Introduction to Voltage Surge Immunity Testing

Transcription

1 IEEE Power Electronics Society Denver Chapter Meeting September 18, 2007 Introduction to Voltage Surge Immunity Testing By Douglas E. Powell and Bryce Hesterman Better technology. Better Results

2 Voltage Surges SLIDE # 2 Transient overvoltages on the ac power system are produced by events such as load switching, capacitor bank switching, equipment faults and lightning discharges The ability of equipment to withstand voltage surges can have a tremendous impact on field reliability Photo credits left to right 1 & 2: Microsoft Word clip art 3:

3 The Nature of Transient Overvoltages SLIDE # 3 Transient overvoltage events are usually of short duration, from several microseconds to a few milliseconds Waveforms can be oscillatory or non-oscillatory (impulsive) The rising wavefront is usually on the order of 0.5 µs to 10 µs The highest overvoltages are caused by direct lightning strikes to overhead power lines Transient overvoltages entering a facility typically range from 10 kv to 50 kv Voltage and current levels are attenuated as the surges propagate [1], [4] (References are on slide 14)

4 Transient Overvoltage Immunity Testing How do you know if your designs are robust enough? Standardized surge testing procedures have been developed to help answer that question. SLIDE # 4 US standard: ANSI/IEEE C , IEEE recommended practice on surge voltages in low-voltage ac power circuits Additional US standards: [7], [9] (Typically available in university libraries) International standard: IEC , 2005 Electromagnetic Compatibility, Testing and measurement techniques Surge immunity test Additional international standards: [5], [6] (Available for purchase at:

5 The Voltage Surge Test Method SLIDE # 5 This presentation provides an overview of IEC , including some of the standard waveforms, and the circuits that are used to produce those waveforms Voltage surge testing is typically done with commercially available surge test equipment The test equipment typically has a surge generator and a coupling/decoupling network (CDN) Combination wave generators produce a specified open circuit voltage waveform and a specified short-circuit current waveform Coupling/decoupling networks couple a surge generator to the equipment being tested and prevent dangerous voltages from being sent back into the ac power system

6 SLIDE # 6 IEC Combination Wave Generator (CWG) Energy is provided by the Voltage Source (U) which charges C c through R c. Once charged, the switch delivers energy into the wave shaping network made up of R S1, R S2, L r and R m. Component values are selected so that they will produce a defined voltage surge into an open circuit and a a defined current surge into a short circuit.

7 CWG 1.2/50 μs Voltage Surge Waveform SLIDE # 7 Open-circuit waveform characteristics: T = Time B - Time A T 1 =1.67T = 1.2 μs ± 30 % T 2 = 50 μs ± 20 % Undershoot 30% of the crest.

8 CWG 8/20 μs Current Waveform SLIDE # 8 Short-circuit waveform characteristics: T = Time B - Time C T 1 =1.25T = 8 μs ± 30 % T 2 = 20 μs ± 20 % Undershoot 30% of the crest.

9 Coupler/Decoupler Network (CDN) SLIDE # 9 IEC defines several CDNs. These are devices intended to couple the CWG voltage surge into your product while simultaneously decoupling it from the facility power. The inductances should be large enough to have a minimal effect on the output of the CWG, while being small enough to allow the equipment under test to function normally. A typical value is 1.5 mh [3], [5]-[7]. Example of a single phase line-to-line CDN

10 Coupler/Decoupler Network (CDN) SLIDE # 10 Example of a single phase line-to-earth CDN

11 Coupler/Decoupler Network (CDN) SLIDE # 11 Examples of three phase line-to-earth and line-to-line CDNs

12 Coupler/Decoupler Network (CDN) SLIDE # 12 IEC provides a decision tree for selecting the correct CDN

13 Links SLIDE # 13 Surge testing equipment (Local) Tutorial on surge testing munity_testing_e_4.pdf t ti Application notes on surge testing Free LT Spice software

