A New Switching Impulse Generator Based on Transformer Boosting and Insulated Gate Bipolar Transistor Trigger Control

energies

Article A New Switching Impulse Generator Based on Transformer Boosting and Insulated Gate Bipolar Transistor Trigger Control

Ming Ren 1, Chongxing Zhang 1, Ming Dong 1,*, Rixin Ye 1 and Ricardo Albarracín 2

1 State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (M.R.); [email protected] (C.Z.); [email protected] (R.Y.) 2 Department of Electrical, Electronics and Automation Engineering and Applied Physics, Polytechnic University of Madrid, Ronda de Valencia 3, Madrid 28012, Spain; [email protected] * Correspondence: [email protected]; Tel.: +86-131-5248-1560

Academic Editor: Issouf Fofana Received: 2 June 2016; Accepted: 8 August 2016; Published: 16 August 2016

Abstract: To make the switching impulse (SI) generator more compact, portable and feasible in field tests, a new approach based on transformer boosting was developed. To address problems such as triggering synchronization and electromagnetic interference involved with the traditional spark gap, an insulated gate bipolar transistor (IGBT) module with drive circuit was employed as the impulse trigger. An optimization design for the component parameters of the primary winding side of the transformer was realized by numerical calculation and error correction. Experiment showed that the waveform parameters of SI and oscillating switching impulse (OSI) voltages generated by the new generator were consistent with the numerical calculation and the error correction. The generator was finally built on a removable high voltage transformer with small size. Thus the volume of the generator is significantly reduced. Experiments showed that the waveform parameters of SI and OSI voltages generated by the new generator were basically consistent with the numerical calculation and the error correction.

Keywords: impulse generator; switching impulse (SI); insulated gate bipolar transistor (IGBT); boosting transformer; impulse waveform parameters

1. Introduction On account of the frequent failures of high voltage power equipment [1–3], more attention has been increasingly focused on the impulse withstand voltage test in the ﬁeld [4], which has become a more stringent and effective method of evaluating the insulation status of power equipment [5–8]. The traditional impulse generator is built on a Marx circuit, which has been widely applied in high voltage testing and insulation assess for many years. However, the Marx generator is labor intensive and time consuming in replacing the output waveform, and its multiple spark airgap switches are sometimes triggered out of synchrony, especially when the preset voltage is not very high. In addition, electromagnetic interference [9] that arises from the spark discharge makes partial discharge detection difﬁcult. In this study, we tried to use an impulse transformer to magnify the input impulse voltage. The entire equivalent circuit model was analytically analyzed to accurately control the generator output by adjusting only the circuit connected to the primary winding side, and on this basis, a parameter optimization method was proposed. In addition, instead of the spark gap of the Marx generator, an insulated gate bipolar transistor (IGBT) was used as a trigger switch owing to its good performance in turning on and cutting off the current with a rapid response time and low noise at the instant of triggering. In this study, the

Energies 2016, 9, 644; doi:10.3390/en9080644 www.mdpi.com/journal/energies Energies 2016, 9, 644 2 of 15 generating circuit of the switching impulse (SI) voltage was initially designed, and its circuit parameters were solved by analytical calculation. Subsequently, the influence of the circuit component parameters on the waveform parameters was analyzed, and an optimized method to select the component parametersEnergies was 2016 proposed., 9, 644 Finally, aperiodic SI voltage and oscillating switching impulse (OSI)2 of 15 voltage were successfully generated by a 50 kV transformer. Moreover, some technical considerations were generating circuit of the switching impulse (SI) voltage was initially designed, and its circuit discussed for improving the output voltage, increasing output power capacity, as well as generating Energiesparameters 2016, 9 , were644 solved by analytical calculation. Subsequently, the influence of the circuit2 of 15 lightningcomponent impulse voltage. parameters on the waveform parameters was analyzed, and an optimized method to generatingselect the component circuit of the parameters switching was impulse proposed. (SI) voltage Finally, was aperiodic initially SI designed, voltage and and oscillatingits circuit 2. Principleparametersswitching of Transformer impulse were (OSI) solved voltage Boosting-Based by analytical were successfully calculation. Impulse generated Subsequently, Generation by a 50 kV thetransformer. influence Moreover, of the circuit some componenttechnical considerations parameters onwere the discussed waveform for parameters improving wasthe outputanalyzed, voltage, and anincreasing optimized output method power to To establishselectcapacity, the as a component well guide as generating for parameters designing lightning was the impulse primaryproposed. voltage. winding Finally, aperiodic side circuit SI voltage and determining and oscillating the circuit parametersswitching based impulse on transformer (OSI) voltage induction,were successfully this generated section by first a 50 proposed kV transformer. a fourth-order Moreover, some equivalent circuit totechnical2. generate Principle considerations aof SI Transformer According were Boos todiscussed theting solution,-Based for improving Impulse waveform Generation the output parameters voltage, increasing in pace with output variations power of the capacity, as well as generating lightning impulse voltage. circuit parametersTo establish were a obtained guide for designing by calculation. the primary Subsequently, winding side an circuit optimization and determining method the wascircuit proposed parameters based on transformer induction, this section first proposed a fourth-order equivalent to select2. the Principle circuit of parameters Transformer Boos by consideringting-Based Impulse the waveform Generation error (S) and impulse magnification ratio (IMRcircuit). to generate a SI According to the solution, waveform parameters in pace with variations of the circuitTo parametersestablish a guide were for obtained designing by the calculation. primary winding Subsequently, side circuit an and optimization determining method the circuit was parameters based on transformer induction, this section first proposed a fourth-order equivalent 2.1. Equivalentproposed Circuit to select Analysis the circuit parameters by considering the waveform error (S) and impulse circuitmagnification to generate ratio a (SIIMR Accordin). g to the solution, waveform parameters in pace with variations of the Thecircuit basic parameters idea for generating were obtained an impulse by calculation. is to input Subsequently, a small an impulse optimization into the method primary was side of proposed2.1. Equivalent to select Circuit the Analysis circuit parameters by considering the waveform error (S) and impulse a transformer and thus to obtain an amplified impulse at the secondary (high-voltage) side. To achieve magnification ratio (IMR). a more effectiveThe basic on-off idea trigger for generating control, an the impulse traditional is to input spark a small gap impulse is replaced into the with primary an IGBT side of module. a transformer and thus to obtain an amplified impulse at the secondary (high-voltage) side. To achieve The2.1. circuit Equivalent diagram Circuit of Analysis the principle for generating SI is sketched as shown in Figure1. Here, a more effective on-off trigger control, the traditional spark gap is replaced with an IGBT module. power electronicThe basiccircuit switch idea diagram for K generating initially of the principle stays an impulse in for the generating is to off input state SIa smallis as sketched a impulse trigger as intoshown switch, the inprimary FigureU0 is side 1. the Here, of voltage a on C1 aftertransformerpower charging, electronic and and thus switchL tois obtain K the initially wave-modulatingan amplified stays in impulsethe off state at inductor the as secondary a trigger for switch,(high generating-voltage) U0 is the side. an voltage OSI To achieve voltageon C1 (it is not adoptedaafter more charging, to effective generate and on -Loff SI).is triggerthe As wave thecontrol,-modulating trigger the traditional switchinductor issparkfor turned generating gap is on,replaced an main OSI withvoltage capacitor an IGBT(it is not module.C 1adopteddischarges to to generateThe circuit SI). Asdiagram the trigger of the switch principle is turned for generating on, main capacitor SI is sketched C1 discharges as shown to inwave Figure-modulating 1. Here, wave-modulating capacitor C2, which is connected in parallel with the primary side of the transformer, powercapacitor electronic C2, which switch is connected K initially in stays parallel in the with off the state primary as a trigger side of switch, the transformer, U0 is the voltage and a onhigh C1- and a high-amplitude SI voltage is induced at the secondary side. afteramplitude charging, SI voltage and L is is the induced wave- atmodulating the secondary inductor side. for generating an OSI voltage (it is not adopted to generate SI). As the trigger switch is turned on, main capacitor C1 discharges to wave-modulating capacitor C2, which is connected in parallel with the primary side of the transformer, and a high- amplitude SI voltage is induced at the secondary side.

