34 Parameters of the model Temperature dependence of physical parameters is implemented S. S. Kalsi, Applications of High Temperature Supercond. to Electric Power Equipment, 2011, Wiley-IEEE N. Bagrets et al, Thermal properties of 2G coated conductor cable materials, Cryogenics 61 (2014) 8 1

35 Parameter Normal state resistivity Thermal conductivity Thermal conductivity Thermal conductivity Specific Heat Material YBCO YBCO Hastelloy Silver YBCO Constant values are assumed if data are not available Value 100 cm at 92 K 7 W/m/K 7 W/m/K 429 W/m/K 1.62 MJ/m3/K F. Roy et al., Magneto-Thermal Modeling of 2GHTS for Resistive FCL Design Purposes, 2008, IEEE TASC Temperature dependence of the heat exchange between the conductor and the liquid nitrogen bath is also considered Sosnowski J., Analysis of the electromagnetic losses generation in the high temperature superconductors, ICSPETO 99, (1999), Realistic values of the resistance and the inductance per unit length are used for modelling the MV feeders Zfeeders = j 0.35 /km

36 Outline Resistive fault current limiters and the state of the art Motivations and case study Numerical model of the resistive SFCL Electromagnetic model Thermal model Coupling with power system Numerical results The exact reference solution Reduced equivalent circuit - a step by step approach Effect of the mesh Heat exchange condition Temperature homogenization Neglecting the thermal effects Conclusion

37 Performance of the system with no FCL A fault occurs at bus F at the most onerous instant The thermal stress on the transformer due to the actual fault current, including the asymmetric component, is assessed by means of the total thermal let-through during the fault Qtransformer t f t f 2 i dt tf The mechanical stress on the transformer is assessed by means of the peak current The voltage disturbance on all customers of the network in assessed by means of the RMS voltage at all buses t 1 2 VRMS (t ) v dt T t Tcycle

38 A peak fault current of 21.4 ka is obtained on the transformer The total thermal let-through during the fault is 12.7*106 A2s. This is close to the limit of 18.8*106 A2s which can be soon approached if the fault occur closer to bus A Sensitive (VR 70 % ) Tolerant (VR 40 % ) Standards EN and EN specify the residual voltage VR on equipment during a disturbance The residual voltage during the fault at all bus of the network is below the threshold of even tolerant equipment

39 Reference Mesh Tape 1 Substrate YBCO Stabilizer Reinforcement Tape 2 26*3 26*3 26*3 26*3 Substrate YBCO Stabilizer Reinforcement. Total number of elements: 936 Two large equivalent circuits with 936 unknowns each are obtained for modeling the coupled electric and the thermal behavior of the FCL Further unknowns are added to the problem for modeling the power system In the following the solution obtained with this mesh will considered as the reference exact solution Tape 3 26*3 26*3 26*3 26*3 Substrate YBCO Stabilizer Reinforcement. 26*3 26*3 26*3 26*3

40 system level Peak current Thermal let-through unlimited limited 21.4 ka 8.8 ka 12.7*106 A2s 2.2*106 A2s 61 % 83 % Both the peak current and the thermal letthrough are greatly reduced The residual voltage during the fault at all bus of the network is well above the threshold of sensitive equipment. Voltage disturbance is prevented.

41 device level In the quenched state the current mainly flows through the stabilizer. An appreciable share also flows through the reinforcement. T map at t = 20 ms During the fault the temperature gap within the whole conductor do not exceed 3 K The conductor is isothermal. A maximum temperature of 129 K is reached after 120 ms

42 Effect of the Mesh A very coarse mesh with 12 elements in total is introduced Tape 1 Substrate YBCO Stabilizer Reinforcement 1*1 1*1 1*1 1*1 Tape 2 Substrate YBCO Stabilizer Reinforcement Tape 3 1*1 1*1 1*1 1*1 Substrate YBCO Stabilizer Reinforcement 1*1 1*1 1*1 1*1 I1 I2 I3 I4 No subdivision along the tape width is assumed. Each component of each of the three tapes is modeled by one single rectangle I5 I6 I7 I8 Total number of elements: 12 I9 I10 Two reduce equivalent circuits with 12 state variables each are obtained for modeling the coupled electric and the thermal behavior of the FCL T1 T2 T3 T4 T5 T6 T7 T8 I11 I12 T9 T10 T11 T12

