JPH10172596A - Fuel cell evaluation method - Google Patents
Fuel cell evaluation methodInfo
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- JPH10172596A JPH10172596A JP8344653A JP34465396A JPH10172596A JP H10172596 A JPH10172596 A JP H10172596A JP 8344653 A JP8344653 A JP 8344653A JP 34465396 A JP34465396 A JP 34465396A JP H10172596 A JPH10172596 A JP H10172596A
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- fuel cell
- partial pressure
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- 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
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- Fuel Cell (AREA)
- Tests Of Electric Status Of Batteries (AREA)
Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、燃料電池の電池特
性の評価方法に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for evaluating cell characteristics of a fuel cell.
【０００２】[0002]
【従来の技術】近年、リン酸型燃料電池は燃料の持つエ
ネルギーを直接電気に変換する発電システムとして注目
されており、国内外で急速に開発が進められている。リ
ン酸型燃料電池の電極反応は、負極側（アノード）でＨ
2 →２Ｈ+ ＋２ｅ、正極側（カソード）で1/2 Ｏ2 ＋２
Ｈ+ ＋２ｅ→Ｈ2 Ｏであり、全体としてはＨ2 ＋1/2 Ｏ
2 →Ｈ2 Ｏ（前記→はいずれも←を含む）となり、セル
の理論電圧はネルンストの式と呼ばれる次式；Ｅth＝Ｅ
o ＋（２．３ＲＴ／ｎＦ） log（ＰH2・ＰO2 1/2／Ｐ
H2O ）（式中、Ｅo はギブス自由エネルギーから求めら
れる電圧）で与えられる。しかし、実際に発電させて得
られる電圧Ｅcellは、理論電圧Ｅthより低い値となり、
この電圧低下分を分極と称している。分極としては、電
子やイオンの抵抗電圧降下による抵抗分極ηohm 、起電
反応を続けるための越えるべきエネルギー障壁に対応す
る活性化分極ηact 、反応物質や生成物質の移動に関連
した濃度分極ηcon の３つがあり、次式（２）のように
示される。 Ｅcell＝Ｅth−ηohm −ηact −ηcon （２）2. Description of the Related Art In recent years, a phosphoric acid fuel cell has attracted attention as a power generation system for directly converting energy of fuel into electricity, and is being rapidly developed in Japan and overseas. In the electrode reaction of the phosphoric acid fuel cell, H
2 → 2H + + 2e, 1/2 O 2 +2 on positive side (cathode)
H + + 2e → H 2 O, and as a whole H 2 +1/2 O
2 → H 2 O (Each of the above → includes ←), and the theoretical voltage of the cell is expressed by the following equation called Nernst equation; E th = E
o + (2.3RT / nF) log (P H2 · P O2 1/2 / P
H2O ), where Eo is the voltage determined from the Gibbs free energy. However, the voltage E cell obtained by actually generating power is lower than the theoretical voltage E th ,
This voltage drop is called polarization. The polarization includes resistance polarization η ohm due to the resistance voltage drop of electrons and ions, activation polarization η act corresponding to the energy barrier to be exceeded to continue the electromotive reaction, and concentration polarization η related to the movement of reactants and generated substances. There are three types of con , which are expressed by the following equation (2). E cell = E th −η ohm −η act −η con (2)
【０００３】抵抗分極は、電流Ｉ（Ａ）に比例し、η
ohm ＝Ｒｅ・Ｉ（ここでＲｅはセルの電気抵抗）で与え
られる。該抵抗分極を下げるには、電極及びセパレー
タ等のカーボン材料の固有抵抗を下げるとともに、該カ
ーボン材料の平滑度を改善する。電解質マトリックス
層を薄くするとともに、マトリックス層と触媒層のリン
酸が不足しないようにセル内にリン酸を貯蔵しておく等
が挙げられる。活性化分極を下げるには、白金又は白
金合金等の触媒種の活性度を向上させる等が挙げられ
る。濃度分極を下げるには、触媒がリン酸で過度に覆
われることのないように触媒層の撥水性を適切にするこ
と。電極基板のガス透過性を良くすること等が挙げら
れる。The resistance polarization is proportional to the current I (A), and η
ohm = Re.I (where Re is the electric resistance of the cell). In order to reduce the resistance polarization, the specific resistance of the carbon material such as the electrode and the separator is reduced, and the smoothness of the carbon material is improved. For example, the thickness of the electrolyte matrix layer may be reduced, and phosphoric acid may be stored in the cell so that phosphoric acid in the matrix layer and the catalyst layer is not insufficient. In order to lower the activation polarization, it is possible to improve the activity of a catalyst species such as platinum or a platinum alloy. To reduce the concentration polarization, the water repellency of the catalyst layer must be appropriate so that the catalyst is not excessively covered with phosphoric acid. Improving the gas permeability of the electrode substrate may be mentioned.
