Pulsed Power Techniques and Measurements

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1 Pulsed Power Techniques and Measurements Presenter: Dr Igor Timoshkin 6 th UHVnet Colloquium High Voltage Technologies and Metrology University of Strathclyde, Glasgow 16 th 17 th January 2013

2 Pulsed Power: Principles Slow charge by primary DC power supply Energy stored capacitively in electrical field or inductively in magnetic field Activation of switch releases energy in ns - µs time interval Low average power consumption: 1-10 kw High peak power pulses: MW 2

3 Application of pulsed power technology High power microwave generation Laser systems Relativistic and plasma physics (energy density >10 12 J/m 3 ) High energy density research for new sources of energy: Controllable fusion, 100 ns impulses, over 1MA current Experimental studies of astrophysical phenomena Testing of insulating materials Impulsive testing ti of power equipment Environmental and bio-medical applications 3

4 Plasma closing gas switches Gas-filled plasma closing switches are widely used in pulsed power technology for generation of short high voltage impulses. There is a growing tendency to use environmentally friendly gases such as air, oxygen, nitrogen or their mixtures in such devices instead of the traditional insulating gaseous switching medium, sulphur hexafluoride, due to its high cost and the environmental issues associated with this gas. 4

5 Plasma closing gas switches Self-breakdown gas-filled plasma closing switch Breakdown events between electrodes Switch developed by Samtech Ltd 5

6 Townsend avalanche mechanism E dn dx e = αn N e N e - linear density of electrons, 1/cm N e dx - number of electrons in the layer with thickness dx CATHODE ANODE x, t The ionization frequency can be expressed as a product of Townsend ionization coefficient,α, and the drift velocity. 6

7 Townsend avalanche mechanism Positive ions hit cathode and generate secondary electrons, each ions generates in average γ secondary electrons. γ is secondary ionisation coefficient, typically γ= With an increase in applied potential, V, ionisation coefficients α and γ increases, however the discharge still requires external ionisation source for generation of current I 0. 7

8 δ = γ ( e α d 1) is coefficient of regeneration δ shows how many electrons generated on the cathode due to passage of one electron emitted from the cathode Townsend criterion : δ = 1 Ignition potential, V T T,, (breakdown voltage) and corresponding field, E T, can be determined from the Townsend criterion. For uniform fields they V T is a function of p d only V T (p d), p - gas pressure ; d inter-electrode electrode distance. This is Paschen s Law 8

9 Paschen s s curve for air 10 Breakdown vo oltage, kv 1 High pressure spark gaps 0, Dp, μm*atm 9

10 Streamers Streamer thin ionised channel which may develop through a positively charged trace of a primary avalanche Secondary avalanches are attracted to the trace 10

11 Avalanche to streamer transition If charge concentration exceeds 10 8, then field due to avalanche head become approximately equal to the background field. N 0 exp(αx c ) ~10 8 or αx c = αd where x c is the critical avalanche length to form streamers. 11

12 Streamer to spark transition Streamer is a cold discharge (room temperature), weakly conductive and short lived. When streamer bridges an inter-electrode gap, the ionisation wave propagates through the streamer with velocity 10 9 cm/s. The streamer channel becomes thermalised and conductive, high current flows through the channel. The spark channel is formed. 12

13 Volt-time time characteristics of air 10 3 ns.atm τp, Formative time only 10-2 Statistical + Formative time Fletcher (1949) Felsenthal and Proud (1965) Kinetic equation Mankowski et.al., Experime 1atm 38atm 3.8atm 7.9atm 27.5atm 41.5atm 52atm Mankowski's equatio Corrected Mankowsk Reduced field E/p, kv/cm/atm 13

14 Field distortion gas switch Dielectric body of the switch HV electrode Insulating gas Trigger ring electrode Ground electrode 14

15 Multi-stage Marx generators Capacitors are charges in parallel, Charging voltage: U 0 Total charging capacitance C t =C+C+ +C (n capacitors) Then the circuit is re-configured (by triggering parallel spark gaps) and capacitors are discharged in series Total discharging capacitance: 1/C t =1/C+1/C+ 1/C Output voltage: V out =V 0 +V 0 +.V 0 (voltage multiplication by a factor of n) 15

16 Multi-stage Marx generators R R R Inverting topology DC SG SG SG C C C R R Non-inverting topology R R DC SG SG SG C C C R R R 16