Figure 1. Circuit diagram of the principle of generating switching impulse (SI). C1: Main charging

Figure 1.capacitor;Circuit diagramC2: wave-modulating of the principle capacitor of; generatingK: power electronic switching switch impulse (insulated (SI). gateC1: Main bipolar charging capacitor;transistorC2: wave-modulating (IGBT)); R1: wave capacitor;-tail resistor; K: R power2: wave- electronichead resistor switch; L: wave (insulated -modulating gate induct bipolaror; T: transistor (IGBT)); FigureRtransformer1: wave-tail 1. Circuit; and resistor; Cdiagram3: load capacit ofR 2the: wave-head or.principle of resistor;generatingL :switching wave-modulating impulse (SI). inductor;C1: Main charging T: transformer; capacitor; C2: wave-modulating capacitor; K: power electronic switch (insulated gate bipolar and C3: load capacitor. transistorThe single (IGBT-phase)); transformerR1: wave-tail shown resistor; in RFi2:gure wave 1- canhead be resistor represented; L: wave by- modulatingan equivalent induct T-typeor; T:circuit ,

as showntransformer in Figure; and 2a.C3: lConsideringoad capacitor. that the winding resistance of the test transformer is relatively Thesmaller single-phase than the transformer reactance and shown that thein Figure leakage1 can resistance be represented is much smaller by an than equivalent the excitation T-type circuit, as shownreactance, inThe Figure single the2 transformera.-phase Considering transformer can be thatshownrepresented the in Fi windinggure by an 1 can equivalent resistancebe represented Γ-type of bycircuit the an testequivalent (Figure transformer 2b) T- type[10]. circuit is relatively, smaller thanas shown the reactancein Figure 2a. and Considering that the leakage that the winding resistance resistance is much of smallerthe test transformer than the excitation is relatively reactance, smaller than the reactance and that the leakage resistance is much smaller than the excitation the transformerreactance, can the betransformer represented can be by represented an equivalent by an equivalentΓ-type circuit Γ-type (Figurecircuit (Figure2b) [10 2b)]. [10].

(a) (b)

Figure 2. (a) T type; and (b) Γ type equivalent circuits of the transformer. L1: Leakage inductance of

the low-voltage winding; L2: leakage inductance of the high-voltage winding; L: leakage inductance; (a) (b) R: winding resistance; R1, R2, Rm: winding resistance of the transformer; Lm: magnetizing inductance;

FigureLm: magnetizing 2. (a) T type inductance; and (b) ofΓ typethe transformer. equivalent circuits of the transformer. L1: Leakage inductance of Figure 2. (a) T type; and (b) Γ type equivalent circuits of the transformer. L : Leakage inductance of the low-voltage winding; L2: leakage inductance of the high-voltage winding; L: 1leakage inductance; the low-voltageR: winding winding; resistanceL;2 R:1 leakage, R2, Rm: winding inductance resistance of the of high-voltagethe transformer; winding; Lm: magnetizingL: leakage inductance; inductance; R: windingL resistance;m: magnetizingR1 inductance, R2, Rm: of winding the transformer. resistance of the transformer; Lm: magnetizing inductance; Lm: magnetizing inductance of the transformer. Energies 2016, 9, 644 3 of 15 Energies 2016, 9, 644 3 of 15 Energies 2016, 9, 644 3 of 15 The entire equivalent equivalent discharge discharge circuit circuit of of the the SI SIvoltage voltage is shown is shown in Figure in Figure 3. Here,3. Here, L is theL is total the The entire equivalent discharge circuit of the SI voltage is shown in Figure 3. Here, L is the total totalequivalent equivalent inductance inductance of the of the wave wave-modulating-modulating and and the the leakage leakage inductance, inductance, and and CC2 2isis the the total total equivalent capacitance inductance of of the the load wave and-modulating the wave-modulatingwave-modulating and the leakage capacitance.capacitance. inductance, and C2 is the total equivalent capacitance of the load and the wave-modulating capacitance.

Figure 3. SI discharge equivalent circuit with IGBT. Figure 3. SI discharge equivalent circu circuitit with IGBT. 2.2. Numerical Calculation 2.2. Numerical Calculation 2.2.1. Oscillating Switching Impulse Voltage 2.2.1. Oscillating Switching Impulse Voltage According to the equivalent circuit previously mentioned, the equivalent circuit of the entire According to the equivalent circuit previously mentioned, the equivalent circuit of the entire systemAccording configuration to the during equivalent discharge circuit can previously be drawn mentioned, as shown in the Figure equivalent 4. circuit of the entire system conﬁgurationconfiguration during dischargedischarge cancan bebe drawndrawn asas shownshown inin FigureFigure4 4..

Figure 4. Equivalent circuit during breakover of the IGBT. u1 and u2 are the potential differences of Figure 4. Equivalent circuit during breakover of the IGBT. u1 and u2 are the potential differences of the capacitor. i1, i2, iL, iR1 are the current flows in this circuit. Figure 4. Equivalent circuit during breakover of the IGBT. u1 and u2 are the potential differences of the the capacitor. i1, i2, iL, iR1 are the current flows in this circuit. capacitor. i1, i2, iL, iR1 are the current ﬂows in this circuit. The loop equation of the equivalent circuit can be expressed by Equation (1) in a fourth-order form: The loop equation of the equivalent circuit can be expressed by Equation (1) in a fourth-order form: The loop equation of the equivalentdd43i circuit can LC be expressed L i by Equation (1) in a fourth-order form: 43m 2 m m LLm C 1 C 2()( C 1 C 2 R 2 L m   LC 1  L m C 1  ddi43m LC 2 L m i m ddttR1 LLm C 1 C 24 43()( C 1 C 2 R 2 L m 3  LC 1  L m C 1  d iddmtt2 LCR 2 Lm d im (1) LLmLmC C1C 2 R2 24 + (Cdd1C i m2R2Lm + L1 L) m3 i m+ ( RLC 21 R+ 1 LmC1+ dt L C)2  ( C R R1 d )t  i  0 (1) L C Rm 22 dd i2 1 2L L i R R m (1) LmC2mR2R 2 2d imdt m RL R mLm dd mtim 2 R2+ 1R1 1+ LmLCm C) 2)+ (C ( C 1R R 2+  1 + 1 )) + 1 i mim  = 0 0 R1 2 dt2 2 1 2 R1 R1 dt R1 R1dt R 1 R 1d t R 1 The initial conditions for Equation (1) are described in Equation (2): The initial conditions for Equation (1) are describeddescribed inin EquationEquation (2):(2): im0t  0  i  0  imdm0i|t=0 = 0   m  0  ddimi t0   dtm|t=0 =0 0   dt t0  2d2t ddimi (2(2))  2 m| = = 0  dt2 tt0  0  d i2m (2)  d3 t  0  d im2 t0 U0  d3t3 |t=0 =  dt i LLU mC2 3 m 0 t0  d i3m U0 dt LLCm2  3 t0  Indeed, it is very difﬁcult to obtain dt the explicitLLCm2 analytical expression for a fourth-order equationIndeed, [11 ].it is To very accurately difficult analyze to obtain the the relationships explicit analytical between expression the circuit for a parameters fourth-order and equation waveform [11]. parameters,To accuratelyIndeed, theit isanalyze fourth-ordervery difficult the relationships to Runge-Kutta obtain the between explicit method analyticalthe was circuit applied expression parameters to solve for anda these fourth waveform ordinary-order equation parameters, differential [11]. equationstheTo accuratelyfourth- [order12– analyze14 ].Runge For Equationthe-Kutta relationships method (1), the was ordinarybetween applied differentialthe to solvecircuit these parameters equations ordinary can and differential be waveform solved byequations introducingparameters, [12– an14the].intermediate fourthFor Equation-order variable,Runge (1), the-Kutta ordinary as expressed method differential was in Equation applied equations (3):to solve can thesebe solved ordinary by introducing differential an equations intermediate [12– variable,14]. For Equation as expressed (1), the in ordinaryEquation differential (3): equations can be solved by introducing an intermediate variable, as expressed in Equation (3): y0 = Fy (3) y' = Fy (3) y' = Fy (3) hhere:ere: 0 T 0 0 0 0 0 T here: y = (y1, y2, y3, y4) , y = (y1, y2, y3, y4) (4) T T y  (,,,)y y  y  y  (4) y  (,,,)y1 y 2 y 3 y 4 , 1 2 3 4 T y  (,,,)y y y y T , y  (,,,)y y  y  y  (4) and the coefficient matrix is expressed1 in 2 Equation 3 4 s (5) and1 (6): 2 3 4 and the coefficient matrix is expressed in Equations (5) and (6):

