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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 2

*

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.) 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

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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 Energies 9, 644 2 of 15 voltage parameters was2016, proposed. Finally, aperiodic SI voltage and oscillating switching impulse (OSI) 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,calculation. increasingSubsequently, output power as generating parameters solved by analytical the capacity, influence as of well the circuit Energies 2016, 9, were 644 2 of 15 lightningcomponent impulse voltage. parameters on the waveform parameters was analyzed, and an optimized method to generating circuit of the switchingwas impulse (SI) voltage initiallySIdesigned, and oscillating its circuit select the component parameters proposed. Finally,was aperiodic voltage and parameters were (OSI) solvedvoltage by analytical calculation. Subsequently, influenceMoreover, of the circuit 2. Principle of Transformer Boosting-Based Impulse Generation switching impulse were successfully generated by a 50 kVthe transformer. some component parameters on thediscussed waveformforparameters analyzed, and an optimized method to technical considerations were improvingwas the output voltage, increasing output power

To establish acomponent guide for parameters designing theimpulse primary winding side circuit and determining the circuit select theas was proposed. Finally, aperiodic SI voltage and oscillating capacity, well as generating lightning voltage. parameters basedimpulse on transformer thisgenerated section by first a fourth-order equivalent switching (OSI) voltage induction, were successfully a 50proposed kV transformer. Moreover, some 2.generate Principle Impulse Generation considerations wereBoosting-Based discussed for improving the output voltage, increasing output power circuit totechnical aofSITransformer According to the solution, waveform parameters in pace with variations of the capacity, as well as generating lightning impulse voltage. circuit parameters wereaobtained by calculation. Subsequently, optimization method To establish guide for designing the primary winding sidean circuit and determining the was circuitproposed parameters based on transformer induction, this first proposed a fourth-order equivalent to select 2. the circuitof parameters by considering thesection waveform Principle Transformer Boosting-Based Impulse Generationerror (S) and impulse magnification circuit to generate a SI According to the solution, waveform parameters in pace with variations of the ratio (IMR).

To parameters establish a guide designing primary winding side circuit determining the circuit circuit werefor obtained bythe calculation. Subsequently, an and optimization method was parameters transformer induction,bythis section first a fourth-order equivalent proposed tobased selectonthe circuit parameters considering theproposed waveform error (S) and impulse 2.1. Equivalent Circuit Analysis circuit to generate SI According to the solution, waveform parameters in pace with variations of the magnification ratioa (IMR). were obtained by calculation. Subsequently, optimization method was side of Thecircuit basic parameters idea for generating an impulse is to input a smallanimpulse into the primary 2.1. Equivalent Circuitthe Analysis proposed to select 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). The basic idea for generating impulse is to input a small into the primary side of a a more effective on-off trigger control,an the traditional spark gapimpulse is replaced with an IGBT module. transformer and thus to obtain an amplified impulse at the secondary (high-voltage) side. To achieve Equivalent Circuitof Analysis The2.1. circuit diagram the principle for generating SI is sketched as shown in Figure 1. Here, a more effective on-off trigger control, the traditional spark gap is replaced with an IGBT module. power electronic switch K initially stays inforthe offinput state assketched a impulse trigger switch, U0 isside the on The basic for generating an impulse is to a small the in primary ofvoltage a circuitidea diagram of the principle generating SI is as into shown Figure 1. Here, C1 after transformer charging, and L is the wave-modulating inductor for generating an OSI voltage (it is and thus to obtain an amplified impulse at the secondary (high-voltage) side. To achieve power electronic switch K initially stays in the off state as a trigger switch, U0 is the voltage on C1 a more effective on-off trigger control, the traditional spark gap is replaced with an IGBT module. after charging, and L is the wave-modulating inductor for generating an OSI voltage (it is not adopted not adopted to generate SI). As the trigger switch is turned on, main capacitor C1 discharges to The circuit diagram the principle for generating SI is sketched shown Figure 1. Here, to generate SI). As the trigger switch turned on, in main capacitor C1 discharges to in wave-modulating wave-modulating capacitor C2of , which is isconnected parallel with theasprimary side of the transformer, power electronic switch K initiallyinstays in the offthe state as a trigger switch, U0 is the voltage C1 capacitor C2, which is connected parallel with primary side of the transformer, and a on highand a high-amplitude SI voltage is induced at the secondary side. after charging, and L isisthe wave-modulating inductor amplitude SI voltage induced at the secondary 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 highamplitude 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 diagram of the principle of generating switching impulse (SI). gate C1 : Main C2: wave-modulating capacitor; K: power electronic switch (insulated bipolarcharging capacitor;transistor C2 : wave-modulating capacitor; K:Rpower electronic switch (insulated gateinductor; bipolarT:transistor (IGBT)); R1: wave-tail resistor; 2: wave-head resistor; L: wave-modulating transformer; andresistor; C 3: load capacitor. 1. Circuit diagram of principle of resistor; generatingL:switching impulse (SI). inductor; C1: Main charging (IGBT)); Figure R R2the : wave-head wave-modulating T: transformer; 1 : wave-tail capacitor; C 2: wave-modulating capacitor; K: power electronic switch (insulated gate bipolar and C3 : load capacitor.