17 Practical compact Marx generator Samtech Ltd 17

18 Marx Generator Model Single stage pulsed power system (capacitive energy storage) Charging resistor C Capacitor bank L Transmission cable DC power supply Gas switch HV probe I(t) Load R(t) Trigger unit Current shunt 2 d I dt + 1 L ( IR) d dt + 1 LC = 0 18

19 Marx Generator Model R M C M R L C L Marx generator Load 19

20 Marx Generator Model Z M 1 = 1+ scm R s C M ( ) M R M V L () s = V s Z L Z L + Z M C M R L C L V L V L V k 1 + a s + b () s =, k, a, b are coefficients, f ( C, R, C R ) V k s 2 1 α α ( t ) = ( ( α t ) exp ( α t ) ) 2 1 exp 1 2 M M L L α 2 2 and α1 are roots of the equation s + a s + b = 0 20

21 Marx generator model V Double exponential impulse α = 1 1 α 2 = 1 R R L M C M C L t < α V 1 L T RISE is small, hence exp ( α 1t ) ( t < T ) = ( 1 exp ( α t )) RISE 2 1, and T rise t t > α V 1 L T RISE << α 2, hence 1 exp ( α 2t ) << 1 exp ( α 1t ) ( t > T ) = exp ( α t ) RISE 1, and These equations are valid for C M >>C L and R L >>R M only 21

22 Resonance charging of capacitors The resonant charging of two capacitors: the voltage across capacitor C 2 is V 2 =2V 1 C 1 /(C 1 +C 2 ) To achieve the maximal possible voltage gain of 2, the capacitance C 1 should be much higher than C 2. Therefore, to achieve the maximal resonant increase of the voltage across the load, the erected capacitance should be significantly higher than the load capacitance, a ce, C MARX >> C L. Switch L C1 C2 22

23 Pulse forming line (PFL) R L =Z 0 V 0 Charging resistor Load Switch DC supply V 0 Z charge >>Z 0 Z load =Z 0 Reflection coefficient Γ=1 Reflection coefficient Γ =0 Switch 1/2V 0 Closes Voltage across the load is 1/2V 0 due to voltage division Γ=1 1 Γ=0 0 23

24 Pulse wave shapes Charging resistor Load R L =Z 0 Switch DC supply Z charge >>Z 0 Z load =Z 0 Reflection coefficient Γ=1 Reflection coefficient Γ =0 1/2V Reflect wave from the generator side 0 travels towards the load Γ=1 1 Γ=0 0 Voltage across the load is 1/2V 0, when this wave reaches the load, the voltage becomes 0 V 24

25 Pulse wave shapes R L =Z 0 Pulse duration is 2T Magnitude is 1/2V o V L Charging resistor Load 1/2V 0 Switch DC supply 0 2T 25

26 Pulse wave shapes R L <Z 0 R L >Z 0 1/2V 0 V L 2T 4T 6T 1/2V 0 1/2V 0 2T 4T 6T 26

27 Spiral voltage-inversion generators When the switch is closed, the travelling wave in the active stripline inverts the electric field vector in this part of the spiral generator. The field vector in the passive, slow part of the generator still has its original direction. Therefore, the field vectors in both lines become coaligned agedradially. aday The output voltage across the load is 2NV 0, where N is the number of turns of the spiral generator This rise-time of the output voltage is governed by the switch inductance, L s, and the characteristic impedance of the stripline, Z 0 : τ s = L s /Z 0. 27

28 Spiral voltage-inversion generators Output voltage V out = - 2NV 0 Rise time of the signal T=L/v where v=1/(µε) 1/2 28

29 Pulse forming line (PFL) Direct polarity Charging resistor Load Switch DC supply 29

30 Pulse forming line (PFL) Reverse polarity Charging resistor Load Switch DC supply 30

31 Blumlein generator Blumlein pulsed forming line (PFL) Z left side = 0 (when switch is closed) Γ= -1 V0 Z0 Load, 2Z0 Z0 V0 Z charge >>Z 0 Switch Z load =2Z 0 Γ=1/2 Γ=1 31

32 Blumlein PFL: Wave-forms Voltage drop across the load is zero, V L = V 0 -V 0 = 0 V 0 Switch is closed Load End 32

33 Blumlein PFL: Wave-forms Coefficient of reflection at load is Γ= ½ V 0 1/2V 0 Load End 1/2V 0 33

34 Blumlein PFL: Wave-forms Waves reflected from both sides of the Blumlein PFL travels towards the load. Magnitude of voltage across the load, V L =V 0 V L V 0 1/2V 0 Load End 1/2V 0 0 2T 34