Energies 2016, 9, 644 4 of 15 and the coefﬁcient matrix is expressed in Equations (5) and (6):   0 1 0 0  0 0 1 0  U T =   = ( 0 ) F   , y0 0, 0, 0, (5)  0 0 0 1  LLmC2 e d c b − a − a − a − a   a = LLmC1C2 y1 = im    LC2 Lm  0 dim  b = C1C2R2Lm +  y = = y2  R1  1 dt   2  LmR1R2  0 d i c = LC + LmC + + LmC y = m = y 1 1 R1 2 2 dt2 3 (6)  L Lm  0 d3i  d = C1R2 + +  y = m = y  R1 R1  3 dt3 4  +   e = R2 R1  y0 = − b y − c y − d y − e y R1 4 a 4 a 3 a 2 a 1 The solution vector y in Equation (3) can be solved by the fourth-order Runge–Kutta equation, and curve u2 of the OSI waveform can be obtained by Equation (7):

di u = L m = L y (7) 2 m dt m 2

2.2.2. Switching Impulse Voltage The analysis method for SI is similar to that for the OSI, and the only difference from the consideration of the OSI is that the wave-modulating inductance in the primary side is not needed, i.e., L = 0; hence, the circuit can be described by a group of third-order differential equations.

2.3. Selection and Optimization of the Circuit Parameters Based on the analytical solution of the circuit parameters, the key parameters of the waveform can be determined with numerical computing, such as peak time Tp, half-peak time T2, enveloping 0 0 line, and oscillation frequency f. Assuming that Tp and T2 of the target impulse voltage are Tp and T2, respectively, the waveform error S can be calculated by Equation (8):

0 2 0 2 (Tp − Tp) (T − T ) S = + 2 2 (8) 0 2 0 2 Tp T2

Apparently, the smaller S is, the closer is the calculated waveform to the target waveform. Consequently, optimal parameters of the component and their combination within a certain range and a minimum S are expected. In addition, the output efﬁciency of the generator should be taken into consideration. IMR is thus introduced to generally evaluate the output efﬁciency of this SI voltage generator, as expressed by Equation (9): U IMR = m (9) U1

Here, Um is the amplitude of the output voltage, and U1 is the charging voltage on C1. In fact, the circuit parameters can hardly meet both the requirements for minimum S and maximum IMR simultaneously. Therefore, the selection of the ﬁnal circuit parameters is a result of a tradeoff between the two key parameters.

2.3.1. Solving the Circuit Parameters for the Given Target Waveform Parameters The main program and subprogram flowcharts to calculate the circuit parameters are shown in Figures5 and6, respectively. Here, the subprogram is used to calculate the waveform curves and parameters using the given circuit component parameters. Initially, parameters C1, Lm and R1 are set to fixed values that can hardly be adjusted in practice, and the specific parameters of the target waveform, Energies 2016, 9, 644 5 of 15 Energies 2016, 9, 644 5 of 15 2.3.1. Solving the Circuit Parameters for the Given Target Waveform Parameters 2.3.1. Solving the Circuit Parameters for the Given Target Waveform Parameters The main program and subprogram flowcharts to calculate the circuit parameters are shown in The main program and subprogram flowcharts to calculate the circuit parameters are shown in FiguresEnergies 2016 5 and, 9, 644 6, respectively. Here, the subprogram is used to calculate the waveform curves5 and of 15 parametersFigures 5 and using 6, respectively. the given circuit Here, component the subprogram parameters. is used Initially, to calcula parameterste the waveform C1, Lm and curves R1 are and set toparameters fixed values using that the cangiven hardly circuit be component adjusted in parameters. practice, and Initially, the specific parameters parameters C1, Lm and of theR1 are target set waveform,tosuch fixed as T valuesp andsuch T thatas2, areT p can and provided. hardly T2, are beprovided. Then, adjusted the expectedThen, in practice, the valueexpected and ranges thevalue for specific rangesC2, L and parameters for RC2, withinL and of R a the2 groupwithin target ofa groupparameterswaveform, of parameters such such as as TT psuchp and, T2 as,TS2 T, andarep, T 2provided.IMR, S andcan IMR be Then, estimatedcan bethe estimated expected several severalvalue times ranges bytimes circular byfor circularC computation2, L and computation R2 within using a usinggroupthe initial the of parameters initial value value and stepsuch and length. as step Tp, length.T2, S and IMR can be estimated several times by circular computation using the initial value and step length.

Figure 5. Program flowchart to calculate the circuit parameters. Figure 5. Program ﬂowchart to calculate the circuit parameters. Figure 5. Program flowchart to calculate the circuit parameters.

Figure 6. Subprogram flowchart of the waveform-parameter calculation. Figure 6. Subprogram flowchart of the waveform-parameter calculation. Figure 6. Subprogram ﬂowchart of the waveform-parameter calculation. Figure 7 shows an example of the S-IMR distribution which can be used for the parameter optimization.Figure 7 Area shows I in an Figure example 7 is composed of the S-IMR of parameterdistribution combinations which can with be used small for errors. the parameterArea II of Figure7 shows an example of the S-IMR distribution which can be used for the parameter theoptimization. parameter Areacombinations I in Figure with 7 is large composed IMRs andof parameter Area III of combinations the intersection with of Areassmall errors.I and II Area provide II ofs theoptimization. parameter Areacombinations I in Figure with7 is large composed IMRs ofand parameter Area III of combinations the intersection with of smallAreas errors. I and II Area provide II ofs the parameter combinations with large IMRs and Area III of the intersection of Areas I and II provides the comprehensive optimal selection area in this distribution. In this area, the circuit parameters are given priority with an optimized combination of larger IMR and small error. Energies 2016, 9, 644 6 of 15

Energiesthe2016 comprehensive, 9, 644 optimal selection area in this distribution. In this area, the circuit parameters are 6 of 15 Energiesgiven 2016priority, 9, 644 with an optimized combination of larger IMR and small error. 6 of 15

the comprehensive optimal selection area in this distribution. In this area, the circuit parameters are given priority with an optimized combination of larger IMR and small error.

