Current-limiting Characteristics of a Modified Flux-coupling Type Superconductin

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(1.Department of Automation Engineering,Fujian Polytechnic of Information Technology,Fuzhou 350003,China;2.China Energy Construction Group Guangdong Electric Power Design and Research Institute Co.,Ltd.,Guangzhou 510663,China;3.School of Electrical Engineering and Automation,Fuzhou University,Fuzhou 350116,China)

Abstract：A modified flux-coupling type superconducting fault current limiter (SFCL) is proposed here for suppressing fault currents.The modified SFCL consists of a coupling transformer,an yttrium barium copper oxide (YBCO) pancake coil,and a controlled switch.By flexibly adjusting the controlled switch’s contact states based on the system operational conditions,the coupling transformer’s primary inductance as well as the YBCO coil’s normal-state resistance are incorporated into the main system for current limitation.Because the modified SFCL has the advantages of resistive and inductive SFCLs,it may improve the power system’s transient behavior.Hence,the SFCL’s effect on the transient stability of a multi-machine power system was also theoretically investigated.Further,simulations were conducted for accessing the SFCL’s performance characteristics under different fault conditions.The results show that using the proposed SFCL can effectively restrain the increased fault current and improve the bus voltage sag;meanwhile,the imitated multi-machine system’s power-angle oscillation can be obviously reduced.

Keywords：Current-limiting characteristics,flux-coupling type SFCL,multi-machine power system,transient stability

1 Introduction

Recently,yttrium barium copper oxide (YBCO)has been developed and widely used as a hightemperature superconducting material.Superconducting power devices that use YBCO-coated conductors have attracted significant attention,with some devices used in actual power grids[1-2].Owing to their well-known technical properties,superconducting electric apparatuses can be used for addressing some technical drawbacks of existing power systems.At the same time,with the continuous expansion of power transmission and distribution systems’ capacities[3-4],fault current levels have been increasing,negatively affecting the stability of power systems with respect to transients.When a serious short-circuit fault occurs in an electric power system,the magnitude of the electromagnetic force caused by the fault current is proportional to the square of its first peak value.Limiting the fault current in its first half-cycle can protect the underlying electric machinery from mechanical stress,and can improve the system’s stability[5].

For suppressing the fault current levels and for improving the reliability and security of power systems to the maximal possible extent,superconducting fault current limiters (SFCLs) have been proposed.Various SFCLs have been suggested by researchers[6-9].Among them,resistive-type SFCLs are advantageous owing to their low loss in the superconducting state,and can exhibit impedance without an external trigger,limiting the fault current in the quench state.Under specific conditions,employing resistive-type SFCLs can be advantageous for enhancing the transient stability of power systems[10-11].Inductive SFCLs have also been widely considered[12-14],and have some distinctive merits,including large design flexibility owing to the turn ratio,separation of the current-limiting device from the power transmission line[15],and low heat loss owing to its very low resistance[16].A flux-coupling type SFCL has been proposed by our research group[17-18],corresponding to an inductive and non-quench-type SFCL.The proposed SFCL consists of superconducting coupling coils and a controlled switch.By testing small-scale prototypes,the SFCL’s current-limiting characteristics can be profiled.However,since sometimes this proposed inductive-type SFCL failed to efficiently maintain the power system’s transient stability,a few proper improvements of the SFCL’s structure and principle should be made.

In this paper,a modified flux-coupling-type SFCL is proposed,and its current-limiting characteristics as well as its impact on the transient stability of a multi-machine power system are investigated.This remainder of this article is organized as follows.Section 2 introduces the structure and principle of the modified flux-coupling-type SFCL.In Section 3,we discuss the mechanism by which the SFCL affects the power system’s transient stability.In Section 4,a detailed model of a multi-machine power system with the proposed SFCL is implemented in Matlab,and simulations are conducted for assessing the SFCL’s behaviors under different fault conditions.In Section 5,the relevant conclusions are summarized.

2 Structure and principle of the modified flux-coupling-type SFCL

Fig.1a schematically shows the circuit of the modified flux-coupling-type SFCL.The proposed SFCL is composed of a coupling transformer (CT),a controlled switch S1,and an YBCO pancake coil.The switch S1and the superconducting coil are respectively connected in series with the CT’s primary and secondary windings.The primary and secondary windings are wound in opposite directions.A metal oxide arrester (MOA),for suppressing the switching overvoltage,is connected in parallel with the CT’s primary winding.L1,L2are the winding self-inductances.Mis the mutual inductance.In addition,Zsis the circuit impedance andSloadis the circuit load.RYBCO/Rmoais recorded as the SFCL/MOA’s normal-state resistance.

In the normal condition,the switch S1is closed,and the SFCL is in the zero-resistance/superconducting state.In accordance with the equivalent circuit of the coupling transformer,the SFCL’s equivalent structure is shown in Fig. 1b,and the coupling transformer’s impedance is

Fig.1 Structure of a modified flux-coupling type SFCL

Considering that the coupling coefficientkand the transformation rationcan be expressed ask=,respectively,we obtainZCT= jωL2(1 -k2)n2/(n2+2kn+1).When an iron core is used for maximizing the coupling,kis approximated by 1 (ZCT≈ 0).The coupling becomes non-inductive,and theMOAis “short-circuited”.Accordingly,the SFCL does not affect the main circuit.

