CN106505563A - Grid-connected converter toughness appraisal procedure under a kind of electric network fault - Google Patents

Abstract

The present invention provides a kind of method grid-connected converter toughness index being estimated under electric network fault, comprises the steps：A：Power system contingency set, failure judgement type is set up, and designs the current transformer model for meeting performance indications requirement；B：The response of current transformer under analysis electric network fault, and calculate transmission curve and the Voltage loop stability criteria of electric current loop respectively；C：Toughness boundary condition of the current transformer with regard to key parameter under grid disturbance is calculated, so as to judge whether this current transformer tolerates the fault type, current transformer toughness is estimated；D：When current transformer does not have tolerance to failure, can return to initial designs and current transformer parameter is changed repeatedly, the design for meeting tolerance electric network fault can be obtained eventually.The assessment on the basis of current transformer meets performance indications requirement, carrying out failure tolerance to grid-connected converter of the invention, forms practical grid-connected converter toughness appraisal procedure, and which can be made to obtain optimization design.

Description

Grid-connected converter toughness appraisal procedure under a kind of electric network fault

Technical field

The present invention relates to a kind of grid-connected converter appraisal procedure, under specifically a kind of electric network fault, grid-connected converter toughness is commented The method that estimates.

Background technology

With the extensive application of the Ac/dc Power Systems such as generation of electricity by new energy, microgrid, D.C. high voltage transmission, as wherein work( The electronic power convertor device of rate Fabric Interface is due to its stable DC busbar voltage, the work of reduction alternating current harmonic content With progressively more and more being used in field of power.Wherein, three-phase voltage source type current transformer (VSC) has steady Qualitative height, the advantages of power factor is controllable, widely used, it is a kind of very representative interface converter device.

Due to containing the semiconductor switch weaker to current handling capability, and converter device control in grid-connected converter In link and Ac/dc Power Systems, failure all has multiformity, thus grid-connected converter is electric with tradition to the response of electric network fault Machine differs widely, and the difference of fault type, electric network composition or abort situation can all make which produce different respondent behaviors.Separately Outer due to sinusoidal pulse width modulation (SPWM) in current transformer and control loop introduce non-linear, cause system to be easily accessible improper Working condition.

However, in practical engineering application, grid side failure would generally largely affect the stable operation of VSC, because And the service requirement of electrical network docking port current transformer is extremely strict.Electrical network is accessed to grid-connected converter and has been formulated accordingly in countries in the world Grid-connected directive/guide, but, the ability that these grid-connected directive/guides can withstand shocks to grid-connected converter does not provide any index will Ask.In existing document to current transformer research mostly be the stable state of VSC is studied under preferable electrical network and under failure right System control method is improved, thus seldom has the operation action of the lower VSC of research concern electric network fault impact.Also document stands Be enough under microvariations be analyzed current transformer small-signal stability, also have document that big signal point is carried out to three-phase VSC systems Analyse and have studied NONLINEAR BIFURCATION phenomenon of VSC etc., but do not pay close attention to grid-connected power electronic equipment emphatically and transport during electric network fault Every trade is that the ability for also failing to bear grid-connected converter electric network fault impact from the effective criterion of design angle proposition is commented Estimate and design.

Content of the invention

For deficiencies of the prior art, the present invention provides grid-connected converter toughness under a kind of electric network fault (Resiliency) method that assesses.I.e. using current transformer jam-tolerant ability as its toughness evaluation index, judge that current transformer exists Whether can guarantee that under the conditions of catastrophic failure that power electronic devices is not damaged, maintain system operation；And ensure current transformer control ring not Be hit impact, failure fast quick-recovery normal operating conditions after terminating；Further, support is provided to system recovery stable state.

A kind of method of grid-connected converter toughness assessment under electric network fault, it is characterised in that comprise the steps：

Step A, power system contingency set is set up, failure judgement type, and design and meet performance indications requirement Current transformer model, specifically includes：

Step A1：The electrical network contingency set towards power electronic equipment security evaluation is marked off, out of order tool is judged Body type, specifically, electric network fault is divided into overcurrent event by the impact first by various typical faults to current transformer operating point Barrier, overvoltage failure, frequency fluctuation failure, phase hit failure and zero sequence or negative-sequence current mutation failure, further according to operating point Can which be divided into Changing Pattern transition failure and soft fault in detail, recover automatically to be divided into failure finally according to failure Transient fault and permanent fault, so that judge out of order particular type；