【０００４】従来、燃料電池の開発に際し、その電池特
性を評価する方法としては、実験室規模の小型の要素電
池を使用した試験を実施し、端子電圧のパラメータ等の
変化を調べることにより性能を把握する方法及び燃料極
又は空気極を個別に電気化学的な実験によりその性能を
評価する方法等が挙げられるが、前者の方法は性能低下
の要因別の評価を定量的に行うことができず、後者の方
法は実電池のように電極と電解質層が組み合わされた状
態における個別電極の特性を調べるには適していない。Conventionally, in the development of a fuel cell, as a method of evaluating the characteristics of the fuel cell, a test using a small element battery of a laboratory scale is performed, and the performance is evaluated by examining changes in terminal voltage parameters and the like. Although there is a method of grasping the performance and a method of individually evaluating the performance of the fuel electrode or the air electrode by electrochemical experiments, the former method cannot quantitatively evaluate the performance degradation factors. On the other hand, the latter method is not suitable for examining the characteristics of an individual electrode in a state where an electrode and an electrolyte layer are combined as in a real battery.
【０００５】また、リン酸型燃料電池の小型単セル試験
を実施することにより電池の端子電圧を電流密度、ガス
組成及び温度等の支配因子により記述する半理論式を導
き出しこれに基づいて電池特性を評価するものとして、
表面が平滑な電極を用いた場合についてBockris & Srin
ivasanの式が提案されている（Fuell Cells ：TheirEle
ctrochemistry,McGraw-Hill Book company(1969),179
頁〜182 頁）。しかしながら、該半理論式は濃度分極項
及び活性化分極項の係数が不確定であり、電池の電圧−
電流特定を定性的に示すのには有用であるが、実際の定
量記述には適していない。Further, a semi-theoretical formula describing the terminal voltage of a battery by controlling factors such as current density, gas composition and temperature by conducting a small single cell test of a phosphoric acid type fuel cell was derived, and the battery characteristics were determined based on this. To evaluate
Bockris & Srin about using electrodes with smooth surface
The ivasan equation has been proposed (Fuell Cells: TheirEle
ctrochemistry, McGraw-Hill Book company (1969), 179
Pp. 182). However, in the semi-theoretical formula, the coefficients of the concentration polarization term and the activation polarization term are uncertain,
It is useful for qualitatively indicating current identification, but is not suitable for actual quantitative description.
【０００６】[0006]
【発明が解決しようとする課題】従って、本発明の目的
は、燃料極、空気極及びこれらに挟まれた電解質層から
構成されるリン酸型燃料電池の端子電圧を電流密度、ガ
ス組成及び温度等の支配因子により記述する特定式を導
き出し、これに基づき電池特性を要因別かつ定量的に精
度良く評価する方法を提供することにある。SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to determine the terminal voltage of a phosphoric acid type fuel cell comprising a fuel electrode, an air electrode and an electrolyte layer sandwiched between the fuel electrode, the air electrode, the current density, the gas composition and the temperature. An object of the present invention is to provide a method for deriving a specific expression described by a governing factor such as the above, and for evaluating the battery characteristics by factor and quantitatively with high accuracy based on the formula.
【０００７】[0007]
【課題を解決するための手段】かかる実情において、本
発明者は鋭意検討を行った結果、前記Bockris & Sri-ni
vasan の式を出発式として修正された端子電圧記述式
が、燃料電池の電池特性を極めて精度良く、要因別かつ
定量的に評価できることを見い出し、本発明を完成する
に至った。Under such circumstances, the present inventors have conducted intensive studies and as a result, have found that the aforementioned Bockris & Sri-ni
The present inventors have found that a terminal voltage description formula modified from the Vasan's formula as a starting formula can evaluate the cell characteristics of a fuel cell with high accuracy, by factor and quantitatively, and have completed the present invention.