Following a fault,the switch S1opens rapidly.Then,a freewheeling circuit,consisting ofL1andRmoa,is formed,for avoiding the switching overvoltage.After the overvoltage is eliminated,the freewheeling circuit is interrupted owing to the MOA’s blocking effect.Further,when the fluxes between the transformer’s two windings no longer cancel out,the non-inductive coupling is destroyed,and the YBCO coil is quenched to its high-resistance state.The current-limiting impedance is

Thereupon,the suggested device’s current-limiting impedance becomes

In the case ofRmoa＞＞n2ωL2,ZSFCL≈RYBCO+jωL2can be achieved.

Compared with our previously proposed flux-coupling-type SFCL,the presently proposed modified SFCL has the following advantages.

(1) The introduction of the YBCO coil can improve this SFCL’s current-limiting capacity,and the existence of the resistance component can more effectively enhance the transient stability of the power system under some specific conditions[19].

(2) Owing to the use of the coupling transformer,the current flowing through the YBCO coil can be adjusted flexibly.By designing a proper transformation ratio,the AC loss of the superconducting coil can be reduced to a certain degree,in contrast with the situation in which the YBCO coil is directly inserted into the main circuit.

To decrease the weight,size,and whole bulk of the modified flux-coupling-type SFCL for large-scale and high-voltage applications,a hybrid coupling transformer consisting of superconducting and conventional materials can be appropriately applied.That is to say,the primary winding (used for the cancellation of fluxes) can be fabricated by superconducting tapes,and the secondary winding used for current limitation can be made of conventional materials.As an aside,the controlled switch S1should be equipped with rapid response and adequate breaking capacity,to ensure that the current limitation can be implemented efficiently.

3 Analysis of transient characteristics for a two-machine power system with the proposed SFCL

In this section,owing to the typical power-angle characteristic of a multi-machine power system,a classic two-machine power system was chosen for analyzing the modified SFCL’s theoretical impact on the transient stability[11,20-22].The two-machine power system is shown schematically in Fig.2,where four SFCLs are respectively installed at the inlet and ending terminals of the two transmission lines.

Fig.2 Schematic diagram of a two-machine power system equipped with the modified flux-coupling type SFCLs

Assuming that a three-phase grounded fault occurs,the transient analysis is conducted as follows. The two-machine power system’s equivalent circuit under the fault condition is shown in Fig.3a.Xd,XT,XL,XpandXgare respectively the generator transient reactance,the transformer reactance,the transmission line reactance,the load impedance,and the ground impedance.Herein,the two transmission lines were considered to be identical,and the distance coefficientcwas introduced to access the fault distance (it is actually the ratio of the fault location to the line length).Therefore,XL1=XL2=XL,XL2a=cXL2,XL2b=(1 -c)XL2,(0≤c≤1).In addition,for more directly analyzing the stability problem,the original delta connection mode was transformed to the star connection mode,as shown in Fig.3b.From Fig.3,the equivalent inductancesX3,X4andX5are

Fig.3 Equivalent circuit of the two-machine power system with the SFCLs under fault condition

The active-power characteristics of the two-machine power system is

whereP1/P2=Active power output of generator 1/2;δ12=Absolute rotor angle (representing the system’s power-angle characteristic);E1/E2=Terminal voltage of generator 1/2;β11/β12/β22represents the phase-angle of the impedanceZ11/Z12/Z22,which can be expressed as

where

Assuming that the mechanical power outputs (Pm1,Pm2) of the two generators are constant,the swing-angle acceleration is

whereδ1/δ2=Rotor angle of generator 1/2;ωn=Synchronous speed;Tj1/Tj2=Inertia time constant of generator 1/2.

The criterion for determining the two-machine power system’s transient stability is that the absolute rotor angle restores its original state or reaches a new steady state after the fault.From Eq.(7),the absolute rotor angle acceleration is

According to Eqs.(5)-(8),α12=f(δ12,β11,β12,β22)can be obtained,and the functionfis introduced for describing the relationship between the independent variables (δ12,β11,β12,β22)and the dependent variable(α12).The relationship is

where

Becauseψ1andψ2are constants,ψ3becomes the major factor affectingf.According to the trigonometric identity,ψ3is

Based on the above mathematical derivation,the relationship betweenα12andδ12is as shown in Fig.4,where three characteristic curves (αⅠ,αⅡandαIII),corresponding to the different operational conditions,are shown.

In the initial state at pointA,the power system is operating in service,such thatP1=Pm1,P2=Pm2and dδ12=0.When a fault occurs,owing to inertia,δ12cannot change instantly.AsP1＜Pm1andP2＞Pm2are achieved,δ12increases until the operating point reachesC.After the SFCLs are triggered in time,the operating point shifts toDand reachesL.Further,the fault is cleared from the power system,and the operating point quickly jumps toH.NowP1＞Pm1andP2＜Pm2are obtained,deceleratingδ12.Since the rotor speed ofG1is yet greater thanG2,δ12continues to increase until the speed difference between the two rotors disappears.The operating point moves toJ,and the two generators reclaim their synchronous speed.For the condition with or without the SFCLs,the system’s acceleration/retardation area isSACDEB/SEGJHLorSAFGB/SGJH.From Fig.4,SAFGB＞SACDEBandSEGJHL＞SGJH,and employing the SFCLs can theoretically reduce the power-angle differences,by improving the transient stability of the two-machine system.