Step A2：Under conditions of performance indications requirement is met, determine the key parameter of current transformer, and Preliminary design goes out one Individual rational three-phase voltage source type grid-connected converter model；

The response of current transformer under step B, analysis electric network fault, and calculate transmission curve and the Voltage loop of electric current loop respectively Stability criteria, specifically includes：

Step B1：The state equation after the decoupling of system dq is represented, current inner loop analysis is carried out to system, and is calculated electricity Stream ring transmission curve, so that it is determined that the voltage and current grade of IGBT switching devices, specifically, first according to synchronously rotating reference frame Function, by under VSC model conversation to dq rotating coordinate systems, determines its state equation；Then as inductance equivalent resistance R_sWhen less, System can be in output current i_oNonlinear phase is introduced into before entering saturation, now system modulation can be regarded as infinity than m, control Voltage v processed_dAnd v_qReach its upper limit V_g,max, now interior circular current i_dReach its marginal value：

For any i_d,ref>i_d,critical, system be in ovennodulation state, its power factor no longer for unit power because Number；

Interior circular current i under ovennodulation state_dWith regard to i_d,refExpression formula be designated as i in description of the invention_d=h_d (i_d,ref), interior circular current thus can be obtained with regard to the equation to current reference value：

D shaft currents i just can be drawn by formula (2)_dWith reference current i_d,refTransitive relation curve；

Step B2：According to the control block diagram of system, outer voltage analysis is carried out to system, and show that Voltage loop stability is sentenced According to specifically, first according to the control block diagram of grid-connected system, it is known that current reference value is given by below equation：

i_d,ref=g_v(e_v)=k_pe_v+k_i∫e_vdt (3)

Wherein, e_v=V_dc,ref-v_dc；

Coupling system state equation and formula (5) can obtain the state equation of voltage loop：

Carry out linearization process to equation, and the characteristic equation of outer loop voltag after arranging, can be obtained be：

This Voltage loop characteristic equation is solved, it can be deduced that outer shroud voltage characteristic equation root track, according in root locus Whether there is characteristic root in RHP, judge whether system is stable, and this is Voltage loop stability criteria；

Step C, toughness boundary condition of the current transformer with regard to key parameter under grid disturbance is calculated, so as to judge this unsteady flow Whether device tolerates the fault type, and current transformer toughness is estimated；

Step D, under step C is to initial parameter after the assessment of current transformer toughness, if current transformer is discontented with this parameter Sufficient its toughness boundary condition, i.e. current transformer do not have tolerance to failure, in return to step A2 during initial designs current transformer model Current transformer voltage loop gain, current loop gain, DC bus capacitor parameter are changed repeatedly, current transformer voltage loop is made Gain, current loop gain, DC bus capacitor parameter all meet the toughness boundary condition of current transformer, obtain and meet tolerance electrical network The design of failure；

B2：According to the control block diagram of system, outer voltage analysis is carried out to system, and draws Voltage loop stability criteria.

The present invention current transformer toughness will be defined as current transformer jam-tolerant ability first, in conjunction with current transformer under electric network fault Transient response, the toughness boundary condition for calculating disturbance using electric current transmission curve and Voltage loop stability analyses, so as to right Current transformer toughness is estimated, and assessment result also further can be applied to the design of grid-connected converter device.With existing There is technology to compare,

The method of grid-connected converter toughness assessment under a kind of above-mentioned electric network fault, in step C, current transformer toughness

The drafting of the deriving analysis and current transformer toughness boundary curve of assessment analytic equation；

After failure occurs, energy equation on electric capacity, energy loss expression formula and electric capacity can be listed by the energy consumption on electric capacity On total regression equation can draw v in fault time_dcTransforming function transformation function v with the time_dc(t)；

In conjunction with formula (5) can draw reference current fault time section with the time transforming function transformation function：

i_d,ref(t)=g_v(e_v)=g_v(V_dc,ref-v_dc(t)) (6)

Thus, it is possible to provide current transformer toughness assessment analytic equation：

Wherein u>0, show that the tough performance of current transformer itself bears such failure；And u<0, show that current transformer itself toughness can not Bear such failure；Analytic equation is assessed by current transformer toughness, can be made with current transformer toughness key parameter as coordinate system Current transformer toughness boundary curve.

The present invention has advantages below and beneficial effect：1st, derive that current transformer toughness assessment analytic equation comes to current transformer The ability of jam-tolerant judged, provides more intuitively foundation for grid-connected converter system stability analysis, and for improving System stability provides important references.2nd, assessment result is may apply in the design of grid-connected converter device, the present invention Toughness appraisal procedure can provide certain guidance to the design of grid-connected converter.