35 Spiral voltage-inversion generators Slow (passive) line Fast (active) line 35

36 Spiral voltage-inversion generators After switch closure the wave starts to propagate along the fast, active line 36

37 Spiral voltage-inversion generators The wave continue to propagate towards the load, reflects from the load and returns back to the switch 37

38 Magnetic compression circuit Consists of LC cells with saturable inductances HV impulse becomes compressed in time due to difference in energy transfer time for each cell L 0 L 1 C 0 C 1 C 2 R L 38

39 Magnetic compression circuit When the ferromagnetic core becomes saturated its permeability, μ r, drops from its maximum value to 1. It means that cell s inductance also reduces sharply. 39

40 Magnetic compression circuit Charging capacitor C 1 : L 0 L 1 V C 0 () t = V ( 1 ωt) 1 0 cos C0 + C1 C 0 C 1 C 0 1 C 2 R L * 2C 1 = max 0, π C0 + C1 ( ) 0 * 0 1 t )= V t = π L Maximum voltage : V = 0 C C C + C 0 1 During this charging process, L 1 is very high, so the voltage across C 2, is zero. 40

41 Magnetic compression circuit When C 1 is fully charged (V 1 is maximum), the core of second inductor becomes saturated and L 2 suddenly decreases Energy accumulated in C 1 is transferred into C 2 C Maximum voltage : V2 max 1, = C + C The compression ratio is t * /t ** C C ( ** 1 ** 1 21 t ) = V t = π L = π C 1 + C 2 The voltage gain is V 2 /V 1 =2C 1 /(C 1 +C 2 ) 41

42 Cockroft- Walton generator Negative ½ wave V AC V 0 I + 0 V 42

43 Cockroft- Walton generator Positive ½ wave V AC V 0 I - 2V 0 43

44 Diagnostics and Measurements High Voltage Dividers Magnitude response or division ratio of the divider: V out / V in Frequency response must sufficient to monitor high speed UH impulses with fast rise time (high dv/dt) 44

45 Response of the divider Input signal v i (t) = Vi SS u(t) Vi SS -amplitude of input step (steady-state) y u(t) - unit step function, u(t)=1 Output signal v o (t) = Vo SS s(t) Vo SS - amplitude of output signal (steady-state) s(t) - normalised step response of the divider 45

46 Response to the step voltage 1 st order transfer function in Laplace domain ( ) 1/ G(s) v(s) ( ) u(s)=1/s Response in time domain v t ( t) k u( t) exp = T res 46

47 Response to the step voltage Long response time: Short response time: t T, exp res hence 1 Tres v ( t) = k[ u( t) 1 ] = k[ 1 1] = 0 and T res t 0, hence exp T 0 res and () t = k[ u() t 0] k u() t v = 47

48 Resistive dividers High voltage Response time of V the resistive divider in arm C e capacitance to earth R 1 and R 2 are resistances of HV and low voltage arms respectively; 1/2R 1 // 1/2R 1 =1/4R 1 1/3 C e 1/3 C e ½ R 1 ½ R 1 2/3C e R 2 1/3 C e Low voltage V out T res =1/4R 1.2/3C e =1/6R 1 C e arm 48

49 Resistive dividers Example 20 pf/m, 1 MV divider 3 m high R 1 =10 kω T res =100 ns 49

50 Resistive dividers: termination Generally, the signal cable is matched at the oscilloscope input to prevent reflections in the signal cable. R 1 Z 0 HV divider R 2 R T Scope Z 0 = R T 50

51 Aqueous CuSO 4 high voltage divider HV arm comprises majority of the PVC tube length. LV arm is made using a pick-up plane (small electrode) situated in the PVC tube at a short distance (a few mm) above the ground plane. Output t from the LV arm passes through the ground plane terminal in a co-axial configuration. Transient voltages, High power Low inductance phosphor bronze HV connector PVC tube CuSO 4 solution (1-2 kω) acrylic support pick up plane earth plane cable matching resistor BNC connector 51

52 Capacitive dividers Division ratio: C 1 /(C 2 + C 1 ) Reduction of oscillations: R D =(L/C e ) 1/4 L R D C 1 C e R T Z 0 C 2 Z 0 = R T <<Z scope Scope 52

