WO2002045197A2 - Direct-current power supply device comprising a number of series-connected fuel cell blocks - Google Patents

Direct-current power supply device comprising a number of series-connected fuel cell blocks Download PDF

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Publication number
WO2002045197A2
WO2002045197A2 PCT/DE2001/004391 DE0104391W WO0245197A2 WO 2002045197 A2 WO2002045197 A2 WO 2002045197A2 DE 0104391 W DE0104391 W DE 0104391W WO 0245197 A2 WO0245197 A2 WO 0245197A2
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WO
WIPO (PCT)
Prior art keywords
cfl
fuel cell
supply device
power supply
cell blocks
Prior art date
Application number
PCT/DE2001/004391
Other languages
German (de)
French (fr)
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WO2002045197A3 (en
Inventor
Josef Lersch
Arno Mattejat
Original Assignee
Siemens Aktiengesellschaft
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Publication of WO2002045197A2 publication Critical patent/WO2002045197A2/en
Publication of WO2002045197A3 publication Critical patent/WO2002045197A3/en

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Classifications

    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04313—Processes for controlling fuel cells or fuel cell systems characterised by the detection or assessment of variables; characterised by the detection or assessment of failure or abnormal function
    • H01M8/04537—Electric variables
    • H01M8/04544—Voltage
    • H01M8/04559—Voltage of fuel cell stacks
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04223—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids during start-up or shut-down; Depolarisation or activation, e.g. purging; Means for short-circuiting defective fuel cells
    • H01M8/04246—Short circuiting means for defective fuel cells
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04313—Processes for controlling fuel cells or fuel cell systems characterised by the detection or assessment of variables; characterised by the detection or assessment of failure or abnormal function
    • H01M8/04664—Failure or abnormal function
    • H01M8/04671—Failure or abnormal function of the individual fuel cell
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04694—Processes for controlling fuel cells or fuel cell systems characterised by variables to be controlled
    • H01M8/04955—Shut-off or shut-down of fuel cells
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/30—Hydrogen technology
    • Y02E60/50—Fuel cells

Abstract

A fuel cell block (3), which has become highly resistive due to a defect and which is connected in series to other fuel cell blocks (3) in a direct-current power supply device (1), impedes the flow of current from the other fuel cell blocks (3). This results in a drop in output of the direct-current power supply device (1). In order to solve for this problem, the invention provides that a power diode (7) is connected in parallel to each fuel cell block (3). This power diode causes the current from the other fuel cell blocks (3) to bypass the defective fuel cell block (3).

Description

Beschreibungdescription
Gleichstromversorgungseinrichtung mit mehreren seriell angeordneten BrennstoffzellenblockenDC power supply device with several fuel cell blocks arranged in series
Die Erfindung betrifft eine Gleichstromversorgungseinrichtung mit mehreren seriell angeordneten Brennstoffzellenblocken.The invention relates to a direct current supply device with a plurality of fuel cell blocks arranged in series.
Ein Brennstoffzellenblock umfasst eine Vielzahl von Brenn- stoffzellen sowie Einrichtungen zur Versorgung und Überwachung der Brennstoffzellen. Die Brennstoffzellen können röhrenförmig oder als Platten ausgestaltet 'sein. In einer Brennstoffzelle wird durch die Zusammenführung von Wasserstoff (H2) und Sauerstoff (02) in einer elektrochemischen Reaktion elektrische Energie und Wärme erzeugt, wobei sich der Wasserstoff und der Sauerstoff zu Wasser (H20) verbinden. Die Brennstoffzellen eines BrennstoffZellenblocks sind elektrisch in Reihe geschaltet und erzeugen während des Betriebs Gleichstrom. Die Spannung, die ein Brennstoffzellenblock während des Betriebs erzeugen kann, hängt