14 References SLIDE # 14 [1] Martzloff, F.D, Coupling, propagation, and side effects of surges in an industrial building wiring system, Conference Record of IEEE 1988 Industry Applications Society Annual Meeting, 2-7 Oct. 1988, vol.2, pp [2] S.B Smith and R. B. Standler, The effects of surges on electronic appliances, IEEE Transactions on Power Delivery, vol. 7, Issue 3, July 1992 pp [3] Peter Richman, Criteria and designs for surge couplers and back-filters, Conference Record of IEEE1989 National Symposium on Electromagnetic Compatibility, May 1989, pp [4] Ronald B. Standler, Protection of Electronic Circuits from Overvoltages, New York: Wiley-Interscience, May Republished by Dover, December [5] IEC (1988) Electrical disturbance tests for measuring relays and protection equipment. Part 1: 1MHz burst disturbance tests. [6] IEC (2006) Electromagnetic compatibility (EMC): Testing and measurement techniques - Ring wave immunity test [7] IEEE/ANSI C , IEEE standard for Surge withstand Capability (SWC) Tests for Relays and Relays Systems Associated with Electric Power Apparatus. [8] IEC (2004) Testing and measurement techniques Electrical fast transient/burst immunity test [9] IEEE/ANSI C IEEE Recommended Practice on Characterization of Surges in Low-Voltage (1000 V and Less) AC Power Circuits

15 Part 2 Simulating Surge Testing SLIDE # 15 It would be great to be able to design equipment that passes the surge tests without having to be re-designed Performing circuit simulations of surge testing during the design phase can help you to understand component stress levels, and prevent costly re-design efforts. IEC provides schematic diagrams of standard surge generator circuits, and describes what waveforms they should produce, but no component values are given. The next part of the presentation reviews a Mathcad file that derives a suitable set of component values for the 1.2/50 μs voltage, 8/20 μs current combination wave generator The presentation concludes with a review of an LT Spice circuit simulation of the combination wave generator coupled to the input section of a power supply

16 Deriving Component Values using Mathcad Define the problem Derive Laplace domain circuit equations for open-circuit voltage and short-circuit current Determine time-domain responses using inverse-laplace transforms Derive expressions for the peak voltage and the peak current Define functions for the waveform parameters in terms of the component values and the initial capacitor voltage Enter the target values of the waveform parameters Set up a Solve Block using the functions and target values Solve for the component values and the initial capacitor voltage SLIDE # 16

17 SLIDE # 17 Combination Wave Surge Generator Bryce Hesterman September 15, 2007 Figure 1. Combination wave surge generator. Figure 1 is a circuit that can generate a 1.2/50 μs open-circuit voltage waveform and a 8/20μs short-circuit current waveform. IEC shows this circuit in Figure 1 on page 25, but it does not give any component values [1]. Instead, Table 2 on page 27 presents two sets of waveform characteristics. The first set is based on IEC It defines each waveform in terms of the front time and time to half value. The definition for the front time makes it awkward to use for circuit synthesis. The second set of characteristics is based on IEC , and it specifies the 10%-90% rise times and the 50%-50% duration times. It appears that it is easier to derive component values from the IEC definitions, so this document takes that approach.

18 SLIDE # 18 Table 1. Waveform Definitions 10%-90% Rise Time 50%-50% Duration Time 1.2/50μs Open-circuit Voltage Waveform 1μs 50μs 8/20μs Short-circuit Current Waveform 6.4μs 16μs Figures 2 and 3 on page 29 of IEC provide graphical definitions of the waveforms. These figures also specify that the undershoot of the surge waveforms be limited to 30% of the peak value. The circuit is first analyzed in the Laplace domain, after which time domain equations are derived. Functions for the waveforms and functions for computing the time to reach a specified level are then derived. The component values are derived using a solve block which seeks to meet the specified waveform characteristics.