Description of the drawings

Fig. 1 is the assessment of grid-connected converter toughness and the schematic flow sheet for designing under electric network fault of the present invention.

Fig. 2 is three-phase voltage source type converter topologies figure of the present invention.

Fig. 3 is grid-connected converter double -loop control figure of the present invention.

Fig. 4 is current transformer d shaft currents i of the present invention_dWith reference current i_d,refTransmission curve.

Fig. 5 a are with voltage loop gain k_vpIt is coordinate system with DC bus capacitor C, changes power attenuation equivalent resistance R_s's Current transformer toughness boundary curve.

Fig. 5 b are with voltage loop gain k_vpIt is coordinate system with DC bus capacitor C, changes load R_LCurrent transformer toughness side Boundary's curve.

Fig. 5 c are with voltage loop gain k_vpWith load R_LFor coordinate system, change the current transformer toughness side of DC bus capacitor C Boundary's curve.

Fig. 5 d are with voltage loop gain k_vpWith load R_LFor coordinate system, change power attenuation equivalent resistance R_sCurrent transformer Toughness boundary curve.

Fig. 5 e are with DC bus-bar voltage C and load R_LWith for coordinate system, change voltage loop gain k_vpCurrent transformer tough Property boundary curve.

Fig. 5 f are with DC bus-bar voltage C and load R_LWith for coordinate system, change power attenuation equivalent resistance R_sCurrent transformer Toughness boundary curve.

Fig. 6 is the Power System Simulator containing three-phase voltage source type current transformer that the present invention builds.

Specific embodiment

Accompanying drawing in below in conjunction with the present invention, to the present invention in technical scheme be clearly and completely described.

Fig. 1 show the assessment of grid-connected converter toughness and the schematic flow sheet for designing, the side under electric network fault of the present invention Method comprises the steps：

A：Power system contingency set, failure judgement type is set up, and designs the unsteady flow for meeting performance indications requirement Device model, step A specifically include following steps：

A1：Mark off the electrical network contingency set towards power electronic equipment security evaluation：Various typical faults are pressed first Electric network fault is divided into overcurrent fault, overvoltage failure, frequency fluctuation failure, phase place and is jumped by the impact to current transformer operating point Become failure and zero sequence or negative-sequence current mutation failure, which is divided into transition failure in detail further according to operating point Changing Pattern and is eased up Become failure, can recover automatically for failure to be divided into transient fault and permanent fault finally according to failure, so as to judge to be out of order Particular type.Electrical network forecast accident towards power electronic equipment security evaluation is divided as shown in table 1；

Table 1 is divided towards the electrical network forecast accident of power electronic equipment security evaluation

A2：Under conditions of performance indications requirement is met, determine the key parameter of current transformer, and Preliminary design goes out a conjunction The three-phase voltage source type grid-connected converter model of reason；

B：The response of current transformer under analysis electric network fault, and calculate respectively electric current loop transmission curve and Voltage loop stable Property criterion, step B are specially：

B1：The state equation after the decoupling of system dq is represented, current inner loop analysis is carried out to system, and is calculated electric current loop Transmission curve, so that it is determined that the voltage and current grade of IGBT switching devices.

The topology diagram of the three-phase voltage source type current transformer first according to Fig. 2, using switch averaging model, can be with Obtain three-phase voltage source converter mathematical model under tri- phase coordinate systems of abc：

According to synchronously rotating reference frame function, VSC is transformed under dq rotating coordinate systems, its state equation is as follows：

As inductance equivalent resistance R_sWhen less, system can be in output current i_oNonlinear phase is introduced into before entering saturation, this When system modulation can be regarded as infinity, control voltage v than m_dAnd v_qReach its upper limit：

Now interior circular current i_dReach its marginal value：

For any i_d,ref>i_d,critical, system be in ovennodulation state, its power factor no longer for unit power because Number.Thus, for seeking electric current loop transmission curve, need exist for for interior circular current carrying out segmentation with regard to the expression formula of reference current examining Consider.