ab von der Anzahl seiner Brennstoffzellen. Durch das serielle anordnen, also das InReihe-Schalten mehrerer BrennstoffZellenblöcke wird die Spannung der Blöcke addiert, so dass auf diese Weise die Gleichstromversorgungseinrichtung eine hohe VersorgungsSpannung er- zielt.A fuel cell block comprises a large number of fuel cells as well as devices for supplying and monitoring the fuel cells. The fuel cells can be designed as a tubular or plates'. In a fuel cell, the combination of hydrogen (H 2 ) and oxygen (0 2 ) in an electrochemical reaction generates electrical energy and heat, the hydrogen and oxygen combining to form water (H 2 0). The fuel cells of a fuel cell block are electrically connected in series and generate direct current during operation. The voltage that a fuel cell block can generate during operation depends on the number of its fuel cells. Arranging them in series, in other words connecting several fuel cell blocks in series, adds the voltage of the blocks, so that the DC power supply device achieves a high supply voltage in this way.
Während des Ablaufs der oben beschriebenen elektrochemischen Reaktion in einem Brennstoffzellenblock ist dieser Brennstoffzellenblock „elektrisch leitfähig* . Bei einer Anzahl von in Reihe geschalteten Brennstoffzellenblocken fließt somit der in einem Brennstoffzellenblock erzeugte elektrische Strom durch die anderen seriell geschalteten BrennstoffZellenblöcke hindurch. Bei einem Defekt eines BrennstoffZellenblocks, durch den die elektrochemische Reaktion innerhalb des Blockes unterbunden wird, weist dieser Block einen gegenüber demDuring the course of the electrochemical reaction described above in a fuel cell block, this fuel cell block is “electrically conductive”. With a number of fuel cell blocks connected in series, the electrical current generated in one fuel cell block thus flows through the other series-connected fuel cell blocks. In the event of a defect in a fuel cell block, which prevents the electrochemical reaction within the block, this block has one opposite
Normalbetrieb erhöhten elektrischen Widerstand auf. Ein solcher Brennstoffzellenblock „behindert* somit den Stromfluß CO 0 t\) P1 P» Normal operation increased electrical resistance. Such a fuel cell block thus “hinders” the flow of electricity CO 0 t \) P 1 P »
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O O O d Φ d rt fr rt φ Q cn Φ Cfl CΛ Φ φ O tr rt P- CΛ Ω d O ι-i P- rt rt rt N cn dO O O d Φ d rt fr rt φ Q cn Φ Cfl CΛ Φ φ O tr rt P- CΛ Ω d O ι-i P- rt rt rt N cn d
3 cn PJ Hi d d H Φ Φ Φ P- cn rt P rt fr d p. d Φ d tr d P N H H Φ d φ P- φ P Hi ιq P- d H d P. d d CΛ rt Φ d P- ιq d Φ cn φ > O O rt φ d U33 cn PJ Hi d d H Φ Φ Φ P- cn rt P rt fr d p. d Φ d tr d P N H H Φ d φ P- φ P Hi ιq P- d H d P. d d CΛ rt Φ d P- ιq d Φ cn φ> O O rt φ d U3
Pi ι-i P N CΛ Ω tr1 Φ φ P- d « d rt P. d ιq φ d H CΛ rt d 3 3 p. P- Φ d P- d Φ φ CΛ tr Φ α ι-i ι-i O *q d * ι-i tr PJ Cfl d l-i CΛ o PJ CSJ Cfl <! < s: Φ d • i H cn φ d P" P- o rt P- φ cn ι-i CΛ O P- Hi <1 φ s: 3 P φ Hl Φ Φ P- d Φ φ X ιq P1 d d n H Φ α N 3 d d: O P- CΛ 3 o P- rt P- PJ ι-i ι-i i-i cn cn φ cn Φ ι-i ^ d rt O Φ d P- cn P- Hi H H d P- rt P- P. rt rt - cn cn P. d= Φ P- φ d d P- PJ >q d cn H O Ω O P" N ι H CΛ O: rt φ ιq ~* -• O O . tr H cnPi ι-i PN CΛ Ω tr 1 Φ φ P- d «d rt P. d ιq φ d H CΛ rt d 3 3 p. P- Φ d P- d Φ φ CΛ tr Φ α ι-i ι-i O * qd * ι-i tr PJ Cfl d li CΛ o PJ CSJ Cfl <! <s: Φ d • i H cn φ d P "P- o rt P- φ cn ι-i CΛ O P- Hi <1 φ s: 3 P φ Hl Φ Φ P- d Φ φ X ιq P 1 ddn H Φ α N 3 dd: O P- CΛ 3 o P- rt P- PJ ι-i ι-i ii cn cn φ cn Φ ι-i ^ d rt O Φ d P- cn P- Hi HH d P- rt P- P. rt rt - cn cn P. d = Φ P- φ dd P- PJ> qd cn HO Ω OP "N ι H CΛ O: rt φ ιq ~ * - • OO. tr H cn
3 PJ φ tr Ω d d rt α tr P. d . d PJ φ p- rt H ι-i N Φ H ι-i H Φ < φ d rt tr d tr ιq Φ Φ < d Φ Φ CΛ d cn Ω PJ α d tr P- φ ιq sQ α P- ι-i Φ3 PJ φ tr Ω d d rt α tr P. d. d PJ φ p- rt H ι-i N Φ H ι-i H Φ <φ d rt tr d tr ιq Φ Φ <d Φ Φ CΛ d cn Ω PJ α d tr P- φ ιq sQ α P- ι- i Φ
O ιq N O: rt φ cn P- P- Φ H d d d CΛ d: Cfl Φ tr P. d φ Φ l-i PJ d P- d d d ^q 1 d -- φ Φ Ω d P P- P. Ω P- Ω £π Φ tr ιq tr rt p- Hi H P- d d d i-i φ P- Cd 3 φ O cn fT d P- CΛ p- tr cn t J X ' cn Φ Φ Φ d φ P>: d CΛ rt P, φ ιq vq Ω d d l-i HiO ιq NO: rt φ cn P- P- Φ H ddd CΛ d: Cfl Φ tr P. d φ Φ li PJ d P- ddd ^ q 1 d - φ Φ Ω d P P- P. Ω P- Ω £ π Φ tr ιq tr rt p- Hi H P- ddd ii φ P- Cd 3 φ O cn fT d P- CΛ p- tr cn t JX ' cn Φ Φ Φ d φ P>: d CΛ rt P, φ ιq vq Ω dd li Hi