The single-phase inRFigure 1 can beresistor; represented by an equivalent T-type T: circuit, transistor (IGBT)); transformer R1: wave-tailshown resistor; 2: wave-head L: wave-modulating inductor; as shown in Figure Considering transformer; and 2a. C3: load capacitor. that the winding resistance of the test transformer is relatively The smaller single-phase transformer shown in Figure can be represented by anthan equivalent T-type circuit, than the reactance and that the leakage1 resistance is much smaller the excitation single-phase transformer in Figure 1 can be represented an equivalent T-type the2a. transformer can be shown represented by an equivalent Γ-type circuit (Figure 2b) [10].circuit, as shownreactance, in The Figure Considering that the winding resistance ofby the test transformer is relatively as shown in Figure 2a. Considering that the winding resistance of the test transformer is relatively smaller than the reactance and that the leakage resistance is much smaller than the excitation reactance, smaller than the reactance and that the leakage resistance is much smaller than the excitation the transformer can be represented by an equivalent Γ-type circuit (Figure 2b) [10]. reactance, the transformer can be represented by an equivalent Γ-type circuit (Figure 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; Lm: magnetizing inductance the transformer. Figure 2. (a) T type; and (b) of Γ type equivalent circuits of the transformer. L1: Leakage inductance of

Figure 2.the (a)low-voltage T type; and (b) Γ type equivalent circuits of the transformer. L : Leakage inductance of winding; L2: leakage inductance of the high-voltage winding; L: 1leakage inductance; the low-voltage winding; L2 R : 1leakage inductance of the L: leakage inductance; R: R: winding resistance; , R2, Rm: winding resistance of high-voltage the transformer;winding; Lm: magnetizing inductance; m: magnetizing the transformer. windingLresistance; R1inductance , R2 , Rm : of winding resistance of the transformer; Lm : magnetizing inductance; Lm : magnetizing inductance of the transformer.

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The entire equivalent equivalentdischarge dischargecircuit circuitofofthe theSISI voltage is shown in Figure 3. Here, L istotal the The entire voltage is shown in Figure 3. Here, L is the The entire equivalent discharge circuit of the SI voltage is shown in Figure 3. Here, L total equivalent inductance of the wave-modulating and the leakage inductance, and C is the total equivalent inductance of the wave-modulating and the leakage inductance, and C2 2is the total equivalent inductance of ofthe theload wave-modulating and the leakage inductance, and C2 is the total and capacitance. equivalent capacitance capacitance of the load and the the wave-modulating wave-modulating capacitance. equivalent capacitance of the load and the wave-modulating capacitance.

Figure 3. SI discharge equivalent circuit with IGBT. Figure 3. 3. SI SI discharge discharge equivalent equivalent circuit circuit with Figure with IGBT. IGBT.