Figure 7. Waveform error and impulse magnification ratio (S-IMR) diagram of the parameter Figure 7. Waveform error and impulse magniﬁcation ratio (S-IMR) diagram of the parameter optimization. The selected initial values are as follows: Lm = 0.9 H, C1 = 10 µF, R1 = 1155 Ω, C2 = 0.1 µF, µ µ optimization.and R2 = The10 Ω. selected The value initial ranges values of C are2 and as R follows:2 are (0.1L, m2) =µF 0.9 and H, (C101, =80 10) Ω, F,respectively.R1 = 1155 ΩThe, C step2 = 0.1 F, and RFigurelengths2 = 10 7. Ωof . Waveformthese The two value parameters error ranges and ofare impulseC 0.12 andµF and magnificationR2 1are Ω, respectively. (0.1, 2) ratioµF and(TheS-IMR red (10,) pointdiagram 80) Ωin, Area respectively. of theIII in parameter Figure The 7 step

lengthsoptimization.is ofselected these as two :The S = parameters 0,selected IMR = 0.88,initial are R values2 0.1 = 56µ FΩ are andand as 1C follows:2Ω = ,1 respectively. µF. Lm = 0.9 H, The C1 = red 10 µF, point R1 = in 1155 Area Ω, IIIC2 in= 0.1 Figure µF, 7 is selectedand as:R2 S= =10 0,Ω.IMR The =value 0.88, rangesR2 = 56 of ΩC2and and CR22 =are 1 µ(0.1F. , 2) µF and (10, 80) Ω, respectively. The step 2.3.2.lengths Impulse of these Waveforms two parameters Solution are U 0.1sing µF the and Given 1 Ω, respectively. Circuit Parameters The red point in Area III in Figure 7 2.3.2. ImpulseisTo selected more Waveforms asintuitively: S = 0, IMR Solution describe = 0.88, R Usingthe2 = 56 influence Ω the and Given C 2of = 1the µF. Circuit circuit Parametersparameters on the impulse waveform, the calculation results are illustrated by discussing the SI and OSI voltages. To2.3.2. more Impulse intuitively Waveforms describe Solution the U inﬂuencesing the Given of the Circuit circuit Parameters parameters on the impulse waveform,  Switching impulse voltage the calculationTo more results intuitively are illustrated describe the by influence discussing of the circuit SI and parameters OSI voltages. on the impulse waveform, If the circuit parameters are given as L = 0, C1 = 10 µF, C2 = 1 µF, Lm = 0.9 H, R1 = 1155 Ω, R2 = 56 • Switchingthe calculation impulse results voltage are illustrated by discussing the SI and OSI voltages. Ω and Uc1 = 400 V, the corresponding SI could satisfy the waveform parameters recommended by the  IEC S60060witching-3 standard impulse [4] v (i.e.,oltage Tp = 250 µs and T2 = 2500 µs), as shown in Figure 6. By changing a single If the circuit parameters are given as L = 0, C1 = 10 µF, C2 = 1 µF, Lm = 0.9 H, R1 = 1155 Ω, R2 = 56 Ω variable, we can observe the variations in Tp, T2 and Um with decreasing Lm and increasing C1, C2, R1 and U =If 400 the V,circuit the correspondingparameters are given SI could as L = satisfy 0, C1 = the10 µF, waveform C2 = 1 µF, parameters Lm = 0.9 H, R recommended1 = 1155 Ω, R2 = 56 by the c1 2 Ωand and R U, c1as = shown 400 V, inthe Figure corresponding 8. The corresponding SI could satisfy parameters the waveform are listed parameters in Table 1. recommended by the IEC 60060-3 standard [4] (i.e., Tp = 250 µs and T2 = 2500 µs), as shown in Figure6. By changing a single IEC 60060-3 standard [4] (i.e., Tp = 250 µs and T2 = 2500 µs), as shown in Figure 6. By changing a single variable, we can observe the variations in Tp, T and Um with decreasing Lm and increasing C , C , R variable, we can observe the variations in Tp, T2 2 and Um with decreasing Lm and increasing C1, C21, R1 2 1 and Rand2, as R2 shown, as shown in Figure in Figure8. The8. The corresponding corresponding parameters parameters are are listed listed in in Table Table 1.1 .

Figure 8. Simulated waveforms of SI voltage.

Figure 8. Simulated waveforms of SI voltage. Figure 8. Simulated waveforms of SI voltage.

Figure 8 and Table1 show that both Tp and T2 decrease with the decrease in Lm. Meanwhile, Tp, T2, and IMR increase with the increase in C1. The increases in Tp, T2, and IMR are not sensitive to the increase in R1. Tp and T2 obviously change along with the changes in R2 and C2. Further, a positive correlation exists between Tp and R2, C2, whereas T2 shows a positive correlation with

C2 and a negative correlation with R2. Therefore, adjusting the element parameters of C2 and R2 is preferable in practice. Because Lm is an inherent parameter of the transformer and has a nonlinear characteristic with the magnetizing current, the nonlinear curve of Lm should be introduced in every step of the calculation to obtain a simulation result closer to the real output. Energies 2016, 9, 644 7 of 15

Table 1. Waveform parameters of SI voltage and their corresponding circuit parameters.

No. C1 (μF) C2 (μF) R1 (Ω) R2 (Ω) Lm (H) Tp (μs) T2 (μs) Um (V) IMR (1) 10 1 1155 56 0.9 250 2500 351.6 0.879 (2) 10 1 1155 56 0.2 205 1193 341.5 0.854 Energies(20163) , 9, 64450 1 1155 56 0.9 298 4895 384.1 0.9607 of 15 (4) 10 5 1155 56 0.9 712 3344 246.0 0.615 (5) 10 1 11550 56 0.9 280 2939 357.1 0.893 (6) Table10 1. Waveform1 parameters1155 of SI voltage336 and0.9 their corresponding724 2079 circuit parameters.286.7 0.717

No. FigureC1 ( µ8 F)and TableC2 (µ F)1 showR1 that(Ω) bothR 2Tp(Ω and) T2L decreasem (H) withTp (µ thes) decreaseT2 (µs) in LUmm. Meanwhile,(V) IMR Tp, T2(1), and IMR 10 increase with 1 the increase 1155 in C 561. The increases 0.9 in T 250p, T2, and 2500IMR are not 351.6 sensitive 0.879 to the increase(2) in 10 R1. Tp and 1 T2 obviously 1155 change 56 along with 0.2 the changes 205 in R2 1193 and C2. Further, 341.5 a positive 0.854 correlation(3) 50 exists between 1 Tp 1155and R2, C2, 56 whereas 0.9T2 shows 298a positive 4895 correlation 384.1 with C2 0.960and a (4) 10 5 1155 56 0.9 712 3344 246.0 0.615 negative correlation with R2. Therefore, adjusting the element parameters of C2 and R2 is preferable (5) 10 1 11,550 56 0.9 280 2939 357.1 0.893 in practice. Because Lm is an inherent parameter of the transformer and has a nonlinear characteristic (6) 10 1 1155 336 0.9 724 2079 286.7 0.717 with the magnetizing current, the nonlinear curve of Lm should be introduced in every step of the calculation to obtain a simulation result closer to the real output. • Oscillating switching impulse voltage  Oscillating switching impulse voltage −1 An OSI waveform is generated when the circuit is underdamped (i.e., R2 < 2[L(C1 + C2)/C1C21] ). An OSI waveform is generated when the circuit is underdamped (i.e., RLCCCC22[ ( 1 2 ) / 1 2 ] ). If the circuit parameters are given as the combination of C = 3 µF, C = 0.22 µF, Lm = 1.3 H, R = 2230 Ω, If the circuit parameters are given as the combination of1 C1 = 3 µF, 2C2 = 0.22 µF, Lm = 1.3 H, R11 = 2230 R = 33 Ω and L = 1.2 mH, the OSI waveform has T of 50 µs, T of 1000 µs, U of 556.0 V and f of 2Ω, R2 = 33 Ω and L = 1.2 mH, the OSI waveform has pTp of 50 µs, T22 of 1000 µs, Umm of 556.0 V and f of 1010 kHz, kHz, as as shown shown in in Figure Figure9. 9. As As LLincreases, increases, thethe waveform oscillation oscillation becomes becomes more more serious, serious, as as shownshown in in Figure Figure 10 10.. Some Some simulations simulations performed performed byby changingchanging circuit parameters CC11, ,CC2,2 R, R1 and1 and R2R are2 are listedlisted in in Table Table2. 2.