P- li Φ ιq φ Ό o cn X rt d O P- H PJ d d > Φ rt Φ - φ Cfl cn ω tr Φ PJP- li Φ ιq φ Ό o cn X rt d O P- HP J dd> Φ rt Φ - φ Cfl cn ω tr Φ PJ
Ω ) P- P. rt P- d CΛ P. ι-i p. s: φ ιq cn d fl ι-i d l-i φ Φ fl to d cn tr d tr fr tr φ φ ι-i ι-i d P- ^q Φ α d J ιq p- P1 P- Hi o • P- P- p- P. n φ d cn cn φ cn d φ φ P1 O ιq Φ φ l-i H Ω rt Cfl PJ Φ ιq - cn 3 α tr d d P- Φ P- CΛ rt rt rt P- H p. I-i cn φ 3 Cfl P. Ω 4 ^ rt d P- fr PJ P-" < σ PJ H ι-i H φ d 4 rt ι-i φ d N P- Cfl -s ι-i <! P- - φ Φ d P4 Φ . Hi Ω φ sQ Φ Φ P- cn Φ P- P- CΛ d φ O P.Ω ) P- P. rt P- d CΛ P. ι-i p. s: φ ιq cn d fl ι-id li φ Φ fl to d cn tr d tr fr tr tr φ φ ι-i ι-id P- ^ q Φ α d J ιq p- P 1 P- Hi o • P- P- p- P. n φ d cn cn φ cn d φ φ P 1 O ιq Φ φ li H Ω rt Cfl PJ Φ ιq - cn 3 α tr dd P- Φ P- CΛ rt rt rt P- H p. Ii cn φ 3 Cfl P. Ω 4 ^ rt d P- for PJ P- "<σ PJ H ι-i H φ d 4 rt ι-i φ d N P- Cfl -s ι-i <! P- - φ Φ d P 4 Φ. Hi Ω φ sQ Φ Φ P- cn Φ P- P- CΛ d φ O P.
O fr Hi d o Φ ι-i φ d P- σ H P- H P P. " tr P- φ P- ι-i φ H Ω Ω φ cn Hi P-O for Hi d o Φ ι-i φ d P- σ H P- H P P. "tr P- φ P- ι-i φ H Ω Ω φ cn Hi P-
3 tr1 Φ ι-i ιq H P- Φ ι-i H O Φ rt d Ω P- P- σ CΛ rt Ω cn to tr tr cn rt ι Hi Φ d φ d P- rt ιq cn P- cn Ω α H Φ Φ P4 P- Φ P- P. rt φ tr O cn Φ to rt rt O Φ N ) 3 tr 1 Φ ι-i ιq H P- Φ ι-i HO Φ rt d Ω P- P- σ CΛ rt Ω cn to tr tr cn rt ι Hi Φ d φ d P- rt ιq cn P- cn Ω α H Φ Φ P 4 P- Φ P- P. rt φ tr O cn Φ to rt rt O Φ N )
Φ P- cn d Φ Ω O p- Φ s: rt φ α Φ P- H tr P- CΛ i-i cn H d d <! Hi Cfl Φ rt cn rt P. d tr H d PJ • CΛ P. P- d1 φ O φ d rt sQ φ Φ Φ d d φ Hi Ω → →Φ P- cn d Φ Ω O p- Φ s: rt φ α Φ P- H tr P- CΛ ii cn H dd <! Hi Cfl Φ rt cn rt P. d tr H d PJ • CΛ P. P- d 1 φ O φ d rt sQ φ Φ Φ dd φ Hi Ω → →
N rt w P- d ιq P) rt ιq Φ Ω rt P- ö Φ φ α 3 rt φ H d P- i-i P ιq tq H N tr P-" Φ d P- Q ι-i cn d • d P- Hl tr ö ι-i φ P- cn p- tr N < H l-i O d Ω < d Hi Φ J φ P-N rt w P- d ιq P ) rt ιq Φ Ω rt P- ö Φ φ α 3 rt φ H d P- ii P ιq tq HN tr P- "Φ d P- Q ι-i cn d • d P- Hl tr ö ι-i φ P- cn p- tr N <H li O d Ω <d Hi Φ J φ P-
P- d d Ω cn d d H d d O o cn Φ d Φ P- 3 sQ tr Φ CΛ s: X PJ P- d Ω d ιq CD d tr Ό CD H ^q CD C: d ι-i 3 c P- rt H l-i i φ tr d cn 3 rt PJ: P- tr P-1 rt tr tr n d J P- cn CΛ tr ιq Ω d tr φ φ d s: cn tr o Φ Φ rt O O tr l-i ι-i φ Φ P1 cn d p. N rt Φ d d rt φ N N cn tr d Φ P cn d PJ cj O φ tr rt P- i-i Hi ^ P. Φ d rt O rtP- dd Ω cn dd H dd O o cn Φ d Φ P- 3 sQ tr Φ CΛ s: X PJ P- d Ω d ιq CD d tr Ό CD H ^ q CD C: d ι-i 3 c P- rt H li i φ tr d cn 3 rt PJ: P- tr P- 1 rt tr tr nd J P- cn CΛ tr ιq Ω d tr φ φ ds: cn tr o Φ Φ rt OO tr li ι-i φ Φ P 1 cn d p. N rt Φ dd rt φ NN cn tr d Φ P cn d PJ cj O φ tr rt P- ii Hi ^ P. Φ d rt O rt
P- P- d Φ P- d P- d Φ φ rt H Ω *q Ω tr ^ d Φ N d O d Hi φ P tr Φ Ω HP- P- d Φ P- d P- d Φ φ rt H Ω * q Ω tr ^ d Φ N d O d Hi φ P tr Φ Ω H
Ω O H d d cn P. d P- p- Φ Φ -> tr cn tr Φ sQ d Φ Φ 3 N d P. P" d fr O tr P. p. φ d P- H PJ rt d P- ι-i J α P- P. d H d s: CΛ CΛ < Φ P. p- N O: ••* 3 rt φ Φ P. P ιq φ φ P- P- ι-i d tr Ω Φ Φ p- d s: d φ tu φ P- P- φ d Ω Cd <! d P- P- Ω P" ιq P- Φ l-i tr H tr O ιq PJ ιq H Φ tr Φ H d P" P- 3 fr H φΩ OH dd cn P. d P- p- Φ Φ -> tr cn tr Φ sQ d Φ Φ 3 N d P. P "d fr O tr P. p. Φ d P- H PJ rt d P- ι- i J α P- P. d H ds: CΛ CΛ <Φ P. p- NO: •• * 3 rt φ Φ P. P ιq φ φ P- P- ι-id tr Ω Φ Φ p- ds: d φ tu φ P- P- φ d Ω Cd <! d P- P- Ω P "ιq P- Φ li tr H tr O ιq PJ ιq H Φ tr Φ H d P" P- 3 for H φ
< Φ σ P. Ω Q tr Φ Ω Φ d rt cn Ω ω P. rt Φ Cfl Φ tr CΛ φ Φ Φ H<Φ σ P. Ω Q tr Φ Ω Φ d rt cn Ω ω P. rt Φ Cfl Φ tr CΛ φ Φ Φ H
Φ φ Cd Φ φ tr i→i : rt d Φ tr CF Ω P CΛ Φ Φ tr φ φ ι-i H Φ O Cfl d l-i "P td d d n cnΦ φ Cd Φ φ tr i → i: rt d Φ tr CF Ω P CΛ Φ Φ tr φ φ ι-i H Φ O Cfl d l-i "P td d d n cn
X H t-i CΛ Hi t-i cn Φ d ι-i rt tr tr ιq rt d P- d P- d P- J fr l-i Φ tr Φ PJ φ d O = t Φ •P Φ rt P- d Cfl fr d Φ d cn t-i d d d P Φ d rt ιq rt P1 CΛ d rt cn cn P- ü d P- d PJ fr Q H Ω ιq H J d d φ o ι-i cn ι-i ιq H P. tr ι ι-i d i-i O: d H Φ rt 3 ιqXH ti CΛ Hi ti cn Φ d ι-i rt tr tr ιq rt d P- d P- d P- J fr li Φ tr Φ PJ φ d O = t Φ • P Φ rt P- d Cfl fr d Φ d cn ti ddd P Φ d rt ιq rt P 1 CΛ d rt cn cn P- ü d P- d PJ fr QH Ω ιq HJ dd φ o ι-i cn ι-i ιq H P. tr ι ι-id ii O : d H Φ rt 3 ιq