When current transformer enters steady-working state, the control ring margin of error accounts for the leading part of control voltage, then have：

Can be released by formula (6) (8), when under dq synchronous rotating frames, as modulation ratio m ＞ 1, control voltage v_d,q The saturation value being up to：

Again according to the formula (3) (4) of system state equation, it is zero to make its differential value, can obtain control voltage v_d,qSaturation value Also meet formula simultaneously：

v_d,saturated=ω_lLi_q-R_si_d+v_d(18)

v_q,saturated=-ω_lLi_d-R_si_q+v_q(19)

Then simultaneous formula (9)-(12) can obtain the interior circular current i under ovennodulation state_d、i_qWith regard to i_d,refExpression formula.Because of which Expression formula is complex, is abbreviated as equation i here_d=h_d(i_d,ref) and i_q=h_q(i_d,ref), thus can obtain interior circular current and close In the equation to current reference value：

By power balance equation, it can be deduced that the electric current transmission equation under stable state, it is reduced equation, system loss only considers Inductance equivalent resistance part：

P_load=P_input-P_loss(22)

D shaft currents i just can be drawn by formula (13)_dWith reference current i_d,refTransitive relation curve, as shown in Figure 4. From transitive relation curve, with reference current i_d,refIncrease, d shaft currents i_dIncrease and reach maximum therewith, thereafter It is in inverse ratio with reference current.D shaft currents i can be calculated to formula (13) derivation_dMaximum：

i_d,max=h_d(h'_d(i_d,ref)=0) (24)

According to d shaft current maximums, it is known that alternating current maximum amplitude, then can determine that then and can bear event The voltage and current grade of the IGBT switching devices of barrier.

B2：According to the double -loop control block diagram of system, as shown in figure 3, outer voltage analysis is carried out to system, and draw voltage Ring stability criteria.

According to the control block diagram of grid-connected system, it is known that current reference value is given by below equation：

i_d,ref=g_v(e_v) (25)

e_v=V_dc,ref-v_dc(26)

g_v(e_v)=k_pe_v+k_i∫e_vdt (27)

In conjunction with the state equation that formula (3) (13) (14) (18) can obtain voltage loop：

Linearization process is carried out to equation, its small-signal model is drawn：

Wherein v_dcV can be approximately_dc,ref, according to formulaCan obtain：

Then the characteristic equation of outer loop voltag is：

This Voltage loop characteristic equation is solved, it can be deduced that outer shroud voltage characteristic equation root track, according in root locus Whether there is characteristic root in RHP, judge whether system is stable.

C：Toughness boundary condition of the current transformer with regard to key parameter under grid disturbance is calculated, so as to judge that this current transformer is No tolerance fault type, is estimated to current transformer toughness.

Event can be drawn according to the total regression equation on the energy equation on electric capacity, energy loss expression formula and electric capacity first V in Downtime_dcWith the transforming function transformation function of time, current transformer toughness assessment analytic equation is then released, current transformer toughness is then passed through The positive negativity of assessment analytical expression, determines the toughness boundary condition of disturbance, so as to judge that can current transformer itself toughness hold Receive such failure.

After failure occurs, and voltage on line side v_sdReduction cause active power lose, it is impossible to meet load power demand, Energy on electric capacity can be consumed to supplement this loss.The energy equation that can be listed on electric capacity is：

Wherein V_dc0T when representing fault occurs₀The DC voltage amplitude at moment, V_dc1T at the end of representing fault₁When straight Stream voltage magnitude, E_lossFor accumulation of the active power loss to fault time.

Analyzed according to above failure process, it is known that and voltage on line side v_sdCan be down in very short time and be close to 0V, for letter Change and calculate, can be considered as in t₀It is down to 0V winks, then energy loss can be expressed as：

E_loss=v_sdi_d(t₁-t₀) (33)

Wherein and voltage on line side v_sdAnd d shaft currents are t when failure occurs₀The voltage at moment, electric current, i.e. its value are stable state When amplitude.

According to the total regression equation on electric capacity, have：

Simultaneous formula (25)-(27) can draw v in fault time_dcTransforming function transformation function with the time.

Then according to formula (18) can draw reference current fault time section with the time transforming function transformation function：

i_d,ref(t)=g_v(e_v)=g_v(V_dc,ref-v_dc(t)) (35)

Thus, it is possible to provide current transformer toughness assessment analytic equation：

Wherein u>0, show that the tough performance of current transformer itself bears such failure；And u<0, show that current transformer itself toughness can not Bear such failure.Analytic equation is assessed by current transformer toughness, it is 60% that can be made in failure depth, trouble duration For 50ms when, with voltage loop gain k_vp, load R_L, power attenuation equivalent resistance R_sAnd the current transformer such as DC bus-bar voltage C Current transformer toughness boundary curve of the toughness key parameter for coordinate system, as shown in Figure 5.