FigureFigure 9. 9.Oscillating Oscillating switchingswitching impulse ( (OSI)OSI) waveform. waveform. Energies 2016, 9, 644 8 of 15

Figure 10. OSI waveform after changing L. Figure 10. OSI waveform after changing L.

The oscillation frequency of OSI is related to both parameters L, C1, C2 and R2. When R2 is very small, f is determined by the combination of L, C1 and C2, as expressed in Equation (10). Tp is actually half of the oscillation period.

11CC f  12 (10) 22Tpπ LC 1 C 2

When R2 increases to a critical damping condition (even to an overdamped condition), the waveform stops oscillating. Therefore, the OSI waveform can be converted to an SI waveform by reducing L or improving R2. In addition, T2 increases with the increase in C1, C2, R1 and R2, and slightly decreases with the increase in L. Similar to SI, IMR can be improved by increasing C1 or decreasing C2. Therefore, changing the values of L, R2 and C2 is effective to adjust the waveform parameters of OSI.

Table 2. Waveform parameters of OSI voltage and their corresponding circuit parameters.

NO. C1 (μF) C2 (μF) R1 (Ω) R2 (Ω) L (mH) Lm (H) Tp (μs) T2 (μs) f (Hz) Um (V) IMR (1) 3 0.22 2.23k 33 1.2 1.3 50 1000 10k 555.0 1.388 (2) 3 0.22 2.23k 33 4.9 1.3 100 855 5.0k 631.4 1.579 (3) 10 0.22 2.23k 33 1.2 1.3 52 1966 9.6k 582.1 1.455 (4) 3 1.12 2.23k 33 1.2 1.3 108 1660 4.6k 353.2 0.883 (5) 3 0.22 2.23k 33 1.2 0.5 50 684 10k 555.0 1.388 (6) 3 0.22 22k 33 1.2 1.3 50 1356 10k 558.0 1.395 (7) 3 0.22 1M 33 1.2 1.3 50 1405 10k 558.2 1.396 (8) 3 0.22 1k 33 1.2 1.3 50 701 10k 553.5 1.384 (9) 3 0.22 2.23k 25 1.2 1.3 50 865 10k 591.3 1.478 (10) 3 0.22 2.23k 120 1.2 1.3 77 1520 - 375.6 0.939 (11) 3 0.22 2.23k 180 1.2 1.3 157 1492 - 359.8 0.900

3. Loop Design of Switching Impulse Generator Based on Transformer Induction

3.1. Insulated Gate Bipolar Transistor Module and Its Drive Circuit

Energies 2016, 9, 644 8 of 15

Table 2. Waveform parameters of OSI voltage and their corresponding circuit parameters.

C C R R L L T T f U No. 1 2 1 2 m p 2 m IMR (µF) (µF) (Ω) (Ω) (mH) (H) (µs) (µs) (Hz) (V) (1) 3 0.22 2.23k 33 1.2 1.3 50 1000 10k 555.0 1.388 (2) 3 0.22 2.23k 33 4.9 1.3 100 855 5.0k 631.4 1.579 (3) 10 0.22 2.23k 33 1.2 1.3 52 1966 9.6k 582.1 1.455 (4) 3 1.12 2.23k 33 1.2 1.3 108 1660 4.6k 353.2 0.883 (5) 3 0.22 2.23k 33 1.2 0.5 50 684 10k 555.0 1.388 (6) 3 0.22 22k 33 1.2 1.3 50 1356 10k 558.0 1.395 (7) 3 0.22 1M 33 1.2 1.3 50 1405 10k 558.2 1.396 (8) 3 0.22 1k 33 1.2 1.3 50 701 10k 553.5 1.384 (9) 3 0.22 2.23k 25 1.2 1.3 50 865 10k 591.3 1.478 (10) 3 0.22 2.23k 120 1.2 1.3 77 1520 - 375.6 0.939 (11) 3 0.22 2.23k 180 1.2 1.3 157 1492 - 359.8 0.900

3. Loop Design of Switching Impulse Generator Based on Transformer Induction

3.1. Insulated Gate Bipolar Transistor Module and Its Drive Circuit

3.1.1. Insulated Gate Bipolar Transistor Module IGBT acts as a trigger-discharge switch. In the SI voltage generating circuit, the IGBT must withstand the voltage on the primary capacitor before discharge, and the maximum voltage must not exceed the peak voltage of the primary side. Additionally, the switching speed of the IGBT mustEnergies be 2016 sufﬁciently, 9, 644 fast, and its on-off time should be very much lesser than the peak time of the9 of SI15 voltage. Figure 11 shows that the selected IGBT module in this study is Model FF100R12RT4 (IGBT Module,Infineon, Inﬁneon,Neubiberg Neubiberg,, Germany Germany),), which consists which of consists two IGBTs of two in IGBTsseries inand series each and IGBT each has IGBT an anti has- anparallel anti-parallel diode to diode follow to the follow current the currentand for andprotection. for protection.

Figure 11. Diagram of the IGBT module principle.

3.1.2. Drive Circuit of Insulated Gate Bipolar Transistor The main function of the IGBT drive circuit is to isolate the control and main circuits. According to the demand, the the cir circuitcuit should should not not only only correctly correctly control control the the on on-off-off of of the the IGBT IGBT but but also also provide provide a certain protection function. In particular, it is supposed to shut off the IGBT when it suffers from overcurrent or overvoltage. This study designs an IGBT drive circuit, and the schematic diagram is shown in Figure 12. The entire drive circuit consists of a 15 V direct current (DC) power source, channels A and B switches, output channels A and B, a feedback circuit, and a protection circuit. Here, the IGBT drive circuit is powered by the 15 V DC power source. Channels A and B respectively correspond to the left and right IGBTs shown in Figure 11. When the channel switch is closed, the corresponding IGBT tube conducts. According to the design purpose, when the channel A switch is closed and the channel B switch is opened, the left side IGBT tube in Figure 11 conducts, and the power supply begins to charge main capacitor C1. After the charging is completed, the channel A switch is disconnected. Next, the channel B switch is closed, and the right side IGBT tube conducts. Then, the main capacitor C1 starts discharging to the primary winding of the transformer. Finally, the secondary side of the transformer induces the desired SI voltage. The output feedback module is mainly used to monitor whether the driver circuit properly works. If abnormal, the driver chip is reset by the protection circuit to protect the driver chip and the IGBT module. Moreover, the driver chip, which mainly completes the control and operation function of the drive circuit, is the core of the entire drive circuit.