19 SLIDE # 19 Derive Laplace domain equations for open-circuit voltage Write Laplace equations for the three currents in Figure 1 for the time after the switch is closed at time t = 0. Assume that the capacitor is fully charged to V dc, and that the initial inductor current is zero. Also, assume that the effects of the charging resistor R c can be neglected. ( ) I 1 ( s) C c s V c ( s ) + V dc ( 1) I 2 ( s) V c ( s) ( 2) R s1 I 3 ( s) V c ( s) L r s I 3 ( s) R m + R ( 3) s2

20 SLIDE # 20 Solve (3) for I 3. I 3 ( s) Rs2 V c ( s) + R m + L r s ( 4) Write a KCL equation for the three currents. I 1 ( s ) I 2 ( s ) I 3 ( s ) 0 ( 5 ) Substitute expressions for the currents from (1), (2), and (4) into (5). C c ( s V c ( s) + V dc ) V c ( s) R s1 V c ( s) 0 ( 6) R s2 + R m + L r s

21 SLIDE # 21 Solve (6) for V c ( s). V c ( s) V dc R s1 ( ) C c R s2 + R m + L r s ( ) r ( 7) s s1 s2 m s 2 R s1 L r C c + C c R s1 R s2 + R m + L r + R s1 + R s2 + R m Write an equation for the open-circuit output voltage. V oc ( s) I 3 ( s) R s2 ( 8)

22 SLIDE # 22 Laplace domain equation for open-circuit voltage Substitute (4) and (7) into (8) V oc ( s) ( ) V dc R s1 R s2 C c R s2 + R m + L r s ( R s2 + R m + L r s) s 2 R s1 L r C c + C c R s1 ( R s2 + R m ) + L r s + R s1 + R s2 + R m ( 9)

23 SLIDE # 23 Use Inverse Laplace Transform to find a time domain equation for open-circuit voltage Use the Mathcad Inverse Laplace function to find a time-domain equation for V out. (Some simplification steps are not shown.) ( 10) V oc 2V dc R s1 R s2 C c sinh ( ) 2 ( ) R 2 s1 R s2 + R m C c 2 R s1 R s2 + R m + 4 R s1 L r C c + L r t 2R s1 L r C c 2 R s1 ( Rs2 + R m ) 2 C 2 C 2 c 2R s1 ( R s2 + R m ) + 4R s1 L 2 c R s1 R s2 + R m r C c + L r exp 2R s1 L r C c ( ) + L r t

24 SLIDE # 24 Simplified time domain equation for open-circuit voltage Expand the hyperbolic sine function in (10) and simplify. t R s2 τ 1 V oc V dc τ 1 1 e L r t τ 2 e ( 11) R s1 L r C c where τ 1 2 R s1 ( Rs2 + R m ) 2 2 C 2 c 2R s1 ( R s2 + R m ) + 4R s1 L 2 ( 12) r C c + L r τ 2 ( ) C c R s1 R s2 + R m + L r 2R s1 L r C c ( ) 2 ( ) R s1 Rs2 + R m C c 2R s1 R s2 + R m + 4R s1 L 2 r C c + L r ( 13)

25 SLIDE # 25 The simplified time domain equation for open-circuit voltage (11) has the same form as the corresponding equation in [2] An equation for the 1.2/50 μs waveform is given in [2] as: V oc t τ 1 AV p 1 e t τ 2 e ( 14) where A τ τ

26 SLIDE # 26 Determine when the peak of the open-circuit voltage occurs Determine the peak value of the open-circuit output voltage by setting the time derivative of (11) equal to zero, and solve for t. t R d s2 t V dc τ τ e d L r t τ 2 e R s2 V dc L r 1 exp t t exp t τ τ exp 1 1 τ τ t 1 exp 2 τ 2 τ 2 0 ( 15) (Simplification steps are not shown.) t ocp τ 1 + τ 2 τ 1 ln ( 16) τ 1 τ 1 and τ 2 are defined in (12) and (13).