Cfl P d P rt o tr Φ ti ιq X ιq P- 3 Ω φ P- P- PJ CΛ φ P- d P- Ω Cd d P- l O dCfl P d P rt o tr Φ ti ιq X ιq P- 3 Ω φ P- P- PJ CΛ φ P- d P- Ω Cd d P- l O d
O P. cn d φ g cn cn d ö PJ P Hi * t→ Ω Ω H CΛ N Λ ιq Φ fr Φ d φ P- Hl ^i d tr φ rt d Φ P- p rt φ P rr s: Ω P- H -* tr tr Φ 4 Hl P- O Ω CΛ tr φ rt ιq tr Φ Hi PJ ι rt I-i O P P- Ω Φ H H cn * P- p- P P- d P. Φ rt ι-s rr . o «q tr φ * H P1 N → cn φ rt Hi ιq P tr rt o P- rt ι-i d P Ω tP P- H d d !T Φ Φ p- ιq P- p. φ φ PJ Φ ι-i ^» Hi φ cn N 3 φ O P Φ tr φ d Hl d φ d d d Φ tr φ φ P- φ P-O P. cn d φ g cn cn d ö PJ P Hi * t → Ω Ω H CΛ N Λ ιq Φ fr Φ d φ P- Hl ^ id tr φ rt d Φ P- p rt φ P rr s: Ω P - H - * tr tr Φ 4 Hl P- O Ω CΛ tr φ rt ιq tr Φ Hi PJ ι rt Ii OP P- Ω Φ HH cn * P- p- P P- d P. Φ rt ι-s rr. o «q tr φ * HP 1 N → cn φ rt Hi ιq P tr rt o P- rt ι-id P Ω tP P- H dd! T Φ Φ p- ιq P- p. φ φ P J Φ ι-i ^ »Hi φ cn N 3 φ OP Φ tr φ d H l d φ ddd Φ tr φ φ P- φ P-
N P. CΛ rt <1 P" Hi ι H rt- P. J Q φ ιq l-i l-i d P- tr ι-i P tr P-1 o dN P. CΛ rt <1 P "Hi ι H rt- P. JQ φ ιq li li d P- tr ι-i P tr P- 1 or
P. Φ Φ H PJ Φ P- Hi Φ p- d d S d P- tr ≤ P- O Cfl Φ φ P- Φ Φ iiP. Φ Φ H PJ Φ P- Hi Φ p- d d S d P- tr ≤ P- O Cfl Φ φ P- Φ Φ ii
P- PJ → C P- O P H tN) P- PJ d H φ Hi P- cn Φ Φ Φ Ω g fl l-i d d P- P-P- PJ → C P- O P H tN) P- PJ d H φ Hi P- cn Φ Φ Φ Ω g fl l-i d d P- P-
Ω CΛ P- P4 3 ιq cn PJ Φ P Φ → vQ Ω cn CQ 1 P- P- ι-i p- g PJ N 1 tr d Ω cn φ H 1 φ o d H tr tr l Φ rt d rt 1 1 φΩ CΛ P- P 4 3 ιq cn PJ Φ P Φ → vQ Ω cn CQ 1 P- P- ι-i p- g PJ N 1 tr d Ω cn φ H 1 φ od H tr tr l Φ rt d rt 1 1 φ
1 d d φ tr d φ 1 H 1 1 P- φ d Hi 1 Cfl l1 d d φ tr d φ 1 H 1 1 P- φ d Hi 1 Cfl l
1 H 1 1 1 H 1 1
CO co t-o > P1 P1 cπ o n σ Cπ o cnCO co to> P 1 P 1 cπ on σ Cπ o cn
P. cn tr td N N cn M cn cn rt ω cn sQ α CΛ rt cn cn Φ PJ N Pl ö cn P. vq CΛ X CΛ cn α vq rt d rt φ H d d PJ d O rt Φ rt rt H Φ Ό d PJ o P- d Φ P- d Φ d Φ Φ Φ P- Φ d dP. cn tr td NN cn M cn cn rt ω cn sQ α CΛ rt cn cn Φ PJ N Pl ö cn P. vq CΛ X CΛ cn α vq rt d rt φ H dd P J d O rt Φ rt rt H Φ Ό d P J o P- d Φ P- d Φ d Φ Φ Φ P- Φ dd
H O ii φ Ü Ü Φ H 0 ü ü 0 O: cn CD d Φ li d Hi CD Hi CD H s: Ü P- rt Φ Hl d dH O ii φ Ü Ü Φ H 0 ü ü 0 O: cn CD d Φ li d Hi CD Hi CD H s: Ü P- rt Φ Hl d d
Ω Hi •s d P- ι Hi O Hi öo li ^q P- q φ • PJ X Φ P- Ω d: p- CΛ d P- Φ vq vq tr Hi J d T) Ω O d Hi o 3 Hi rt •P ü cn Ω d Φ cn Φ fr Ω tr d Φ Φ PJ Ω fr cnΩ Hi • sd P- ι Hi O Hi öo li ^ q P- q φ • P J X Φ P- Ω d: p- CΛ d P- Φ vq vq tr Hi J d T) Ω O d Hi o 3 Hi rt • P ü cn Ω d Φ cn Φ for Ω tr d Φ Φ PJ Ω for cn
N Ω cn PJ tr tr H d N P- Hi N Φ PJ CΛ tr d 23 d P- rt tr CΛ rt tr rt φ P. p. Φ tr rt fi Φ cn rt ι Φ Ω φ d ü rt P- cn ιq ü P- tr Φ rt cn • Ω PJ tr P- CΛ p- dN Ω cn PJ tr tr H d N P- Hi N Φ PJ CΛ tr d 23 d P- rt tr CΛ rt tr rt φ P. p. Φ tr rt fi Φ cn rt ι Φ Ω φ d ü rt P- cn ιq ü P- tr Φ rt cn • Ω P J tr P- CΛ p- d
P- φ O PJ H rt Φ cn tr d P" rt J ü o rt cn O: H P1 P- Φ rt p- tr Φ O rt α d HP- φ O PJ H rt Φ cn tr d P "rt J ü o rt cn O: HP 1 P- Φ rt p- tr Φ O rt α d H
Φ d Hi P1 X ii P- φ -> rt EP r→ φ O H φ E P. O: Ω ü φ ü H rt J P- d H Φ Ü ΩΦ d Hi P 1 X ii P- φ -> rt EP r → φ OH φ E P. O: Ω ü φ ü H rt J P- d H Φ Ü Ω
Φ Hi J o P- Φ d ω P- 3 Φ O P- φ Ω tr Φ Ü O P. Φ P Φ O li p- trΦ Hi J o P- Φ d ω P- 3 Φ O P- φ Ω tr Φ Ü O P. Φ P Φ O li p- tr
IS d φ N Φ Ω 3 tr d d d d P1 Φ - g d li PJ ^ CΛ H 3 ii vq PJ d 3 Ω d tr P- Φ P" tr < PJ H tr vq d tr cn p H Φ d φ rt Cd <J Φ Φ σ < Cd tr P. cn P-1 d cn d Φ Hi P- H PJ α Φ φ P- Hi d ii < ti φ P- to O vq φ li rt P-IS d φ N Φ Ω 3 tr dddd P 1 Φ - gd li PJ ^ CΛ H 3 ii vq PJ d 3 Ω d tr P- Φ P "tr <PJ H tr vq d tr cn p H Φ d φ rt Cd < J Φ Φ σ <Cd tr P. cn P- 1 d cn d Φ Hi P- HP J α Φ φ P- Hi d ii <ti φ P- to O vq φ li rt P-
Ω O: φ i-> Ω P li rt Ω O: s: Ω O: P. N d cn rt Ω CΛ o O Φ H d P- H Φ Φ H Φ d φ tr Ω cn Φ tr q cn Φ tr Ω P- tr O d d H N tr Ό P. •P 3 H d cn Φ Ω P. ω H cn P PΩ O: φ i- > Ω P li rt Ω O: s: Ω O: P. N d cn rt Ω CΛ o O Φ H d P- H Φ Φ H Φ d φ tr Ω cn Φ tr q cn Φ tr Ω P- tr O dd HN tr Ό P. • P 3 H d cn Φ Ω P. ω H cn PP
PJ fr d J O H rt fr H fr H Ω Hi »* rt P> P- PJ < rt d O tr P Ω O P vq flPJ for d JOH rt for H for H Ω Hi » * rt P> P- PJ <rt d O tr P Ω OP vq fl