【０００８】すなわち、本発明は、水素が反応する燃料
極、酸素が消費される空気極、これら２つの電極に挟ま
れた電解質層から構成される燃料電池において、次式
（１）；That is, the present invention relates to a fuel cell comprising a fuel electrode where hydrogen reacts, an air electrode where oxygen is consumed, and an electrolyte layer sandwiched between these two electrodes, the following formula (1):
【０００９】[0009]
【数３】 (Equation 3)
【００１０】（式中、Ｖは燃料電池端子電圧、ｉは電流
密度、ＰH2O は水蒸気分圧(atm) 、ＰH2は水素分圧(at
m) 、ＰO2は酸素分圧(atm) 、Ｔは反応温度（Ｋ）、ａ
及びｂは交流電流密度の分圧依存性に関する定数、φは
２．３ＲＴ／ｎＦ（ここで、Ｒはガス定数で８．３１４
Ｊ／mol 、ｎは反応に関与するする電子数ｎ＝２、Ｆは
ファラデー定数を示す）、Ｆ（Ｔ) は擬似開回路電圧、
ｒは内部抵抗（Ω・cm2 ）、βＨ(1) は第１水素分圧係
数、βＨ(2) は第２水素分圧係数、ＤＨは水素拡散項係
数、βＯ(1) は第１酸素分圧係数、βＯ(2) は第２酸素
分圧係数、ＤＯは酸素拡散項係数を示す。）で表わされ
る特性式に基づいて電池特性を評価することを特徴とす
る燃料電池の評価方法を提供するものである。(Where V is the fuel cell terminal voltage, i is the current density, P H2O is the water vapor partial pressure (atm), and P H2 is the hydrogen partial pressure (at
m), P O2 is oxygen partial pressure (atm), T is reaction temperature (K), a
And b are constants relating to the partial pressure dependence of the AC current density, φ is 2.3 RT / nF (where R is a gas constant of 8.314
J / mol, n is the number of electrons involved in the reaction n = 2, F is the Faraday constant), F (T) is the pseudo open circuit voltage,
r is the internal resistance (Ω · cm 2 ), βH (1) is the first hydrogen partial pressure coefficient, βH (2) is the second hydrogen partial pressure coefficient, DH is the hydrogen diffusion term coefficient, and βO (1) is the first oxygen The partial pressure coefficient, βO (2) is the second oxygen partial pressure coefficient, and DO is the oxygen diffusion term coefficient. The present invention provides a method for evaluating a fuel cell, which is characterized by evaluating cell characteristics based on a characteristic expression represented by (1).
【００１１】[0011]
【発明の実施の形態】本発明において、前記端子電圧記
述式（１）は、下記のBockris & Srinivasanの式（３）
を出発式として、修正され求められる。すなわち、次式
（３）；DESCRIPTION OF THE PREFERRED EMBODIMENTS In the present invention, the terminal voltage description equation (1) is expressed by the following Bockris & Srinivasan equation (3).
As a departure ceremony, it is corrected and required. That is, the following equation (3):
【００１２】[0012]
【数４】 (Equation 4)
【００１３】（式中、Ｖ、Ｒ、Ｔ、ｎ、Ｆ、ＰH2、
ＰO2、ｒ及びｉは前記と同じ、ＥO は基準電位、ＰH2O
は水蒸気分圧、ｉOAはアノード交換電流密度（mA／c
m2 ）、ｉLAはアノード限界電流密度（mA／cm2 ）、ｉ
OCはカソード限界電流密度（mA／cm2 ）、ｉLCはカソー
ド限界電流密度（mA／cm2 ）、αA はアノード移動係数
及びαCはカソード移動係数を示す。）において、右辺
の第３項は抵抗分極、第４項及び第６項は活性化分極、
第５項及び第７項は濃度分極を示す。ここで、活性化分
極及び濃度分極項は多孔質電極特有な構造依存性に係わ
る要素が介入し、温度や反応依存性は未知であるため、
未知の係数βＨ(1) 、βＨ(2) 、βＯ(1) 、βＯ(2) で
置き換え、次式（４）を得る。(Where V, R, T, n, F, P H2 ,
P O2 , r and i are the same as above, E O is the reference potential, P H2O
Is the partial pressure of water vapor, i OA is the anode exchange current density (mA / c
m 2 ), i LA is the anode limiting current density (mA / cm 2 ), i
OC is the cathode limit current density (mA / cm 2 ), i LC is the cathode limit current density (mA / cm 2 ), α A is the anode transfer coefficient, and α C is the cathode transfer coefficient. ), The third term on the right side is resistance polarization, the fourth and sixth terms are activation polarization,
The fifth and seventh terms indicate concentration polarization. Here, the activation polarization and the concentration polarization term involve elements related to the structural dependence specific to the porous electrode, and the temperature and reaction dependence are unknown,
Substituting unknown coefficients βH (1), βH (2), βO (1), βO (2) gives the following equation (4).
【００１４】[0014]
【数５】 (Equation 5)
【００１５】（式中、記号は前記と同じ）(Wherein the symbols are the same as above)
【００１６】また、交換電流密度の分圧依存性を考慮し
て、該交換電流密度をアルレニウス式に置き換え、さら
に、温度一定の条件下では指数関数項と常数との積が一
定となるため、これを定数ξとして置き換え次式（５）
及び（６）を得る。In consideration of the partial pressure dependency of the exchange current density, the exchange current density is replaced by the Arrhenius equation. Further, under constant temperature conditions, the product of the exponential function term and the constant becomes constant. This is replaced by the constant 次 and the following equation (5)
And (6) are obtained.
【００１７】[0017]
【数６】 (Equation 6)
【００１８】また、限界電流密度は次式（７）で記述さ
れる。The limit current density is described by the following equation (7).