27 SLIDE # 27 Find the peak value of the open-circuit voltage Determine the peak value of the open-circuit output voltage by substituting (16) into (11). τ 1 + τ 2 V p R s2 V dc τ L 2 r τ 1 τ 1 + τ 2 τ 2 ( 17)

28 SLIDE # 28 Derive Laplace domain equation for short-circuit current Write a Laplace equation for the short-circuit output current by combining (4) and (7), and setting R s2 0. I sc ( s) s 2 R s1 L r C c V dc R s1 C c ( ) s + R s1 R m C c + L r + R s1 + R m ( 18)

29 SLIDE # 29 Use Inverse Laplace Transform to find a time domain equation for short-circuit current Use the Mathcad Inverse Laplace function to find a time-domain equation for the short-circuit current and simplify. I sc V dc exp L r ω sc t τ sc sin( ω sc t) ( 19) where τ sc 2R s1 L r C c R s1 R m C c + L r ( 20) ω sc 4R s1 2R ( + m ) R s1 L r C c R s1 Rm C c L r 2R s1 L r C c ( 21)

30 SLIDE # 30 The simplified time domain equation for short-circuit current (19) doesn't have same form as the corresponding equation in [2] Note that the equation given for the short-circuit current in [2] has a different form than (19). ( ) It AI t k t ( ) p exp ( 22) τ An equation of this form cannot be produced by an RLC circuit. It is only an approximation, and doesn't account for the undershoot.

31 SLIDE # 31 Determine when the peak of the short-circuit current occurs Find the time when the short-circuit current reaches its peak value by setting the time derivative of (19) equal to zero and solving for t. d dt t V dc exp τ sc L r ω sc ( ) sin ω sc t 2 2 V dc 1 + τ sc ωsc exp L r τ sc ω sc t τ sc ( 23) 1 cos ω sc t + atan τ sc ω 0 sc (Simplification steps are not shown.) t scp atan( τ sc ω sc ) ω sc ( 24) τ sc and ω sc are defined in (20) and (21).

32 SLIDE # 32 Find the peak value of the short-circuit current Write an equation for the peak value of the short-circuit current by substituting (24) into (19). V dc τ sc exp I p Lr 1 + τsc ( ) atan τ sc ω sc τ sc ω sc 2 ωsc 2 ( 25 )

33 SLIDE # 33 Find the peak undershoot of the short-circuit current Inspection of (23) and (24) shows that the first negative peak of the short-circuit current occurs at: t sc_min atan( τ sc ω sc ) + π ω sc ( 26) The value of the first negative peak of the short-circuit current is found by substituting (26) into (19). I sc_min V dc τ sc exp ( ( ) + π ) atan τ sc ω sc τ sc ω sc 2 2 L r 1 + τ sc ωsc ( 27)

34 SLIDE # 34 Define a vector of the unknown variables (component values and initial capacitor voltage) Define a vector of the component values and the initial capacitor voltage. X C c L r R s1 R s2 R m V dc ( 28)

35 SLIDE # 35 Define a function for computing the open-circuit voltage Define a function for computing the open-circuit voltage using (11)-(13). V oc ( X, t) := C c X 0 L r X 1 R s1 X 2 R s2 X 3 R m X 4 V dc X 5 ( ) 2 ( ) A R s1 Rs2 + R m C c 2R s1 R s2 + R m + 4R s1 L 2 r C c + L r R s1 L r C c τ 1 A 2R s1 L r C c τ 2 C c R s1 ( R s2 + R m ) + L r A t R s2 τ 1 V dc τ 1 1 e L r t τ 2 e ( 29)

36 SLIDE # 36 Define a function for computing the peak open-circuit voltage Define a function for computing the peak open-circuit voltage using (12), 13), and (17). V p ( X) := C c X 0 L r X 1 R s1 X 2 R s2 X 3 R m X 4 V dc X 5 ( ) 2 ( ) A R s1 Rs2 + R m C c 2R s1 R s2 + R m + 4R s1 L 2 r C c + L r R s1 L r C c τ 1 A 2R s1 L r C c τ 2 C c R s1 ( R s2 + R m ) + L r A τ 1 + τ 2 ( 30) R s2 V dc τ L 2 r τ 1 τ 1 + τ 2 τ 2