2.2. Numerical Calculation 2.2. Numerical Calculation Calculation 2.2. Numerical 2.2.1. Oscillating Switching Impulse Voltage 2.2.1. Oscillating Switching Switching Impulse 2.2.1. Oscillating Impulse Voltage Voltage According to the equivalent circuit previously mentioned, the equivalent circuit of the entire According to to the the equivalent equivalent circuit circuit previously previously mentioned, the the equivalent equivalent circuit circuit of of the the entire According entire system configuration during discharge can be drawnmentioned, as shown in Figure 4. system configuration during discharge can be drawn as shown in Figure 4. system configuration during discharge can be drawn as shown in Figure 4.

Figure 4. Equivalent circuit during breakover of the IGBT. u1 and u2 are the potential differences of Figure 4. Equivalent circuit during breakover thecircuit. IGBT. u1 and u2 are the potential differences of the capacitor. i1, i2, iL,circuit iR1 areduring the current flowsof inofthe this Figure 4. Equivalent breakover 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 equivalent circuit can LC be expressed by Equation (1) in a fourth-order form: d 4i L d 3i LLm C1C2 d 4i4m  (C1C2 R2 Lm  LC2 Lm ) d3i3m  ( LC1  Lm C1  m 2 m m R LLm C1C24 dt 4  (C1C2 R2 Lm  ) dt3  ( LC1  Lm C1  1 (1) 2 d im RL12 LmL)mddt 3id3mim+ (RLC im2 R2 Lm + LC LLmLmCC1 C +1 Lm C1 + 22 dt4dt + (Cd12C 1R 2R 2  R (1) dt 1  L C )  ( C R  )  i  0 (1) m 2 2 d i2 1 2 R R R2 + R1R1m LL LRmLm ddidi m m Lm CL RC 2m 2R12 2  L Cd) im m 2 R R t d t  ( C R   ) i  0 1 1 1 mim = 0 2 ( C1 1R22 + R1 + R1 ) dt + R1 R + Lm Cm2 ) 2dt2dt+ R R1 R1 dt R1 1 1 The initial conditions for Equation (1) are described in Equation (2): The The initial initial conditions conditions for for Equation Equation (1) (1) are are described described in in Equation Equation (2): (2):  i  0  m t 0  iimm |tt=00= 00     dim   di t 0  0 m d i    dt dmt |t=0 =0 0  2d2t t  0 (2) (2)  dddt2i2mim|t=0 =0 0  t 0  d i  2 (2)  m  d 3t  0   dd3it3m2 |tt= 00 = LLU0C dt im U 0m 2 d  d 3i3m t  0  LLU 0C d t  3 t 0  m 2  Indeed, it is very difficult to obtain LLm C2analytical expression for a fourth-order  dtthe explicit equation [11].it is Tovery accurately the between the circuit and waveform Indeed, difficultanalyze to obtain therelationships explicit analytical expression for aparameters fourth-order equation [11]. Indeed, the it is very difficult to obtain thebetween explicit analytical expression for and athese fourth-order equation [11]. parameters, fourth-order Runge-Kutta method applied to solve ordinary differential To accurately analyze the relationships thewas circuit parameters waveform parameters, To accurately analyze the relationships between the circuit parameters and waveform parameters, the fourth-order Runge-Kutta method applied to solve these ordinary equations [12– equations [12–14]. For Equation (1), thewas ordinary differential equations candifferential be solved by introducing the fourth-order Runge-Kutta method was applied to solve these ordinary differential equations [12– 14].intermediate For Equationvariable, (1), the ordinary differential equations an as expressed in Equation (3): can be solved by introducing an intermediate 14]. For Equation (1), the ordinary differential equations can be solved by introducing an intermediate variable, as expressed in Equation (3): variable, as expressed in Equation (3): y0 = Fy (3) y' = Fy (3) y' = Fy (3) here: here: T T y0 = (y1 , y2 , y3 , y4 ) , y0 = (y10 , y20 , y30 , y40 ) (4) here: T T     (4)  y  ( y , y , y , y ) y   ( y1 , y2 , y3 , y4 ) , 1 2 3 4 T (4) y   ( y1 , y2 , y3 , y4 )T , y  ( y1 , y2 , y3 , y4 ) and the coefficient matrix is expressed in Equations (5) and (6): and the coefficient matrix is expressed in Equations (5) and (6):