43 system level exact solution coarse mesh 3*4*(1*1) No difference arises at the system level with the two mesh

44 device level exact solution coarse mesh 3*4*(1*1) A slightly lower maximum temperature of 127 K ( 1.5%) is reached at the end of the fault with the coarse mesh Very small differences arise at the device level with the two mesh The detail of current and temperature diffusion within the tape do not affect the results

45 Adiabatic assumption I1 I2 I3 No heat exchange is assumed between the conductor and the liquid nitrogen bath I4 I5 I6 I7 I8 Thermal conductances between he nodes and the thermal rework are not considered I9 I10 I11 I12 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

46 device level system level exact solution coarse mesh 3*4*(1*1) adiabatic Very small differences arise both at the device and at the system level with non-adiabatic and adiabatic conditions No significant temperature increase is obtained at the end of the fault in adiabatic condition

47 Total instantaneous power P(t ) J 2 ds S Total instantaneous heat exchange with the bath Q(t ) f (T (t ) T far ) Total power T Tfar Total heat exchange Even in realistic condition at any instant the heat exchanged with the bath is negligible with respect to the power injected in to conductor due to joule loss. Heat exchange condition can be neglected.

48 Merging the three tapes in one Tape 1 Tape 2 Tape 3 Equivalent Tape An unique equivalent domain of equal total cross section is introduced for each of the component of the three tapes A coarse mesh with no subdivision is used for each of the components Total number of elements: 4 Not in scale Not in scale Two reduce equivalent circuits with 4 state variables each are obtained for modeling the coupled electric and the thermal behavior of the FCL I1 I2 I3 I4 T1 T2 T3 T4

49 device level system level exact solution coarse mesh + adiabatic + merged tapes No difference are obtained at the system level Negligible difference appear at the device level A higher maximum temperature of K ( +1 %) is reached at the end of the fault

50 Homogenization of the temperature within the conductor No temperature difference is assumed between one component of the tape and the adjacent one T1 T3 T2 Thermal resistances between the nodes of the thermal rework are substituted by short circuits ( k ) T1 A thermal network with one active node is obtained. One state variables is needed Both each capacities and losses of all components are summed up to give a unique parameter Ctot Ptot T1 I1 No changes occur on the electric network I2 I3 I4 T4

51 device level system level exact solution coarse mesh + adiabatic + merged tapes + temp. homogen. No difference are obtained at the system level A small difference appears at the device level A higher maximum temperature of K (+4.6%) is reached at the end of the fault

52 Neglecting the thermal effects No thermal model is associated to the electromagnetic one Ctot T1 Also during the fault the conductor is supposed to operate at a constant and uniform temperature T = Tfar The limiting effect is due to the transition to the nor,mal stat due to the current above Ic only I1 No changes occur on the electric network Ptot I2 I3 I4

53 device level system level exact solution coarse mesh + merged tapes + neglecting thermal effects Due to higher current predicted of the conductor unreliable results can arise especially in case e of light fault A higher peak current is predicted for the transformer A much higher current is predicted for the FCL

54 Conclusion An equivalent circuit of the device was obtained on a rigorous base without introducing any a priory assumption The equivalent circuit was coupled with the model of real word distribution network and the effects of the device on the network where evaluated A reduced equivalent circuit was arrived at by means of a step by step approach. Simplifying assumption were introduced and their effect on the results at the system was analyzed A simple equivalent circuit with adiabatic Ctot T1 assumption and no details of the current and temperature diffusion is enough for Ptot I1 evaluating the effect of on the power system I2 and for estimating the over-temperature of I3 the device I4