37 SLIDE # 37 Define a function for computing the short-circuit current Define a function for computing the short-circuit current using (19)-(21). I sc ( X, t) := C c X 0 L r X 1 R s1 X 2 R s2 X 3 R m X 4 V dc X 5 τ sc 2R s1 L r C c R s1 R m C c + L r ( 31) ω sc ( ) R s1 4R s1 + 2R m L r C c R s1 Rm C c L r 2R s1 L r C c t V dc exp τ sc L r ω sc sin( ω sc t)

38 SLIDE # 38 Define a function for computing the peak short-circuit current Define a function for computing the peak value of the short-circuit current using (25). I p ( X) := C c X 0 L r X 1 R s1 X 2 R s2 X 3 R m X 4 V dc X 5 τ sc 2R s1 L r C c R s1 R m C c + L r ( 32) ω sc V dc τ sc ( ) R s1 4R s1 + 2R m exp ( ) atan τ sc ω sc τ sc ω sc 2 2 L r 1 + τ sc ωsc L r C c R s1 Rm C c L r 2R s1 L r C c

39 SLIDE # 39 Define a function for the peak undershoot of the short-circuit current Define a function for computing the value of the first negative peak of the short-circuit current using (27). I min_sc ( X) := C c X 0 L r X 1 R s1 X 2 R s2 X 3 R m X 4 V dc X 5 τ sc 2R s1 L r C c R s1 R m C c + L r ( 33) ω sc V dc τ sc exp ( ) R s1 4R s1 + 2R m atan τ sc ω sc τ sc ω sc L r C c R s1 Rm C c L r 2R s1 L r C c ( ( ) + π ) 2 2 L r 1 + τ sc ωsc

40 SLIDE # 40 Define a function for to determine when the open-circuit voltage reaches a specified percentage of the peak value Define a function for computing the time at which the open-circuit voltage reaches a specified percentage of the peak value. The initial time value of the solve block can be used to get the function to find values before or after the peak. Given V oc ( X, t ) V p ( X) t10 7 > 0 P 100 ( 34) T oc ( X, P, t) := Find() t

41 SLIDE # 41 Define a function for to determine when the short-circuit current reaches a specified percentage of the peak value Define a function for computing the time at which the short-circuit current reaches a specified percentage of the peak value. The initial time value of the solve block can be used to get the function to find values before or after the peak. Given I sc ( X, t) I p ( X) P 100 t10 7 > 0 ( 35) T sc ( X, P, t) := Find() t

42 SLIDE # 42 Enter the target performance specifications Enter the target peak open-circuit voltage: V peak := 1000 Enter the target 10%-90% rise time for the open-circuit voltage: t ocr := Enter the target 50%-50% duration time for the open-circuit voltage: t ocd := Enter the target 10%-90% rise time for the short-circuit current: t scr := Enter the target 50%-50% duration time for the short-circuit current: t scd := Enter the target percent undershoot for the short-circuit current: P scu := 25

43 SLIDE # 43 Enter initial guess values Enter initial guess values for the components and the initial capacitor voltage. C c := L r := R s1 := 10 R s2 := 10 R m := 1 V dc := 1100 Define a vector of the initial guess values. X := C c L r R s1 R s2 R m V dc

44 SLIDE # 44 Compute the waveform parameters using the initial guesses and compare the results with the target values Compute the 50%-50% duration time for the open-circuit voltage. ( ) T 9 6 oc ( X, 50, ) = T 6 oc X, 50, 5 10 Target value t ocd = Compute the peak value of the short-circuit current. I p ( X) = 560 V peak Target value: I peak := I 2 peak = 500

45 SLIDE # 45 Compute the 10%-90% rise time for the short-circuit current. ( ) T sc ( X, 10, ) T sc X, 90, = Target value t scr = Compute the 50%-50% duration time for the short-circuit current. ( ) T sc ( X, 50, ) T sc X, 50, = Target value t scd = Compute the percent undershoot for the short-circuit current. I min_sc ( X) I p ( X) 100 = 14 Target value P scu = 25