53 Coaxial current shunt V m (t) = R m i(t) ) + L di/dt, where L = inductance of the shunt I(t) I(t) () I(t) Nichrome wires Nichrome wires B(t) B(t)=0 Coaxial cable: Signal to scope B(t) Copper tubular body Resistance of Nichrome wires is 10 s mω 53

54 Rogowski coil and current transformer B=µ 0 NI/l B(t) I(t) l B=µ 0 NI/2πR I(t) R 54

55 Rogowski coil and Current transformer Flux: Φ=B.A B(t) M - mutual inductance, A area of each turn A M A M= Φ/I=µ 0 NIA/l, Φ=µ 0 NIA/2πR M v coil (t) = - dφ/dt = -M.dI/dt I () t = 1 vcoil ()dt t M 55

56 Current transformer If R+r << Lω (R is external resistance, no integration circuit, r is internal resistance of the coil) dφ dt = L di dt and I () t = Φ L = I N V ( t) = IR = I R N The coil gives direct measure of the current (coil operates as a current transformer) 56

57 D-dot probes Conical/hemispherical sensor E(t) I () t = dq( t) dd( t) de( t) = Aeff = Aeff ε 0 ε r dt dt dt I(t) Q(t)=D.A eff V(t)=I(t).Z 0 Z 0 57

58 D-dot sensors: Flush plate Flush plate sensor in plane-plane topology V s (t) A = 2 eff πr E(t) = V s /d A eff E s (t)=v s (t)/d V 0 () t I() t = Z0 = Aeff ε 0ε r Z0 des dt ( t) I(t) Dielectric V S ( t ) = k V ( t ) 0 dt where k = A eff d ε ε Z 0 r 0 Z 0 V 0 (t)=i(t).z 0 58

59 Ground plane D-dot sensors: Conical and flush plate close up view of flush plate sensor A eff conical sensor Dielectric Ground plane ( 59

60 Plasma channel drill Spark discharges are formed repetitively inside the rock Fragmentation of rock by plasma channels results in effective drilling of narrow holes Applications to cutting side-tracks and multilateral drilling to increase oil production S.J. MacGregor, S. Turnbull, Plasma channel drilling process, US patent US , I. Timoshkin, J. Makersie, S. MacGregor, Plasma channel miniature hole drilling technology, IEEE Transactions on Plasma Science, Vol. 32, No. 5, 2004, p

61 Spark discharge processing of brittle solids Wilson, M.P. and Balmer, L. and Given, M.J. and MacGregor, S.J. and Timoshkin, I.V., An investigation of spark discharge parameters for material processing with high power ultrasound, Minerals Engineering, 20 (12). 2007, pp

Pulsed Electric Field Bio-action For a plane membrane placed in a water a charge polarisation density is produced at

Thus the electro-mechanical forces exerted on both sides of the membrane are equal but act in opposite directions

The forces compress and stretch the membrane and may form a pore but do not result in any translational movement. I.

62 Pulsed Electric Field Bio-action For a plane membrane placed in a water a charge polarisation density is produced at the two interfaces. The charge on the two surfaces is of the same magnitude but opposite sign. Thus the electro-mechanical forces exerted on both sides of the membrane are equal but act in opposite directions balanced. The forces compress and stretch the membrane and may form a pore but do not result in any translational movement. I. Timoshkin, SJ S.J. MacGregor, R.A. Fouracre, BHCi B.H Crichton, JGA J.G Anderson, Transient electrical field across cellular membranes - pulsed electric field treatment of microbial cells, Journal of Physics D: Applied Physics, 39 (1). 2006, pp

63 Impulsive corona precipitation of fine and ultra-fine particles Airborne fine particles generated by internal combustion engines, power plants and other industrial and domestic sources pose a potential health risk. Particles of size less than 2.5 um (PM2.5) can stay airborne for long periods of time and can penetrate deep into the lungs. Effective management of PM2.5 particles is required A. Mermigkas, I. Timoshkin, S. Macgregor, M. Given, M. Wilson, T. Wang, Superposition of DC Voltage and Submicrosecond Impulses for Energization of Electrostatic Precipitators, IEEE Trans Plasma Science, v.40, n.10, 2012, pp

64 64

Code No: RR Set No. 1

Code No: RR Set No. 1 Code No: RR410209 Set No. 1 1. What are the gases mainly used in insulating medium at high pressures? Which is more suitable? Why? What about its dielectric strength? Explain. [16] 2. (a) Define time lags