Φ d tr r→ H d Φ fr φ Ω tr d d φ H Φ Φ Cfl ü N rt Φ t cn li cn ii rt d P" rt φ vq > d cn P- d tr Φ P- cn d d PJ H P- rt <q d d rt PJ * vq rt tr φ d d vq O: d ii d d ι d PJ Φ d P- φ O v d cn P1 cn P1 O d CΛ d Φ r→ Φ d O P- P d d φ Ω d P CΛ d 3 <! p. J EP d P" P" o tr Hi d PJ: vq rt P- d Hl P P vq p. X fr ι cn vq q <! tö o Φ ω CΛ rt CΛ cn vq Φ φ H PJ Hi vq rt tr1 Φ Ω vq Hi P. C d: ω φ cn φ O < H ti d li "P φ P- PJ vq Hi N cn N P. Φ rt tr cn INI d rtΦ d tr r → H d Φ fr φ Ω tr dd φ H Φ Φ Cfl ü N rt Φ t cn li cn ii rt d P "rt φ vq> d cn P- d tr Φ P- cn dd PJ H P- rt <qdd rt PJ * vq rt tr φ dd vq O: d ii dd ι d PJ Φ d P- φ O vd cn P 1 cn P 1 O d CΛ d Φ r → Φ d O P- P dd φ Ω d P CΛ d 3 <! P. J EP d P "P" o tr Hi d PJ: vq rt P- d Hl PP vq p. X fr ι cn vq q <! Tö o Φ ω CΛ rt CΛ cn vq Φ φ H PJ Hi vq rt tr 1 Φ Ω vq Hi P. C d: ω φ cn φ O <H ti d li "P φ P- P J vq Hi N cn N P. Φ rt tr cn INI d rt
P. P. P P P. ii Φ cn H cn φ Φ tr Φ ts c_j. Φ PJ Ω d rt Φ Φ P- d P- Φ cn Φ Φ H OP. P. P P P. ii Φ cn H cn φ Φ tr Φ ts c_j. Φ PJ Ω d rt Φ Φ P- d P- Φ cn Φ Φ H O
Φ p- Cfl φ P- P- rt tr O H d Φ 21 d d Φ H tr d tr ts d Φ P- P- ü fl P rt P- P" Ω HiΦ p- Cfl φ P- P- rt tr O H d Φ 21 d d Φ H tr d tr ts d Φ P- P- ü fl P rt P- P "Ω Hi
CΛ φ Ω < CΛ φ d J Φ 3 tr d P- P- d Cfl ü φ vq CΛ d vq li d Ω Ω rt Ü d PJ tr Hi tr o P- ü PJ d P- P- cn cn Ω o rt H φ rt cn cn Φ H tr tr d Cd O H φ vq NCΛ φ Ω <CΛ φ d J Φ 3 tr d P- P- d Cfl ü φ vq CΛ d vq li d Ω Ω rt Ü d P J tr Hi tr o P- ü P J d P- P- cn cn Ω o rt H φ rt cn cn Φ H tr tr d Cd OH φ vq N
•s < rt li Φ P- P- rt vq rt d rt ι Φ rt tr Ω cn H Ω Φ d P- Φ d H 3 P- d Φ Φ • s <rt li Φ P- P- rt vq rt d rt ι Φ rt tr Ω cn H Ω Φ d P- Φ d H 3 P- d Φ Φ
P- φ Φ ι H Ω d rt P. O Φ Ü o J tr N φ Ω O tr P- d tr Ω vq Φ <i Ω tr rt P"P- φ Φ ι H Ω d rt P. O Φ Ü o J tr N φ Ω O tr P- d tr Ω vq Φ <i Ω tr rt P "
P. li P φ Φ PJ tr P . Φ φ Hi P" cn Hi P1 X H tr 3 PJ d cn P1 tr CΛ P- CΛ d Φ tr H P" φ tr cn fr P rt vq P- ii Hi Φ rt Hl rt P. PJ N J < P" H vq O: rt P- Φ p. d H rt O: P- Φ ^ l-i P- CΛ Φ rt vq d d rt N P- P> N φ d li φ Φ rr- P- Φ Ω d Ω P- cn cn d Ω Φ PP. li P φ Φ PJ tr P. Φ φ Hi P "cn Hi P 1 XH tr 3 PJ d cn P 1 tr CΛ P- CΛ d Φ tr HP" φ tr cn fr P rt vq P- ii Hi Φ rt Hl rt P. PJ NJ <P "H vq O: rt P- Φ p. d H rt O: P- Φ ^ li P- CΛ Φ rt vq dd rt N P- P> N φ d li φ Φ rr- P- Φ Ω d Ω P- cn cn d Ω Φ P
CΛ d rt tr fi Φ d P. Φ ** φ rt d Φ d li d rt ii tr Ω CΛ fr d tr Cd O rt O d f tr tr rt P. li φ P- o ι Φ 3 P1 Φ P. Ω P. Φ CΛ PJ tr rt Φ vq Φ li p. O H vq Φ Φ P1 CΛ d rt tr fi Φ d P. Φ * * φ rt d Φ d li d rt ii tr Ω CΛ fr d tr Cd O rt O df tr tr rt P. li φ P- o ι Φ 3 P 1 Φ P. Ω P. Φ CΛ PJ tr rt Φ vq Φ li p. OH vq Φ Φ P 1
PJ φ O d cn ti ü X PJ rt PJ tr P- rt rt o li rt J ii Φ Φ Hl vq P O: d H 3 Ω P. φ PJ φ • d Φ Φ φ -> H φ d P1 <! φ tr P Hl d < d OPJ φ O d cn ti ü XP J rt P J tr P- rt rt o li rt J ii Φ Φ Hl vq PO: d H 3 Ω P. φ PJ φ • d Φ Φ φ -> H φ d P 1 < ! φ tr PH l d <d O
P. d Hi P- tr P P- M d cn d d d cn p. vq P P rt O H Φ P Φ N d o d X frP. d Hi P- tr P P- M d cn d d d cn p. vq P P rt O H Φ P Φ N d o d X fr
Cfl d h→ Cfl Φ φ P ii C tr W P- CΛ tr PJ d vq d H H P- cn P- Φ vq ti cn P- Φ ιq d rt d rt φ Hi Hi φ P CΛ s: Φ Φ φ Φ 1 d φ d vq φ rt rt d cn vq HCfl dh → Cfl Φ φ P ii C tr W P- CΛ tr PJ d vq d HH P- cn P- Φ vq ti cn P- Φ ιq d rt d rt φ Hi Hi φ P CΛ s: Φ Φ φ Φ 1 d φ d vq φ rt rt d cn vq H
P- cn • Φ P- PJ P- O: Cfl P- P1 CΛ H P- ω v → Φ vq Φ P- O φ → Φ φ CΛ P. α d cn *3 P CΛ d PJ d Ω X o ii φ φ P- Cfl CΛ φ p- tr Ω tr Hi d Φ P- tr o . Φ p- Φ X p- rt P1 Φ fr p- 3 P. fr Φ Ό Φ fr P P. φ tr φ Hi d d φ 3 H φ φ cn P- α tA φ d 3 φ ü p- rt Hl P- p- P- rt Φ Φ d rt P- N CΛ tr H d P- KP- cn • Φ P- PJ P- O: Cfl P- P 1 CΛ H P- ω v → Φ vq Φ P- O φ → Φ φ CΛ P. α d cn * 3 P CΛ d P J d Ω X o ii φ φ P- Cfl CΛ φ p- tr Ω tr Hi d Φ P- tr o. Φ p- Φ X p- rt P 1 Φ for p- 3 P. fr Φ Ό Φ for P P. φ tr φ Hi dd φ 3 H φ φ cn P- α tA φ d 3 φ ü p- rt Hl P - p- P- rt Φ Φ d rt P- N CΛ tr H d P- K
P- cn φ Φ Φ d d rt α li φ φ Φ d H P li ιq 3 Φ rt P" P- vq rt p- cn d φ α H H P- Φ «q Φ α P- P- P- P- ii P- rt d P" H O: Ω rt φ φ Cfl d P. CΛ cn H H Φ d cn J Φ CΛ cn J cn CT P- Cfl P. M • d td → O Ω tr • Φ Ü φP- cn φ Φ Φ dd rt α li φ φ Φ d HP li ιq 3 Φ rt P "P- vq rt p- cn d φ α HH P- Φ« q Φ α P- P- P- P- ii P - rt d P "HO: Ω rt φ φ Cfl d P. CΛ cn HH Φ d cn J Φ CΛ cn J cn CT P- Cfl P. M • d td → O Ω tr • Φ Ü φ