46 SLIDE # 46 Enter weighting factors for each of the target values The weighting factors help guide the solution to the desired outcome. Enter the weighting factor for V peak. K Vp := 1 Enter the weighting factor for t ocr. K ocr := 1 Enter the weighting factor for t ocd K ocd := 1 Enter the weighting factor for I peak. K Ip := 1 Enter the weighting factor for t scr. K scr := 20 Enter the weighting factor for t scd K scd := 20 Enter the weighting factor for P scu K scu := 5

47 SLIDE # 47 Define a solve block to find the component values and the initial capacitor voltage Given V p ( X) V peak K Vp I p ( X) K Vp K I Ip K Ip ( 36) peak ( ) T oc ( X, 10, ) T oc X, 90, t ocr K ocr K ocr ( ) T oc ( X, 50, ) T oc X, 50, t ocd K ocd K ocd

48 SLIDE # 48 ( ) T sc ( X, 10, ) T sc X, 90, t scr K scr K scr ( ) T 6 sc ( X, 50, 3 10 ) T 6 sc X, 50, t scd K scd K scd I min_sc ( X) I p ( X) 100 P scu K scu < K scu

49 ( ) T sc ( X, 10, ) T sc X, 90, t scr K scr K scr SLIDE # 49 ( ) T sc ( X, 50, ) T sc X, 50, t scd K scd K scd I min_sc ( X) I p( X) 100 P scu K scu < K scu X := Minerr( X) C c L r R s1 R s2 R m V dc := X

50 SLIDE # 50 The solve block finds the component values and the initial capacitor voltage that minimize the error in the solve block equations Computed component values and initial capacitor voltage C c = L r = R s1 = R s2 = R m = V dc = 1082

51 SLIDE # 51 Compute the waveform parameters using the solve block outputs and compare the results with the target values Compute the peak value of the open-circuit voltage. Target value: V p ( X) = 1000 V peak = 1000 Compute the 10%-90% rise time for the open-circuit voltage. ( ) T oc ( X, 10, ) T oc X, 90, = Target value t ocr =

52 SLIDE # 52 Compute the 50%-50% duration time for the open-circuit voltage. ( ) ( T oc X, 50, ) T oc X, 50, = Target value t ocd = Compute the peak value of the short-circuit current. I p ( X) = 500 Target value: I peak = 500

53 SLIDE # 53 Compute the 10%-90% rise time for the short-circuit current. ( ) ( T sc X, 10, ) T sc X, 90, = Target value t scr = Percent error ( ) ( T sc X, 10, ) T sc X, 90, t scr 100 = 4.3 t scr

54 SLIDE # 54 Compute the 50%-50% duration time for the short-circuit current. ( ) T sc ( X, 50, ) T sc X, 50, = Target value t scd = Percent error ( ) T sc ( X, 50, ) T sc X, 50, t scd t scd 100 = 4.0 Compute the percent undershoot for the short-circuit current. I min_sc ( X) I p ( X) 100 = 27.7 Target value 30%

55 SLIDE # 55 Compute the ratio of the initial capacitor voltage to the peak open-circuit voltage. V dc V p ( X) = 1.08 Compute τ 1, τ 2, τ sc and ω sc. R s1 L r C c τ 1 := τ 1 = R s1 ( Rs2 + R m ) C c 2R s1 ( R s2 + R m ) + 4R s1 L 2 r C c + L r τ 2 := C ( + ) C c R s1 R s2 R m + L r 2R s1 L r C c 2 ( + ) 2 2 C c 2 ( + ) + 4 R s1 2 Rs2 R m 2 2 R s1 R s2 R m 4 R s1 L 2 r C c + L r τ 2 = τ sc 2R s1 L r C c := τ R s1 R m C c + L sc = r ω sc 4R s1 2R ( + m ) R s1 L r C c R s1 Rm C c L r := ω 2R s1 L r C sc = c

56 SLIDE # 56 n Set up a range variable for graphing. n := t := n V oc ( X, t n ) I sc ( X, t n ) 0.3 I peak t n Figure 2. Open-circuit voltage and short-circuit current.