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and the coefficient matrix is expressed in Equations (5) and (6):    F= 

0 0 0 − ae

1 0 0 − da

0 1 0 − ac

0 0 1 − ba

  T U0  )  , y0 = (0, 0, 0, LLm C2 

 a = LLm C1 C2       b = C1 C2 R2 Lm + LCR2 Lm  1   c = LC1 + Lm C1 + LmRR1 R2 + Lm C2 1   Lm L   d = C R + + 2 1  R1 R1     e = R2 + R1 R

 y1 = im       y10 = didtm = y2    2 y20 = ddti2m = y3   3   y30 = ddti3m = y4      y0 = − b y − c y − d y − e y 4 a 4 a 3 a 2 a 1

1

(5)

(6)

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): u2 = Lm

dim = Lm y2 dt

(7)

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 line, and oscillation frequency f. Assuming that Tp and T2 of the target impulse voltage are Tp0 and T20 , respectively, the waveform error S can be calculated by Equation (8): S=

( Tp − Tp0 )2 Tp0 2

+

( T2 − T20 )2 T20 2

(8)

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): Um I MR = (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 Figures 5 and 6, 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,

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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 The5main program and subprogram flowcharts toiscalculate the circuitthe parameters shown in Figures and 6, respectively. Here, the subprogram used to calculate waveformare curves Energies 2016, 9, 644 5 and of 15 Figures 5 and 6, 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 parameters using thecan given circuit Initially, parameters C1, Lm and R1 are set to fixed values that hardly becomponent adjusted inparameters. practice, and the specific parameters of the target to fixed values that can hardly be adjusted in practice, and the specific parameters of the target such as T and T , are provided. Then, the expected value ranges for C , L and R within a group p 2 2 2 waveform, such as Tp and T2, are provided. Then, the expected value ranges for C2, L and R2 withinof a waveform, such ,and are Then, theestimated expected value forcircular Ccomputation 2, L and R2 within parameters suchas asTTpsuch , T2as ,TS2T IMR can be estimated severalseveral timesranges by circular usinga pand group of parameters p, T2provided. , S and IMR can be times by computation group of parameters such as Tp,length. T2, S and IMR can be estimated several times by circular computation the initial value value and step using the initial andlength. step 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 Figure 7 Area shows example of the S-IMR distribution which can with be used the parameter optimization. I inanFigure 7 is composed of parameter combinations smallfor errors. Area II of

Figure 7 shows anFigure example of the S-IMR distribution which can with be used the parameter optimization. I in 7 islarge composed of parameter smallfor errors. II of the parameter Area combinations with IMRs and Area III ofcombinations the intersection of Areas I and IIArea provides optimization. Area I in Figure 7 is composed of parameter combinations with small errors. Area II of the parameter combinations with large IMRs and Area III of the intersection of Areas I and II provides 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.

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Energiesthe 2016, 9, 644 comprehensive optimal selection area in this distribution. In this area, the circuit parameters are 6 of 15 Energies 2016, 9, 644

given priority with an optimized combination of larger IMR and small error.

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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

Figureoptimization. 7. Waveform error and impulse magnification ratio (S-IMR) diagram of the parameter The selected initial values are as follows: Lm = 0.9 H, C1 = 10 µ F, R1 = 1155 Ω, C2 = 0.1 µ F, optimization. selected initial values as follows: L 2) =µ F0.9 H,(10, C1 =80)10Ω,µF, R1 = 1155 Ω, 2 = 0.1 µF, and R2 = The 10 Ω. The value ranges of Care 2 and R2 are (0.1, m and respectively. TheCstep and RFigure Ω. The two value ranges C0.1 R2 1are (0.1, 2)ratio µF and (10,point 80) Ω, respectively. The lengths of Waveform these parameters are µF and Ω, respectively. The red in Area III inparameter Figure 7 step 2 = 10 7. 2 and error andof impulse magnification (S-IMR) diagram of the is of selected S =parameters 0, IMR = 0.88, 20.1 = 56 and 2Ω, = 1respectively. µ F. Lm = 0.9 H,The lengths these as: two areRvalues µFΩare and Area Figure optimization. The selected initial as1Cfollows: C1 =red 10 µpoint F, R1 =in1155 Ω,III C2 in = 0.1 µ F, 7 is andas: R2 S == 100,Ω.IMR The=value ofΩ C2and andCR22 = are (0.1, 2) µ F and (10, 80) Ω, respectively. The step selected 0.88,ranges R2 = 56 1 µF. 2.3.2. Impulse Waveforms Solution Using Circuit Parameters lengths of these two parameters are 0.1 µFthe andGiven 1 Ω, respectively. The red point in Area III in Figure 7 isTo selected as: S = 0, IMR = 0.88, RUsing 2 = 56 Ω and C2 = 1 µ F. 2.3.2. Impulse Waveforms Solution the Given Circuit more intuitively describe the influence of the circuit Parameters parameters on the impulse waveform,