Figure 12. Schematic diagram of the IGBT drive circuit.

3.2. Design of the Main Circuit

3.2.1. Charging Circuit Because the collector–emitter of the IGBT cannot withstand a negative voltage, it should be connected in series with a diode, which blocks the reverse voltage, or a rectifier. Further, the charging circuits also need a large series resistance r as a current-limiting resistor. However, it extends the charging time of the circuit. The diagram of the charging circuit is shown in Figure 13.

Energies 2016, 9, 644 9 of 15

Infineon, Neubiberg, Germany), which consists of two IGBTs in series and each IGBT has an anti- parallel diode to follow the current and for protection.

Figure 11. Diagram of the IGBT module principle.

3.1.2. Drive Circuit of Insulated Gate Bipolar Transistor Energies 2016, 9, 644 9 of 15 The main function of the IGBT drive circuit is to isolate the control and main circuits. According to the demand, the circuit should not only correctly control the on-off of the IGBT but also provide a certaina certain protection protection function. function. In In particular, particular, it itis is supposed supposed to to shut shut off off the the IGBT IGBT when when it it suffers from overcurrent or overvoltage. This study study designs designs an an IGBT IGBT drive drive circuit, circuit, and and the the schematic schematic diagram diagram is shown is shown in Figure in Figure 12. The 12. Theentire entire drive drive circuit circuit consists consists of a of 15 a 15V direct V direct current current (DC) (DC) power power source, source, channels channels A A and and B B switches, switches, output channels A and B, a feedback circuit, and a protection circuit. Here, the IGBT drive circuit is poweredpowered by the 15 V DCDC powerpower source.source. Channels A and B respectively correspond to the left and right IGBTs shownshown inin FigureFigure 1111.. When the channel switch is closed, the corresponding IGBT tube conducts. According to to the design purpose, when the channel A switch i iss closed and the channel B switch is is opened, opened, the the left left side side IGBT IGBT tube tube in Figure in Figure 11 conducts, 11 conducts, and the and power the power supply supply begins beginsto charge to charge main capacitor C . After the charging is completed, the channel A switch is disconnected. main capacitor C1. After the1 charging is completed, the channel A switch is disconnected. Next, the Next, the channel B switch is closed, and the right side IGBT tube conducts. Then, the main capacitor channel B switch is closed, and the right side IGBT tube conducts. Then, the main capacitor C1 starts Cdischarging1 starts discharging to the primary to the winding primary of winding the transformer. of the transformer. Finally, the Finally,secondary the side secondary of the transformer side of the inducestransformer the desired induces SI the voltage. desired The SI voltage.output feedback The output module feedback is mainly module used is mainlyto monitor used whether to monitor the whetherdriver circuit the driver properly circuit works. properly If abnormal, works. If the abnormal, driver chip the driveris reset chip by the is reset protection by the protectioncircuit to protect circuit theto protect driver thechip driver and the chip IGBT and module. the IGBT Moreover, module. Moreover,the driver chip, the driver which chip, mainly which completes mainly the completes control andthe controloperation and function operation of functionthe drive of circuit, the drive is the circuit, core of is the entire core of drive the entire circuit. drive circuit.

Figure 12. Schematic diagram of the IGBT drive circuit. Figure 12. Schematic diagram of the IGBT drive circuit.

3.2. Design of the Main Circuit 3.2. Design of the Main Circuit

3.2.1. Charging Circuit Because the collector–emittercollector–emitter of the IGBT cannot withstand a negative voltage, it shouldshould be connected in series with a diode, which blocks blocks the the reverse reverse voltage, voltage, or or a a rectifier. rectiﬁer. Further, Further, the charging circuits also need a large series resistance r as aa current-limitingcurrent-limiting resistor. However, it extends the charging time of the circuit. The diagram of the charging circuit isis shownshown inin FigureFigure 1313.. Energies 2016, 9, 644 10 of 15

Figure 13. Diagram of the charging circuit. AC: alternating current. Figure 13. Diagram of the charging circuit. AC: alternating current. Changing the polarity of the output can be achieved by reversing the connections of diode D Changingand the IGBT. the After polarity the ofIGBT the is output turned can on, bemai achievedn capacitor by C reversing1 can be fully the charged connections within of 3 diode–5 time D and constants (T = rC1). Before the discharge is triggered, the IGBT should be shut off to ensure that the the IGBT. After the IGBT is turned on, main capacitor C1 can be fully charged within 3–5 time constants discharge circuit is isolated from the power supply. The value of the withstand voltage of diode D (T = rC1). Before the discharge is triggered, the IGBT should be shut off to ensure that the discharge must be greater than the maximum peak of the output from the power supply, and its through- circuit is isolated from the power supply. The value of the withstand voltage of diode D must be greater current capability should exceed the value ωC1Um. To determine the value of r, both the maximum than the maximum peak of the output from the power supply, and its through-current capability current limited by the IGBT parameter and the charging time determined by C1 should be taken into ω shouldconsideration. exceed the value C1Um. To determine the value of r, both the maximum current limited by the IGBT parameter and the charging time determined by C1 should be taken into consideration. 3.2.2. General Circuit Figure 14 shows the general circuit to generate the SI voltage. The two IGBT module tubes are connected in series and used as switches for the charging and discharging circuits. Secondary voltage of Ta must be matched with the primary voltage of T, i.e., the maximum output of Ta should be greater than the maximum input of T. Considering circuit efficiency, C1 should be determined by C3, which is the equivalent capacitance of T or the test sample. Converted into the primary side of T, C3 and C2 can be combined into C2'. Thus, IMR can be estimated by Equation (11): CR IMR k 11  RR (11) CC12 12

Figure 14. General circuit to generate the SI voltage based on the transformer.

4. Experimental Results Based on the earlier theoretical discussion, each test was implemented according to the following procedures: i Determine the target impulse waveform parameters, such as output voltage, rise time, half peak time and oscillating frequency; ii Define the immutable parameters of the circuit component, such as charging capacitor and transformer; iii Run S-IMR diagram for parameter optimization; iv Adjust the component according to the calculated parameters; v Make a comparison between the actual output and the target impulse waveform. The voltage waveforms were recorded by a digital oscilloscope (WaveSurfer 64Xs-B, LeCroy, New York, NY, USA) and a high voltage probe (P6015, Tektronix, Beaverton, OR, USA) which is in

Energies 2016, 9, 644 10 of 15

Figure 13. Diagram of the charging circuit. AC: alternating current.