H li d rt rt Φ X H, O d CΛ Ω rt d - Ω Ω Φ ü P. φ Φ 3 fr rt P- P. P-H li d rt rt Φ X H, O d CΛ Ω rt d - Ω Ω Φ ü P. φ Φ 3 fr rt P- P. P-
CΛ Ω li J d P- Φ cn Φ d 3 Φ tr d vq φ Φ tr tr P Hi rt d Hl φ d d d ΩCΛ Ω li J d P- Φ cn Φ d 3 Φ tr d vq φ Φ tr tr P Hi rt d Hl φ d d d Ω
M rt tr Ω d d d P- fr P- P- ii Φ d Φ P- P- rt φ P- φ ü tr d d d Φ ü trM rt tr Ω d d d P- for P- P- ii Φ d Φ P- P- rt φ P- φ ü tr d d d Φ ü tr
P- fi tr q P" cn Φ rt Ω rt Φ d ιq o cn Ω d d d d Λ p- PJ d *«« vq Ω 3 Ω cn d O α cn cn φ rt P- tr d CΛ CΛ H Φ tr d H φ O: tP tr tr rt ii 3 P- P- α P- Ω rt Φ Ό •s P. P. Cfl vq Si Φ d Ξ tr Ω CΛ > HP- fi tr q P "cn Φ rt Ω rt Φ d ιq o cn Ω dddd Λ p- P J d *« «vq Ω 3 Ω cn d O α cn cn φ rt P- tr d CΛ CΛ H Φ tr d H φ O: tP tr tr rt ii 3 P- P- α P- Ω rt Φ Ό • s PP Cfl vq Si Φ d Ξ tr Ω CΛ> H
P- Hi φ cn N P- rt P. tr P- Cd φ p- P- d P. rt P- d d P- fr P- "P tr P- d X OP- Hi φ cn N P- rt P. tr P- Cd φ p- P- d P. rt P- d d P- for P- "P tr P- d X O
Ω rt d o P- cn H vq d li H P. o Φ d H < P. d vq Ü P. Φ d φ Φ d CΛ p- 3 tr d Cd P. PJ Φ rt Φ Φ H φ rt li O o φ cn P. φ • li P- Hi n <J rt CΛ ii P. p. φ d Ü Cd - d n H Φ Φ Ω 3 d H rt -> H P li cn J J p. Φ d CΛ φ J φ Hi O Ü d: d rt cn tr ! cn o Φ φ tα P- rt • d PJ H d Φ P cn d d "•» 3 Φ d 1 ti rt Φ tr1 Φ PJ rt Hi P- p- P- Ω P- p. P- φ cn ιq CΛ P d <! d cn o PJ P- Φ Φ H d PJ Hi cn d φ tr P. Φ Φ P- oΩ rt do P- cn H vq d li H P. o Φ d H <P. d vq Ü P. Φ d φ Φ d CΛ p- 3 tr d Cd P. PJ Φ rt Φ Φ H φ rt li O o φ cn P. φ • li P- Hi n <J rt CΛ ii P. p. φ d Ü Cd - dn H Φ Φ Ω 3 d H rt -> HP li cn JJ p. Φ d CΛ φ J φ Hi O Ü d: d rt cn tr! cn o Φ φ tα P- rt • d P J H d Φ P cn dd "•» 3 Φ d 1 ti rt Φ tr 1 Φ PJ rt Hi P- p- P- Ω P- p. P- φ cn ιq CΛ P d <! D cn o PJ P- Φ Φ H d PJ Hi cn d φ tr P. Φ Φ P- o
1 P. p. Φ d Ω 3 d d P- P- 1 EP d 1 rt φ H rt P- -> H P ii1 P. p. Φ d Ω 3 dd P- P- 1 EP d 1 rt φ H rt P- - > HP ii
1 P- ü 1 tr 1 cn P φ P. 3 1 φ cn Φ Φ φ 11 P- ü 1 tr 1 cn P φ P. 3 1 φ cn Φ Φ φ 1
Φ 1 1 1 d 1 d ti 3 Φ 1 1 1 d 1 d ti 3
O O IV) tv> P1 P1 cn o cπ o Cπ o cπOO IV) tv> P 1 P 1 cn o cπ o Cπ o cπ
CΛ tfl Φ CΛ d N cn td φ cn CΛ α CΛ rt N CΛ Ω H tr CΛ cn rt P- CO rt Φ W rt p, O t ii cn frCΛ tfl Φ CΛ d N cn td φ cn CΛ α CΛ rt N CΛ Ω H tr CΛ cn rt P- CO rt Φ W rt p, O t ii cn fr
Φ H P- rt d Φ rt r→ P- Ω rt P- Ω d d o tr P- PJ rt d d d H P- d Φ tr X Φ Ω o ii Φ d ii P. P4 o o d tr φ tr d X d Ω li PJ Φ d cn d d \-> d d H Φ φ p- tr oΦ H P- rt d Φ rt r → P- Ω rt P- Ω ddo tr P- PJ rt ddd H P- d Φ tr X Φ Ω o ii Φ d ii P. P 4 ood tr φ tr d X d Ω li PJ Φ d cn dd \ -> dd H Φ φ p- tr o
P- P H o P" Hi Ω φ O PJ vq P- P- d tr d P- vq vq d vq J: vq H Ω Ω d li φ P P- 3 J Φ Hi fr CΛ O 3 cn P1 φ φ vq rt P- P- Ω cn φ P. d > • X fr tr Φ P. ~- CΛ Ω Hi d d N CΛ d → rt P. d cn d cn tr P. cn P1 rt d tr J 3 rt P- t→ rt tr P4 tr φ tr ö cn Φ Φ Φ φ N Φ d rt VD cn P- J Φ Φ CΛ Φ Ω : i→ dP- PH o P "Hi Ω φ O PJ vq P- P- d tr d P- vq vq d vq J: vq H Ω Ω d li φ P P- 3 J Φ Hi fr CΛ O 3 cn P 1 φ φ vq rt P- P- Ω cn φ P. d> • X fr tr Φ P. ~ - CΛ Ω Hi dd N CΛ d → rt P. d cn d cn tr P. cn P 1 rt d tr J 3 rt P - t → rt tr P 4 tr φ tr ö cn Φ Φ Φ φ N Φ d rt VD cn P- J Φ Φ CΛ Φ Ω: i → d
O rt d P. o Φ Φ rt P- H cn Cd d p- vq . rt O 3 P- 3 ü Hi li tr EP φ p- tr Hi d EP Φ o Ω Hi d N Ω ü H d ü P. rt d P- rt d: X d P- d ΦO rt d P. o Φ Φ rt P- H cn Cd d p- vq. rt O 3 P- 3 ü Hi li tr EP φ p- tr Hi d EP Φ o Ω Hi d N Ω ü H d ü P. rt d P- rt d: X d P- d Φ
P- Hl d 3 Ω Φ tr Φ "« tr P1 Φ φ H P1 σ P. O φ Φ rt • tr PJ d vq H d N vq P fr d o fr P> cn P1 d es P- Φ φ 3 d 3 li Ω vq φ to rtP- Hl d 3 Ω Φ tr Φ " « tr P 1 Φ φ HP 1 σ P. O φ Φ rt • tr PJ d vq H d N vq P fr do fr P> cn P 1 d es P- Φ φ 3 d 3 li Ω vq φ to rt
N Φ d P. tr tr rt P- O rt • Φ d d Ω Φ CΛ ii J φ J TI d tr cn H φ . d - tr ü φ CO P" 3 Cfl Φ ii fr- Cfl CΛ tr p- φ d t Ω P- d d φ X J cn φ Ω Hi O: P- H d O rt rt Ω rt d X li *P d Φ tr vq vq d P- Φ fr tflN Φ d P. tr tr rt P- O rt • Φ d d Ω Φ CΛ ii J φ J TI d tr cn H φ. d - tr ü φ CO P "3 Cfl Φ ii fr- Cfl CΛ tr p- φ dt Ω P- dd φ XJ cn φ Ω Hi O: P- H d O rt rt Ω rt d X li * P d Φ tr vq vq d P- Φ for tfl