D：When current transformer does not have tolerance to failure, can return to initial designs and current transformer parameter is repaiied repeatedly Change, the design for meeting tolerance electric network fault can be obtained eventually.

For further explaining the correctness of current transformer toughness appraisal procedure of the present invention, flat in MATLAB/simulink emulation In platform, transformator, power supply and impedance module build three-phase alternating current electrical network system as shown in Figure 6, and the system includes public electric wire net (being equivalent to voltage source), transmission line (comprising line impedance), chopper, non-ideal transformer, buses at different levels, three-phase to be studied Voltage source converter, other local load (being equivalent to constant power load) etc., are wherein built such as Fig. 2 institutes using Universal bridge circuit Show three-phase voltage source type current transformer, and build the voltage x current double -loop control shown in Fig. 3.Three-phase voltage source type current transformer parameter is such as Shown in table 2.

2 three-phase voltage source type current transformer parameter of table

Simulating, verifying is carried out to the response of system by Cycle by Cycle emulation, by changing current transformer toughness key parameter, can To be analyzed the variation tendency of current transformer toughness by simulation waveform, its parameter change is as shown in table 3 to current transformer Toughness.Can To find when current transformer adopts different design parameters, for the tolerance degree of failure is different, the result and unsteady flow of table 3 The current transformer toughness boundary curve result that device toughness assessment analytic equation is drawn out is consistent, and this also demonstrates electric network fault of the present invention The correctness of lower grid-connected converter toughness appraisal procedure.

3 parameter change of table is to current transformer Toughness

Under electric network fault of the present invention, the toughness assessment of grid-connected converter can also further apply the design process of current transformer, If the changer of initial designs is unsatisfactory for the requirement which tolerates impact capacity, designer can be made to return initial designs carries out data Modification, through design iteration process, can finally provide the grid-connected converter design for meeting tolerance electric network fault.

The above, the only specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, any Belong to those skilled in the art the invention discloses technical scope in, the change or replacement that can readily occur in all are answered It is included within the scope of the present invention.Therefore, protection scope of the present invention should be defined by scope of the claims.

Claims (2)

1. a kind of method that grid-connected converter toughness is assessed under electric network fault, it is characterised in that comprise the steps：

Step A, power system contingency set is set up, failure judgement type, and design the unsteady flow for meeting performance indications requirement Device model, specifically includes：

Step A1：The electrical network contingency set towards power electronic equipment security evaluation is marked off, out of order concrete kind is judged Type, specifically, electric network fault is divided into overcurrent fault, mistake by the impact first by various typical faults to current transformer operating point Voltage failure, frequency fluctuation failure, phase hit failure and zero sequence or negative-sequence current mutation failure, further according to operating point change rule Can which be divided into rule transition failure and soft fault in detail, recover automatically for failure to be divided into instantaneous event finally according to failure Barrier and permanent fault, so that judge out of order particular type；

Step A2：Under conditions of performance indications requirement is met, determine the key parameter of current transformer, and Preliminary design goes out a conjunction The three-phase voltage source type grid-connected converter model of reason；

The response of current transformer under step B, analysis electric network fault, and calculate respectively electric current loop transmission curve and Voltage loop stable Property criterion, specifically includes：

Step B1：The state equation after the decoupling of system dq is represented, current inner loop analysis is carried out to system, and is calculated electric current loop Transmission curve, so that it is determined that the voltage and current grade of IGBT switching devices, specifically, first according to synchronously rotating reference frame letter Number, by under VSC model conversation to dq rotating coordinate systems, determines its state equation；Then as inductance equivalent resistance R_sWhen less, it is System can be in output current i_oNonlinear phase is introduced into before entering saturation, now system modulation can be regarded as infinity than m, control Voltage v_dAnd v_qReach its upper limit V_g,max, now interior circular current i_dReach its marginal value：

$i_{d,critical}=\frac{v_{sd}{R}_s+\sqrt{v_{sd}^2{R}_s^2-(R_s^2+{\mathrm{\&omega;}}_l^2{L}^2)(v_{sd}^2-V_{g,max}^2)}}{R_s^2+{\mathrm{\&omega;}}_l^2{L}^2}---\left(1\right)$

For any i_d,ref>i_d,critical, in ovennodulation state, its power factor is no longer unit power factor to system；