Changing the polarity of the output can be achieved by reversing the connections of diode D and the IGBT. After the IGBT is turned on, main capacitor C1 can be fully charged within 3–5 time constants (T = rC1). Before the discharge is triggered, the IGBT should be shut off to ensure that the discharge circuit is isolated from the power supply. The value of the withstand voltage of diode D must be greater than the maximum peak of the output from the power supply, and its through- Energiescurrent2016 capability, 9, 644 should exceed the value ωC1Um. To determine the value of r, both the maximum10 of 15 current limited by the IGBT parameter and the charging time determined by C1 should be taken into consideration. 3.2.2. General Circuit 3.2.2.Figure General 14 Circuit shows the general circuit to generate the SI voltage. The two IGBT module tubes are connectedFigure in 14 series shows and the used general as switches circuit forto generate the charging the SI and voltage. discharging The two circuits. IGBT Secondarymodule tubes voltage are ofconnectedTa must in be series matched and with used the as primaryswitchesvoltage for the charging of T, i.e., theand maximum discharging output circuits. of T aSecondaryshould be vol greatertage thanof Ta themust maximum be matched input with of theT. Considering primary voltage circuit of efﬁciency,T, i.e., the maximumC1 should beoutput determined of Ta should by C3 be, which greater is thethan equivalent the maximum capacitance input of of TT. orConsidering the test sample. circuit Converted efficiency, into C1 should the primary be determined side of T, C by3 and C3, Cwhich2 can beis the combined equivalent into capacitanceC2'. Thus, IMR of Tcan or the be estimatedtest sample. by Converted Equation (11): into the primary side of T, C3 and C2 can be combined into C2'. Thus, IMR can be estimated by Equation (11): C R ≈ · 1 · 1 IMR k CR0 (11) IMR kC1 +11C2 R1 + R 2  RR (11) CC12 12

Figure 14. General circuit to generate the SI voltage based on the transformer. Figure 14. General circuit to generate the SI voltage based on the transformer. 4. Experimental Results 4. Experimental Results Based on the earlier theoretical discussion, each test was implemented according to the followingBased procedures: on the earlier theoretical discussion, each test was implemented according to the following procedures: i Determine the target impulse waveform parameters, such as output voltage, rise time, half peak i Determinetime and o thescillating target impulsefrequency; waveform parameters, such as output voltage, rise time, half peak ii timeDefine and the oscillating immutable frequency; parameters of the circuit component, such as charging capacitor and ii Deﬁnetransformer; the immutable parameters of the circuit component, such as charging capacitor iii andRun transformer; S-IMR diagram for parameter optimization; iiiiv RunAdjustS-IMR the diagramcomponent for according parameter to optimization; the calculated parameters; ivv AdjustMake thea compar componentison between according the to actual the calculated output and parameters; the target impulse waveform. v MakeThe voltage a comparison waveforms between were the recorded actual output by a digital and the oscilloscope target impulse (WaveSurfer waveform. 64Xs-B, LeCroy, New York, NY, USA) and a high voltage probe (P6015, Tektronix, Beaverton, OR, USA) which is in The voltage waveforms were recorded by a digital oscilloscope (WaveSurfer 64Xs-B, LeCroy, New York, NY, USA) and a high voltage probe (P6015, Tektronix, Beaverton, OR, USA) which is in parallel connection with C3. Further, the IMR and error sources between the actual and theoretical waveforms are analyzed in this section.

4.1. Experimental Results and Analysis

In the test, a 200 V/50 kV transformer, designated as T, is used, and Lm = 0.8455 H. The leakage inductance is 1.55 mH, which needs to be included in L during the numerical calculation. The value of the total capacitance in parallel with the secondary side of T is 500 pF. In practice, we should minimize the number of the components that need to be adjusted to promote efﬁciency and cost savings. In our test, all the parameters of the components in the primary side circuit were kept unchanged except for R2, C2 and L. Actually, the impulse voltage waveform can be effectively changed by adjusting R2, C2 and L. Figure 15b–d shows the actual waveforms under different circuit parameter combinations. In the presence of leakage inductance with the order of millihenries, OSI waveform can be generated without L but with small damping resistance R2. The decrease of the damping resistance and increase of L Energies 2016, 9, 644 11 of 15 parallel connection with C3. Further, the IMR and error sources between the actual and theoretical waveforms are analyzed in this section.

4.1. Experimental Results and Analysis

EnergiesFigure2016, 9 15b, 644–d shows the actual waveforms under different circuit parameter combinations.11 of In 15 the presence of leakage inductance with the order of millihenries, OSI waveform can be generated without L but with small damping resistance R2. The decrease of the damping resistance and increase ofwill L leadwill to lead more to moreintense intense oscillation oscillation of the waveformof the waveform and larger and IMR larger. Decreasing IMR. Decreasing wave-tail wave resistor-tail resistorR1 can significantlyR1 can significantly reduce Treduce2 within T2 awithin limited a limited range, butrange,T2 willbut T not2 will be endlesslynot be endlessly increased increased by the byincrease the increase in R1, i.e.,in R as1, i.e.,R1 asincreases, R1 increases,T2 will T2 will tend tend to saturate. to saturate. If the If the load load capacitance capacitanceC3 Cis3 convertedis converted to tothe the primary primary circuit circuit by by multiplying multiplying it it with with the the transformer transformer ratio, ratio, the the valuevalue ofof equivalentequivalent capacitance C2’’ would would become become very very large. large. Therefore, Therefore, an ins insufficientufficient value of C1 wouldwould limit the amplitude of the output impulse and lengthen Tp.. The The comparison comparison of of the the actual actual and and calculated calculated waveform waveform parameters parameters are listed listed in in Table Table3. It 3. reveals It reveals that the that influence the influence of each of component each component parameter parameter of the voltage of the waveform voltage waveformis the same is as the that same in the as foregoingthat in the theoreticalforegoing theoretical analysis. analysis. It is is worth worth noting noting that that by using by using the IGBT, the IGBT,the impulse the impulse voltages voltages are smoothly are smoothlyproduced. produced.The high- frequencyThe high-frequency oscillation oscillationthat overlapped that overlapped on the impulse on the waveform, impulse waveform,which is attributed which is to attributed the jitter of to tthehe traditional jitter of the spark traditional gap, does spark not gap, exist does in notthe existIGBT in-triggered the IGBT-triggered impulses. impulses.

Figure 15. SISI waveforms waveforms under under different different circuit parameters.

Energies 2016, 9, 644 12 of 15

Table 3. Comparisons of the actual waveform parameters and the numerical results under different circuit parameters.

Charging Output Voltage Output Circuit Parameters Peak Time Half-Peak Time Voltage Amplitude Efﬁciency Subﬁgure No. L C C C R R T T ’ T T ’ U U ’ e 1 2 3 1 2 U (V) p P e (%) 2 2 e (%) m m m IMR (mH) (µF) (µF) (pF) (Ω) (Ω) C1 (µs) (µs) p (µs) (µs) 2 (kV) (kV) (%) 15a 1.55 10 1 500 1300 56 160 1532 1549 −1.1 6188 6272 −1.3 8.4 8.67 −3.1 52.5 15b 1.55 10 0 500 300 10 170 356 359 −0.84 3224 3442 −6.3 12.0 12.58 −4.6 70.6 15c 1.55 4.7 0 500 130 25 200 310 315 −1.6 2782 2706 2.8 8.16 8.4 −2.9 40.8 15d 1.55 4.7 0 500 1000 4 190 250 251 −0.40 2395 2391 0.18 9.84 10.5 −6.3 51.8 15e 2.9 6.8 0 500 100,000 4 200 396 401 −1.2 3500 3657 −4.3 15.0 15.7 −4.5 75 15f 4.02 6.8 0 500 1000 4 200 471 470 −0.21 3300 3402 −3.0 14.8 15.6 −5.1 74 0 0 0 Note: Tp, T2 and Um represent the actual waveform parameters; Tp, T2 and Um represent the calculated waveform parameters; ep, e2 and em represent error between the actual and calculated waveform parameters. Energies 2016, 9, 644 13 of 15

4.2. Control of Impulse Magniﬁcation Ratio

As analyzed earlier, increasing L or decreasing R2 can relatively improve IMR in a limited range. Additionally, if the variation in the time parameters of the waveforms (Tp and T2) is permitted in a certain range, C1 should be chosen to be as large as possible to enhance the circuit efﬁciency and IMR. In general, the time parameters and IMR are considered to be a contradictory pair during the adjustment of the waveform and output level. However, our theoretical analysis indicates that decreasing the leakage inductance (Lm) and the equivalent capacitance (part of C3) of the transformer can effectively reduce waveform parameters Tp and T2, which may provide an effective solution to the contradiction. In other words, if the leakage inductance, winding resistance, and equivalent capacitance of the transformer are sufﬁciently small, waveform oscillation would be easier to produce, and the oscillation frequency would be higher; thus, Tp would be smaller. Therefore, choosing a transformer with small leakage inductance, winding resistance, and equivalent capacitance is necessary.