Ω Φ 3 tr φ •P Ω vq φ d 3 li O tr d φ φ Φ cn J cn rt d CΛ vq d P- rt P- tr P φ fr P) fr P- PJ α P- Hi PJ d P- d O ü tfl φ H tr cn H CΛ P- φΩ Φ 3 tr φ • P Ω vq φ d 3 li O tr d φ φ Φ cn J cn rt d CΛ vq d P- rt P- tr P φ fr P ) for P- PJ α P- Hi PJ d P- d O ü tfl φ H tr cn H CΛ P- φ
PJ tr H p. rt H φ d d Φ cn Hi vq P- rt H PJ H H cn Φ CΛ P- Φ o ii fr P- Φ PJ d d Φ cn Φ Ü Ω N rt d Φ tfl vq P" φ Φ P> P- rt Ω P rt o rt Φ d P-1 P. cn P- cn tr Φ d li li d d φ H cn H tr P- dPJ tr H p. rt H φ dd Φ cn Hi vq P- rt H PJ HH cn Φ CΛ P- Φ o ii fr P- Φ PJ dd Φ cn Φ Ü Ω N rt d Φ tfl vq P "φ Φ P> P- rt Ω P rt o rt Φ d P- 1 P. cn P- cn tr Φ d li li dd φ H cn H tr P- d
Φ Ω t→ CO Cd d O φ P4 d P- *1 Φ Φ d Φ d 1 P- N *P d rt CΛ PJ H rt fr r→ Cd φ P. P. → φ H P P1 vq P- P- P d vq P1 cn tfl φ φ p- p - d rt d Ω α Φ H P1 X φ Φ Φ d v φ φ d cn rt H P1 P- Φ rt d Hi tr d cπ P- P- Φ P- ii H fr d 21 d P. d d cn Φ J O Φ vq P1 d vQ P. d φ Λ d q H rt φ d P- tr φ N ii 3 rt P- d Hi d rt li . P- φ s:Φ Ω t → CO Cd d O φ P 4 d P- * 1 Φ Φ d Φ d 1 P- N * P d rt CΛ PJ H rt fr r → Cd φ PP → φ HPP 1 vq P- P- P d vq P 1 cn tfl φ φ p- p - d rt d Ω α Φ HP 1 X φ Φ Φ dv φ φ d cn rt HP 1 P- Φ rt d Hi tr d cπ P- P- Φ P- ii H fr d 21 d P. dd cn Φ JO Φ vq P 1 d vQ P. d φ Λ dq H rt φ d P- tr φ N ii 3 rt P- d Hi d rt li. P- φ s:
P. P. rt d φ P. CΛ Cfl H r-> vq P1 CΛ d Hl O d ιq Hi d vq P. φ P- P- φ 3 d cn cn rt li O Φ cn Φ O: H P1 PJ Hi H φ N CΛ Φ Φ φ P. α d iiPP rt d φ P. CΛ Cfl H r-> vq P 1 CΛ d Hl O d ιq Hi d vq P. φ P- P- φ 3 d cn cn rt li O Φ cn Φ O: HP 1 PJ Hi H φ N CΛ Φ Φ φ P. α d ii
P P- d rt Ω H Φ 3 fr Φ li O φ CΛ Hi P- O Φ rt cn P- H Φ P- CΛ φ P.P P- d rt Ω H Φ 3 fr Φ li O φ CΛ Hi P- O Φ rt cn P- H Φ P- CΛ φ P.
Φ rt »q O tr d O d O rt P- CΛ fr P4 CJ d CΛ N Ω ü P1 O Ω d ti Φ rt dΦ rt »q O tr d O d O rt P- CΛ fr P 4 CJ d CΛ N Ω ü P 1 O Ω d ti Φ rt d
P J rt Λ Hi J ti 3 d rt ti d rt Φ φ σ P- rt Φ tr P. l→ Hi tr Φ M cn Φ P.P J rt Λ Hi J ti 3 d rt ti d rt Φ φ σ P- rt Φ tr P. l → Hi tr Φ M cn Φ P.
P Φ Hi Ω cn O P- H PJ d r Φ Ω rt d Φ Hi PJ li cn d d Φ CP Φ Hi Ω cn O P- H PJ d r Φ Ω rt d Φ Hi PJ li cn d d Φ C
CΛ P- N rt tr J rt H cn P- P rt H tr d φ d N → cn Hl Hi Φ d tiCΛ P- N rt tr J rt H cn P- P rt H tr d φ d N → cn Hl Hi Φ d ti
Ω φ cn o φ Φ d O Ω Ω CO ü s: rt P- Φ d rt tr Φ rt P1 P- φ d= H vq tr ü P. rt α cn Hi J tr tr CΛ P- ) φ d vq • P- P1 Φ Φ d P- tr Φ Φ < J φ P. Φ r→ Φ P- Hi d Φ rt <! Cfl Ω d tr O: P" rt p- Ω ü P- X O d Φ Φ φ N cn d d VO O Ω tr p : Q P1 Ω Φ Φ Ω d tr rt d d= Ü rt >i X d t-ι φ Φ vq d ü tr d tr P" O: d f d d tr d CΛ li d rtΩ φ cn o φ Φ d O Ω Ω CO ü s: rt P- Φ d rt tr Φ rt P 1 P- φ d = H vq tr ü P. rt α cn Hi J tr tr CΛ P- ) φ d vq • P- P 1 Φ Φ d P- tr Φ Φ <J φ P. Φ r → Φ P- Hi d Φ rt <! Cfl Ω d tr O: P "rt p- Ω ü P- XO d Φ Φ φ N cn dd VO O Ω tr p: QP 1 Ω Φ Φ Ω d tr rt dd = Ü rt> i X d t-ι φ Φ vq d ü tr d tr P "O: dfdd tr d CΛ li d rt
Φ Cfl P- tr Φ α d P< φ • vq vq vq Φ d Φ φ Ω φ E Φ tr CΛ >q rt N P- Cfl ΦΦ Cfl P- tr Φ α d P <φ • vq vq vq Φ d Φ φ Ω φ E Φ tr CΛ> q rt N P- Cfl Φ
H li CΛ H P- Φ i→ cn Φ φ φ d q H P- fT P- Φ d P* Cd rt H d Ω Ω P- φ Ω P- o n 3 PJ φ rt ü P1 CΛ cn Ω Φ d li O ti Ü X o tr tr t→ d tr Ω rt d d J tr Ω φ s . tr d Φ CO Ω Φ o P- 3 Φ rt rtH li CΛ H P- Φ i → cn Φ φ φ dq H P- fT P- Φ d P * Cd rt H d Ω Ω P- φ Ω P- on 3 PJ φ rt ü P 1 CΛ cn Ω Φ d li O ti Ü X o tr tr t → d tr Ω rt dd J tr Ω φ s. tr d Φ CO Ω Φ o P- 3 Φ rt rt
00 d PJ fr d α tr H P- tr tr p- Φ J cn d Φ ~> fr d 3 ii <i P- d Φ Φ00 d PJ for d α tr H P- tr tr p- Φ J cn d Φ ~> for d 3 ii <i P- d Φ Φ
CΛ r→ o d Φ φ i→ rt PJ cn P- Φ P. H H rt co 3 d < p. Φ P d d P-CΛ r → o d Φ φ i → rt PJ cn P- Φ P. H H rt co 3 d <p. Φ P d d P-
O: r+ rt d vq Hi H O: Φ d rh Φ d φ vq H Φ cn cπ CΛ Φ H φ vq PO: r + rt d vq Hi H O: Φ d rh Φ d φ vq H Φ cn cπ CΛ Φ H φ vq P
Hi o Φ o Cfl Φ Φ Ω rt Ω tr li tr1 Φ O •P P1 d • rt H PJ CΛ li CΛ ΦHi o Φ o Cfl Φ Φ Ω rt Ω tr li tr 1 Φ O • PP 1 d • rt H PJ CΛ li CΛ Φ
Hi Hi li P. ii α fr d tr J rt P- Cfl φ n 3 PJ Φ 3 P- O CΛ d o P- rt HHi Hi li P. ii α fr d tr J rt P- Cfl φ n 3 PJ Φ 3 P- O CΛ d o P- rt H
P Hi Φ tr P- rt Φ P- Φ P cn rt P- rt <i H ^ Hl Cfl es Hi o tr ii < P. HP Hi Φ tr P- rt Φ P- Φ P cn rt P- rt <i H ^ Hl Cfl es Hi o tr ii <P. H
Φ N P> H Φ o φ tfl CΛ H 3 rt PJ cn Φ Φ PJ rt PJ rt d Hi H J vq φ φ o tr rt Φ ^ P- P. P ü CO rt Φ P- . d rt PJ H H Λ N ι P d ii d 3 ΦΦ N P> H Φ o φ tfl CΛ H 3 rt PJ cn Φ Φ PJ rt PJ rt d Hi HJ vq φ φ o tr rt Φ ^ P- P. P ü CO rt Φ P-. d rt P J HH Λ N ι P d ii d 3 Φ