57 SLIDE # 57 It appears that it is not possible to exactly meet the specifications using this circuit. The problem is meeting the short-circuit rise and duration times while keeping the current undershoot less than 30%. The errors in the current timing parameters are less than 5% when using the calculated component values. Information about the origin of the combination wave test is provided in [3],[6]. An analysis of a surge generator that takes shunt stray capacitance on the output is given in [4]. The US surge standard, which closely follows the international standard, provides additional information [5]. References [1] IEC (2005) Electromagnetic Compatibility: Testing and measurement techniques Surge immunity test. [2] Ronald B. Standler, "Equations for some transient overvoltage test waveforms," IEEE Transactions on Electromagnetic Compatibility, Vol. 30, No. 1, Feb [3] Peter Richman, "Single-output, voltage and current surge generation for testing electronic systems," IEEE International Symposium on Electromagnetic Compatibility, August, 1983, pp [4] Robert Siegert and Osama Mohammed, "Evaluation of a hybrid surge testing generator configuration using computer based simulations," IEEE Southeastcon, March 1999, pp [5] ANSI/IEEE C , "IEEE recommended practice on surge voltages in low-voltage ac power circuits." [6] Ronald B. Standler, Protection of Electronic Circuits from Overvoltages, New York: Wiley-Interscience, May Republished by Dover, December 2002.

58 1.2/50 μs Voltage, 8/20 μs Current Combination Wave Generator SLIDE # 58 PWL(0 10u 10.01u 5) V2.tran 0 100u 0 0.1u.model SWITCH SW(Ron=1m Roff=1Meg Vt=2.5 Vh=-0.5 1k V1 1082V Vc Rc Rm Lr Cc S1 6.04µF µH Rs1 Out_P Rs Out_M

59 1.2/50 μs Voltage Waveform SLIDE # 59 50% 50% duration = 50.4 μs (Target = 50 μs)

60 1.2/50 μs Voltage Waveform SLIDE # 60 10% -90% rise time = 1.05 μs (Target = 1.0 μs)

61 8/20 μs Current Waveform SLIDE # 61 50% -50% duration = 16.7 μs (Target = 16 μs) Undershoot = 27.4% (Target 30%)

62 8/20 μs Current Waveform SLIDE # 62 10% -90% rise time = 6.2 μs (Target = 6.4 μs)

63 8/20 μs CWG with CDN and Power Supply SLIDE # 63 PWL(0 0 {Ts} 0 {Ts u} 5) V2 Combination Wave Generator.model SWITCH SW(Ron=1m Roff=1Meg Vt=2.5 Vh=-0.5.tran ms 37.49ms 0.1u.param Ts = 37.5ms Rc 1k V Vc Cc S1 6.04µF Rs Rm 0.94 Lr 10.4µH Rs Out_P 2 kv Open Circuit Out_M Rectifier, Filter & Load Bus_P Power System Model Series resistance = 0.1 ohm Parallel resistance = 2 ohm Line-line inductance = 100 uh K12 L1 L2 0.5 K23 L2 L3 0.5 K31 L3 L1 0.5 L1 SINE( ) 100µH V3 Conduit Resistance = 75 mohm Line-conduit inductance = 100 uh L2 100µH L3 100µH Conduit 100 ft 1/2" Steel EMT Coupling/Decoupling Network C3 1µF L4 1.5mH C1 1µF L5 C2 1.5mH 1µF C8 18µF EMI Filter K67 L6 L L6 1mH L7 1mH Ground 3.3nF C4 0.22µF MUR460 D2 D1 MUR460 D1_A C5 C7 470µ 3.3nF Local Ground MUR460 D4 D3 MUR460 ESR = 0.2ohm ESL = 15nH C6 R1 80 Bus_M

64 8/20 μs Combination Waveform SLIDE # 64 Peak Open-circuit voltage = 1 kv

65 8/20 μs Combination Waveform SLIDE # 65 Peak Open-circuit voltage = 2 kv

66 Advanced Energy Industries, Inc. All Rights Reserved. SLIDE # 66