4.3. Error Sources Table3 indicates that the main differences between the parameters of the actual and calculated waveforms are Tp and T2. The results of smaller Tp in most cases are caused by the underestimation of 0 the leakage inductance of the transformer. T2 is also generally smaller than T2 when T2 is relatively small, which may be because the resistance of the magnetizing branch of the transformer is ignored in the calculation. Generally, the theoretical and practical studies on the technology based on IGBT triggering control and transformer induction proved that generating different types of SI voltage is possible, including SI and OSI recommended by the IEC60060-3 standard [4]. Furthermore, the waveform parameters to output a SI voltage can be easily adjusted by changing the parameters of the primaryside circuit elements.

5. Discussion

5.1. Technical Requirements in Achieving a Higher Amplitude and Larger Capacity Output Voltage As stated earlier, to achieve higher voltage and larger capacity output of the SI voltage, two methods can be considered. One is that using a voltage doubling circuit or improving the output voltage of the voltage regulator enhances the voltage of the transformer primary side. In this case, the IGBT module is required not only to withstand the working voltage with higher amplitude for a long time but also to have a bigger energy discharge capability. The other is choosing a transformer with a greater transformation ratio. Under the circumstances, the intrinsic parameters of the transformer will also increase with the increase in the transformation ratio, which causes the output waveform to accordingly change. At this time, a T-type equivalent circuit of the transformer should be considered, instead of the Γ-type equivalent circuit. Thus, more accurate numerical analysis result of the output waveform can be obtained.

5.2. Technical Requirements in Achieving Lightning and Oscillating Lightning Impulse Voltage By the same principle utilized in this paper, lightning impulse voltage can also be realized technically. However, the following technical issues need to be considered.

(1) Because the peak time of the lightning impulse voltage is much smaller than that of the SI voltage, a faster switch response speed of the IGBT module is correspondingly required. (2) The single phase transformer, which is used to generate the lightning impulse voltage, needs to withstand the impulse voltage with a much shorter rise time. Thus, the transformer must guarantee sufﬁcient insulating strength against damage under high impulse work condition, which is a necessary technical premise to output a lightning impulse voltage without failure. Energies 2016, 9, 644 14 of 15

(3)EnergiesWith 2016,regard 9, 644 to lightning impulse voltage with smaller peak time and half-peak time, a tighter14 of 15 match among the circuit parameters (including the transformer parameters) should be ensured to toachieve achieve steady steady and and controllable controllable output. output. Dueto Due the increase to the increase of the transformer of the transformer workingfrequency, working ftherequency,Γ-type (or the T-type) Γ-type equivalent (or T-type) circuit equivalent of the transformer, circuit of whichthe transformer, is originally which applied is to originally generate appliedan SI voltage, to generate cannot an be SI effectively voltage, cannot used to be analyze effectively the loop used of to the analyze lightning the impulse loop of voltage.the lightning Thus, impulseconsidering voltage. the winding Thus, capacitances considering and the stray winding capacitances capacitances of transformer and stray [15], a capacitances high-frequency of transformerequivalent circuit [15], a musthigh-frequency be utilized equivalent (Figure 16 ).circuit However, must thisbe utilized model (Figure will certainly 16). However, increase this the modelcomplexity will certainly of the equivalent increase circuit the complexity of the entire of systemthe equivalent and makes circuit the numericalof the entire analysis system theory, and makeswhich providesthe numerical guidance analysis in building theory, the whic actualh provides circuit, moreguidance difﬁcult. in building the actual circuit, more difficult.

Figure 16. High-frequency equivalent circuit of transformer. Rs1: Winding resistance of the primary Figure 16. High-frequency equivalent circuit of transformer. Rs1: Winding resistance of the primary side; Rs2: winding resistance of the secondary side; Lk1: leakage inductance of the primary side; Lk2: side; Rs2: winding resistance of the secondary side; Lk1: leakage inductance of the primary side; Lk2: leakage inductance of the secondary side; Cp: winding capacitance of the primary side; Cs: winding leakage inductance of the secondary side; Cp: winding capacitance of the primary side; Cs: winding capacitance of the secondary side; and Cps1, Cps2: winding stray capacitance between the primary side capacitance of the secondary side; and Cps1, Cps2: winding stray capacitance between the primary side and the secondary side.

6. Conclusions 6. Conclusions In this present paper, a new compact and removable SI generator based on transformer boosting In this present paper, a new compact and removable SI generator based on transformer boosting was developed with IGBT control. An optimization design method was proposed by considering was developed with IGBT control. An optimization design method was proposed by considering both of the output efficiency and waveform errors. By numerical calculation and error correction, the both of the output efﬁciency and waveform errors. By numerical calculation and error correction, component parameters of the primary side of the transformer, such as the magnetic inductance, the component parameters of the primary side of the transformer, such as the magnetic inductance, leakage inductance, winding resistance and equivalent capacitance, were determined for the target leakage inductance, winding resistance and equivalent capacitance, were determined for the target SIs. SIs. To address the synchronization problem which is usually caused by multiple spark gaps, an IGBT To address the synchronization problem which is usually caused by multiple spark gaps, an IGBT with with drive circuit was employed as the impulse trigger. It was proven that the IGBT within the range drive circuit was employed as the impulse trigger. It was proven that the IGBT within the range of of the forward withstand voltage can well replace the traditional sphere gap switch. The generator the forward withstand voltage can well replace the traditional sphere gap switch. The generator was was finally built on a removable high voltage transformer with small size. The experiment showed ﬁnally built on a removable high voltage transformer with small size. The experiment showed that the that the waveform parameters of SI and OSI voltages generated by the new generator were consistent waveform parameters of SI and OSI voltages generated by the new generator were consistent with the with the numerical calculation and the error estimation. numerical calculation and the error estimation.

Acknowledgments: The authors would like to thank the project supported by the National Natural Science Foundation of China (Grant No. 51507130), China Postdoctoral Science Foundation (Grant No. 2014M560777), Special China China Postdoctoral Postdoctoral Science Science Foundation Foundation (Grant (Grant No. 2016-11-141158) No. 2016-11 and-141158) Shaanxi and International Shaanxi International Cooperation Cooperationand Exchanges and Foundation Exchanges (Grant Foundation No. 2016KW-072). (Grant No. 2016KW-072).

Author Contributions: Ming Ren and Ming Dong conceived and designed the experiments; experiments; Rixin Ye Ye performed the experiments; Chongxing Zhang analyzed the data and wrote the paper; Ricardo Albarracín gave some thesubstantive experiments; suggestions Chongxing and guidance Zhang analyzed for the research. the data and wrote the paper; Ricardo Albarracín gave some substantive suggestions and guidance for the research. Conﬂicts of Interest: All authors declare that there is no conﬂict of interests regarding the publication of this paper. Conflicts of Interest: All authors declare that there is no conflict of interests regarding the publication of this paper.References

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