• α= vq φ Φ . P* P- rt P- d cn P- CΛ Φ J. Φ d P. d Φ rt Hl Cfl• α = vq φ Φ. P * P- rt P- d cn P- CΛ Φ J. Φ d P. d Φ rt Hl Cfl
PJ P tr φ Cd d ≤: Cπ P rt ö CΛ d rt O φ cn rt H- Φ → d *q P- P- P- oP J P tr φ Cd d ≤: Cπ P rt ö CΛ d rt O φ cn rt H- Φ → d * q P- P- P- o
Φ Φ Φ -J H P P- M Φ P- vq Φ H P1 Ω d P1 vq φ ω P cn d P d P H φ Φ 1 H 3 J Q φ vi> cn v tr P. Φ Φ φ cn P- φ Hi Ω EP tr s: P- tr P P. d P- CΛ C d N φ P- 3 d Φ P P- PJ tr ΦΦ Φ Φ -JHP P- M Φ P- vq Φ HP 1 Ω d P 1 vq φ ω P cn d P d PH φ Φ 1 H 3 JQ φ vi> cn v tr P. Φ Φ φ cn P- φ Hi Ω EP tr s: P- tr P P. d P- CΛ C d N φ P- 3 d Φ P P- PJ tr Φ
P1 to PJ rt P- P TI o. Φ t O P- tr d d P Φ tr1 tr P- φ d Ω Φ tiP 1 to PJ rt P- P TI o. Φ t O P- tr dd P Φ tr 1 tr P- φ d Ω Φ ti
O: Φ Ω φ P cn P. J Φ P- N d PJ o φ vq cn Φ P. P4 d H li tr 3 H cnO: Φ Ω φ P cn P. J Φ P- N d PJ o φ vq cn Φ P. P 4 d H li tr 3 H cn
Ω cn tr rt P. rt P- P" 1 O X CΛ li P H cn Ω φ P4 a P- Φ O: H p- d P- 1Ω cn tr rt P. rt P- P "1 OX CΛ li PH cn Ω φ P 4 a P- Φ O: H p- d P- 1
Φ d • d o p- Φ Ω PJ φ -> Φ tr P- CΛ Ü Ω P- TI Ω d rtΦ d • do p- Φ Ω PJ φ - > Φ tr P- CΛ Ü Ω P- TI Ω d rt
Φ ti d n Hi Cfl φ 1 P- tr d J P- PJ 1 fr Ω P- tr vq d vq i φ φ J P1 1 d P-1 φ Φ tr vq 1 Φ Cfl α Ω H Φ tr 1 H ü P" Φ - 1 rt H O l d 1 d ΦΦ ti dn Hi Cfl φ 1 P- tr d J P- PJ 1 fr Ω P- tr vq d vq i φ φ JP 1 1 d P- 1 φ Φ tr vq 1 Φ Cfl α Ω H Φ tr 1 H ü P "Φ - 1 rt HO ld 1 d Φ
1 ii 1 P" 1 1 H H 1 ii 1 P "1 1 HH
Mit Hilfe der zu allen Brennstoffzellenblocken seriell angeordneten Leistungsdiode 19 wird erreicht, dass- bei einem Absinken der Versorgungsspannung der Gleichstromversorgungseinrichtung 1 unter die Spannung des Gleichstromnetzes 13 ein Stromfluß in unerwünschter Richtung durch die Brennstoffzel- lenmodule 3 verhindert wird. With the aid of the power diode 19, which is arranged in series with all fuel cell blocks, it is achieved that, if the supply voltage of the direct current supply device 1 drops below the voltage of the direct current network 13, a flow of current in the undesired direction through the fuel cell modules 3 is prevented.

Claims

Patentansprüche claims
1. Gleichstromversorgungseinrichtung (1) mit mehreren seriell angeordneten Brennstoffzellenblocken (3) , d a d u r c h g e k e n n z e i c h n e t , dass zu jedem Brennstoffzellenblock (3) eine Leistungsdiode (7) parallel angeordnet ist.1. DC power supply device (1) with several series-arranged fuel cell blocks (3), so that a power diode (7) is arranged in parallel with each fuel cell block (3).
2. Gleichstromversorgungseinrichtung (1) nach Anspruch 1, g e k e n n z e i c h n e t d u r c h einen Reserve- Brennstoffzellenblock (5) .2. DC power supply device (1) according to claim 1, g e k e n n z e i c h n e t d u r c h a reserve fuel cell block (5).
3. Gleichstromversorgungseinrichtung (1) nach Anspruch 1 oder 2, g e k e n n z e i c h n e t d u r c h eine Überwa- chungseinrichtung, die zur Überwachung der Leistungsdioden (17) vorgesehen ist.3. DC power supply device (1) according to claim 1 or 2, g e k e n n z e i c h n e t d u r c h a monitoring device which is provided for monitoring the power diodes (17).
4. Gleichstromversorgungseinrichtung (1) nach einem der Ansprüche 1 bis 3, g e k e n n z e i c h n e t d u r c h eine zu allen Brennstoffzellenblocken (3) seriell angeordnete Leistungsdiode (19) .4. DC power supply device (1) according to one of claims 1 to 3, g e k e n n z e i c h n e t d u r c h a to all fuel cell blocks (3) serially arranged power diode (19).
5. Gleichstromversorgungseinrichtung (1) nach Anspruch 4, g e k e n n z e i c h n e t d u r c h einen den Brenn- stoffzellenblöcken (3) parallel zuschaltbaren elektrischen Widerstand (9) . 5. DC power supply device (1) according to claim 4, g e k e n n z e i c h n e t d u r c h one of the fuel cell blocks (3) in parallel electrical resistance (9).
PCT/DE2001/004391 2000-11-30 2001-11-21 Direct-current power supply device comprising a number of series-connected fuel cell blocks WO2002045197A2 (en)

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DE10059392.5 2000-11-30

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