Interior circular current i under ovennodulation state_dWith regard to i_d,refExpression formula be designated as i in description of the invention_d=h_d(i_d,ref), by This can obtain interior circular current with regard to the equation to current reference value：

$f_d\left(i_{d,ref}\right)=\left\{\begin{array}{cc}{i}_{d,ref}& i_{d,ref}\&le;i_{d,critical}\\ h_d\left(i_{d,ref}\right)& i_{d,ref}>i_{d,critical}\end{array}\right.---\left(2\right)$

D shaft currents i just can be drawn by formula (2)_dWith reference current i_d,refTransitive relation curve；

Step B2：According to the control block diagram of system, outer voltage analysis is carried out to system, and draws Voltage loop stability criteria, Specifically, first according to the control block diagram of grid-connected system, it is known that current reference value is given by below equation：

i_d,ref=g_v(e_v)=k_pe_v+k_i∫e_vdt (3)

Wherein, e_v=V_dc,ref-v_dc；

Coupling system state equation and formula (5) can obtain the state equation of voltage loop：

$C\frac{{\mathrm{de}}_v}{\mathrm{dt}}+\frac{3}{2}\frac{v_{\mathrm{sd}}{f}_d\left(g_v\left(e_v\right)\right)-R_s(f_d^2\left(g_v\left(e_v\right)\right)+f_d^2\left(g_v\left(e_v\right)\right))}{v_{\mathrm{dc}}}-\frac{v_{\mathrm{dc}}}{R_L}=0---\left(4\right)$

Carry out linearization process to equation, and the characteristic equation of outer loop voltag after arranging, can be obtained be：

${\mathrm{\&lambda;}}^2+\frac{3}{2C}\frac{v_{sd}{f}_d^{\&prime;}-2R_s(f_d{f}_d^{\&prime;}+f_q{f}_q^{\&prime;})}{V_{dc,ref}}(k_p\mathrm{\&lambda;}+k_i)=0---\left(5\right)$

This Voltage loop characteristic equation is solved, it can be deduced that outer shroud voltage characteristic equation root track, according in root locus whether There is characteristic root in RHP, judge whether system is stable, and this is Voltage loop stability criteria；

Step C, toughness boundary condition of the current transformer with regard to key parameter under grid disturbance is calculated, so as to judge that this current transformer is No tolerance fault type, is estimated to current transformer toughness；

Step D, under step C is to initial parameter after the assessment of current transformer toughness, if current transformer is unsatisfactory for which under this parameter Toughness boundary condition, i.e. current transformer do not have tolerance to failure, to becoming during initial designs current transformer model in return to step A2 Stream device voltage loop gain, current loop gain, DC bus capacitor parameter are changed repeatedly, increase current transformer voltage loop Benefit, current loop gain, DC bus capacitor parameter all meet the toughness boundary condition of current transformer, obtain meet tolerance electrical network therefore The design of barrier；

B2：According to the control block diagram of system, outer voltage analysis is carried out to system, and draws Voltage loop stability criteria.

2. the method that grid-connected converter toughness is assessed under a kind of electric network fault according to claim 1, it is characterised in that：Institute State the drafting of the deriving analysis and current transformer toughness boundary curve of current transformer toughness assessment analytic equation in step C；

After failure occurs, can be listed by the energy consumption on electric capacity on energy equation on electric capacity, energy loss expression formula and electric capacity Total regression equation can draw v in fault time_dcTransforming function transformation function v with the time_dc(t)；

In conjunction with formula (5) can draw reference current fault time section with the time transforming function transformation function：

i_d,ref(t)=g_v(e_v)=g_v(V_dc,ref-v_dc(t)) (6)

Thus, it is possible to provide current transformer toughness assessment analytic equation：

$u=i_{d,critical}-i_{d,ref}\left(t_1\right)=\frac{v_{sd}{R}_s+\sqrt{v_{sd}^2{R}_s^2-(R_s^2+{\mathrm{\&omega;}}_l^2{L}^2)(v_{sd}^2-V_{g,max}^2)}}{R_s^2+{\mathrm{\&omega;}}_l^2{L}^2}-g_v(V_{dc,ref}-v_{dc}(t_1\left)\right)---\left(7\right)$

Wherein u>0, show that the tough performance of current transformer itself bears such failure；And u<0, show that current transformer itself toughness can not be born Such failure；Analytic equation is assessed by current transformer toughness, the change with current transformer toughness key parameter as coordinate system can be made Stream device toughness boundary curve.