Fig.4 Qualitative relationship between the absolute rotor angle δ12 and its own acceleration α12

4 Simulation results and discussion

For quantitatively evaluating the suggested SFCL’s current-limiting characteristics and its effect on the transient stability of a multi-machine power system,the simulation model corresponding to Fig.2 was created in Matlab.The simulation parameters and their values are listed in Tab.1.Fig.5 shows the quench and recovery model of the imitated YBCO coil[23],wheret0,t1,andt2denote the quench-starting time,the first recovery-starting time,and the secondary recovery-starting time,respectively.The imitated YBCO coil’s recovery time was set to be under 0.5 s,for matching up the auto-reclosing’s operation.

Fig.5 Quenching and recovery characteristics of the imitated YBCO coil

Tab.1 Main simulation parameters of the system model

Herein,we assumed that a three-phase fault occurs at different fault locations,and introduced the position coefficient (kx=Xf/XL;Xf=fault location;XL=line length).The fault occurrence time was set tot=1 s.The fault duration was set to 400 ms.The simulation results are quantified in terms of the following four technical indices.

μ:Current-limiting ratio regarding the fault current’s first peak value.

β:Current-limiting ratio regarding the fault current’s steady value.

Δδ/(°):Peak-to-peak value of the absolute rotor angle.

η:Calculated as (Δδwithout-SFCL-Δδwith-SFCL)/Δδwithout-SFCL

4.1 Current-limiting performance of the modified SFCL

Figs.6-8 show the current-limiting behavior of the SFCL3/SFCL4 when the fault respectively happens at the inlet (kx=0) and midpoint (kx=0.5) of line2.Figs.9-10 show the waveforms of the bus-voltage dip,for different fault conditions.Owing to the employment of the SFCLs,the fault currents are effectively suppressed within acceptable ranges.Meanwhile,the bus-voltage sag is significantly improved.The current-limiting performance is summarized in detail in Tab.2.When the position coefficientkis respectively 0 and 0.5,the voltage level of bus 1 is respectively maintained at 71.4% and 85%of the normal value.During the current-limiting operations,there is no indication of an over-voltage induced in the SFCLs.Thus,they prevent voltage surges from damaging the power system’s robustness.For bus 2,similar results are obtained.

Tab.2 Comparison of fault currents at different locations

Fig.6 Performance characteristics of SFCL3 when kx=0

Fig.7 Performance characteristics of SFCL4 when kx=0

Fig.8 Performance characteristics of SFCL4 when kx=0.5

Fig.9 Voltage characteristics of the bus1/2 when kx=0

4.2 Transient stability assessment with the SFCL

In this section,taking into account changes in the faults’ locations,faults’ clearance times and current-limiting parameters,the modified SFCLs’impact on the two-machine system’s transient stability is imitated,as the results are shown in Figs.11-13 and Tabs.3-5.

From the results shown in Figs.11-13 and Tabs.3-5,we conclude that:①SFCLs reduce the angle oscillation and system recovery time;② As the fault clearance time increases,the system’s transient stability decreases,even losing step without the SFCLs.However,after installing the SFCLs the system’s transient stability is clearly reclaimed;③The system’s power-angle differenceis riotously out of proportion to the SFCL’s impedance ratio(λ=ωL2/).With increasingλ,the power-angle difference Δδincreases first and then decreases.That is to say,there is an optimal solution to the SFCL’s impedance ratio for improving the transient stability.

Overall,the aforementioned simulation analysis confirms the SFCLs’ positive impact on the system’s transient stability.

Fig.11 Power-angle curves of the two-machine power system under different locations

Fig.12 Power-angle curves of the two-machine power system under different fault clearance times

Fig.13 Power-angle curves of the two-machine power system under different current-limiting parameters

Tab.3 Comparison of fault currents at different locations

Tab.4 Comparison of transient stability of three different cleaning times

Tab.5 Comparison of fault currents at different ratios

5 Conclusions

This paper proposed a modified flux-couplingtype SFCL as a novel control method for inhibiting fault currents and for increasing the performance robustness of power grids.Based on the theoretical analysis and numerical simulations,the following conclusions can be drawn.

(1) By comparison with existing methods,we conclude that the proposed SFCL effectively suppresses fault currents and improves the bus voltage sag.

(2) Using the SFCL in multi-machine power systems suppresses power-angle oscillations and strengthens the systems’ fault recovery capacity.Even if the fault clearance time increases,the systems’transient stability can also be enhanced without losing step.

(3) The system’s power-angle differenceis riotously out of proportion to the SFCL’s impedance ratio.Therefore,there is an optimal solution to the SFCL’s impedance ratio for improving the system’s transient stability.