the calculation results are illustrated by discussing the SI and OSI voltages.

To more intuitively describe theUsing influence of the circuit parameters on the impulse waveform, 2.3.2. Impulse Waveforms Solution the Given Circuit Parameters  Switching impulse voltage the calculation results are illustrated by discussing the SI and OSI voltages. To more intuitively describe the influence of the circuit parameters on the impulse waveform,



If the circuit parameters are given L = 0, C1 =the 10 SI µ F,and C2 =OSI 1 µvoltages. F, Lm = 0.9 H, R1 = 1155 Ω, R2 = 56 the calculation results are illustrated byas discussing

Switching voltage Ω and Uc1 =impulse 400 V, the corresponding SI could satisfy the waveform parameters recommended by the

IEC Switching impulse 60060-3 standard [4]voltage (i.e., 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, can observe the variations in L Tp=, T and and C22,=R56 1 If thewe circuit parameters are given as 0,2 C 1 = U 10mµwith F, C2decreasing = 1 µ F, Lm L=m0.9 H,increasing R1 = 1155 C Ω,1, R and Uand V, the corresponding SI could satisfy the waveform parameters recommended by the c1 =R400 2, as shown in Figure 8. The corresponding parameters are listed in Table 1. Ω and Uc1 = 400 V, the corresponding SI could satisfy the waveform parameters recommended by the IEC 60060-3 standard [4] (i.e., Tp = 250 µs and T2 = 2500 µs), as shown in Figure 6. 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 the the variations in in TpT, pT, T with decreasing Lm and increasing C , ,RC1 2 , R1 2 2and variable, we observe can observe variations andU Um m with decreasing Lm and increasing C1, C21 and Rand , as shown in Figure 8. The corresponding parameters arelisted listed Table 2 R2, as shown in Figure 8. The corresponding parameters are in in 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 Table 1 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.

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) (1) 10 1 1155 56 0.9 250 2500 351.6 (2) 10 1 1155 56 0.2 205 1193 341.5 Energies(3) 2016, 9, 644 50 1 1155 56 0.9 298 4895 384.1 (4) 10 5 1155 56 0.9 712 3344 246.0 (5) 10 1 11550 56 0.9 280 2939 357.1 1. Waveform and0.9 their corresponding circuit parameters. (6) Table 10 1 parameters 1155 of SI voltage 336 724 2079 286.7

IMR 0.879 0.854 0.9607 of 15 0.615 0.893 0.717

No. Figure C1 (µF) C2 (µF) R1 that (Ω) bothR2Tp(Ω) T p (µs) T 2 (µs) in LUmm (V) IMRTp, m (H) 8 and Table 1 show and T2Ldecrease with the decrease . Meanwhile,

T2(1) , and IMR the increase in C561. The increases in T250 p, T2, and 2500 IMR are not sensitive0.879 to the 10 increase with 1 1155 0.9 351.6 (2) 1155 change56along with 0.2 the changes 205 in R21193 341.5 a positive 0.854 increase in10R1. Tp and1T2 obviously and C2. Further, (3) 50exists between 1 384.1 correlation Tp 1155 and R2, C2,56whereas 0.9 T2 shows 298 a positive4895 correlation with C20.960 and 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 AnAn OSI waveform (i.e., R