【数７】 (Equation 7)
【００１９】（式中、Ａ／ＡO は単位電極面積当たりの
触媒有効表面積、Ｄは拡散係数、Ｐは酸素分圧ＰO2また
は水素分圧ＰH2、δは拡散層の厚みを示し、ｎ及びＦは
前記に同じ。） ここで、触媒有効表面積や拡散層厚みを一定と考える
と、限界電流密度を分圧で除したものは一定の係数とな
る。これを拡散項係数と呼び、燃料極と空気極のそれぞ
れにおいて、水素拡散項係数ＤＨと酸素拡散項係数ＤＯ
が次式のように定義される。 ＤＨ＝ｉLA／ＰH2 （８） ＤＯ＝ｉLC／ＰO2 （９） これらの関数を（４）式に代入すると式（10）のように
なる。(Where A / A O is the effective surface area of the catalyst per unit electrode area, D is the diffusion coefficient, P is the oxygen partial pressure P O2 or hydrogen partial pressure P H2 , δ is the thickness of the diffusion layer, and n And F are the same as above.) Here, assuming that the catalyst effective surface area and the diffusion layer thickness are constant, a value obtained by dividing the limiting current density by the partial pressure is a constant coefficient. This is called a diffusion term coefficient. At each of the fuel electrode and the air electrode, the hydrogen diffusion term coefficient DH and the oxygen diffusion term coefficient DO
Is defined as follows: DH = i LA / P H2 (8) DO = i LC / P O2 (9) By substituting these functions into equation (4), equation (10) is obtained.
【００２０】[0020]
【数８】 (Equation 8)
【００２１】（式中、記号は前記に同じ。φは２．３Ｒ
Ｔ／ｎＦである。） さらに、式（10）を展開して、次式（11）を得る。(Wherein the symbols are the same as above. Φ is 2.3R
T / nF. Further, the expression (10) is expanded to obtain the following expression (11).
【００２２】[0022]
【数９】 (Equation 9)
【００２３】（式中、記号は前記に同じ、以下式中の記
号も同様であり、この記載を省略する。）また、式（1
1）において、Ｆ（Ｔ）＝ＥO ＋βＨ(1)log（ξA ）＋
βＯ(1)log （ξC ）とおくと式（１）となり、端子電
圧を温度、分圧及び電流密度の関数として記述すること
ができる。(In the formula, the symbols are the same as those described above, and the same applies to the symbols in the following formulas, and the description is omitted.)
In 1), F (T) = E O + βH (1) log (ξ A ) +
If βO (1) log (ξ C ) is given, equation (1) is obtained, and the terminal voltage can be described as a function of temperature, voltage division, and current density.
【００２４】次に式（11）において、係数ＢＯ(1) 、β
Ｈ(1) 、βＯ(2) 、βＨ(2) 、ＤＨ及びＦ（Ｔ）を算出
する。各係数を実験的に求めるには、未知数の数に併せ
て、異なった条件で端子電圧を測定し、これら連立方程
式をニュートン・ラプソン法などを用いて求めることも
可能であるが、実際には未知数が多くなると計測誤差な
どが微妙に影響するため、値を定めることは非常に困難
になる。また、交換電流密度の分圧依存性に関する指数
ａ及びｂは直接求めるのが難しく、燃料極側の水素分圧
依存性についてはａ＝１を仮定し、酸素分圧依存性につ
いては０．７〜０．８程度と考えられるので、ここでは
ｂ＝3/4 と仮定する。また、水蒸気分圧依存性について
は、常圧条件で実際の電極反応が生じているところで
は、分圧が高く log（ＰH2O ）はゼロ（０）と考えて以
下では無視することとする。係数の算出の際に使用した
リン酸型燃料電池の仕様は、後述の燃料電池の特性評価
の際に使用したものと同様のものである。Next, in equation (11), the coefficients BO (1), β
H (1), βO (2), βH (2), DH and F (T) are calculated. To obtain each coefficient experimentally, it is also possible to measure the terminal voltage under different conditions according to the number of unknowns, and to obtain these simultaneous equations using Newton-Raphson method, etc. When the number of unknowns increases, it becomes very difficult to determine a value because measurement errors and the like have a subtle effect. Further, it is difficult to directly obtain the indices a and b relating to the partial pressure dependence of the exchange current density. It is assumed that a = 1 for the hydrogen partial pressure dependence on the fuel electrode side and 0.7 for the oxygen partial pressure dependence. Since it is considered to be about 0.8, it is assumed here that b = 3/4. Regarding the water vapor partial pressure dependency, where an actual electrode reaction occurs under normal pressure conditions, the partial pressure is high and log (P H2O ) is considered to be zero (0), and is ignored in the following. The specifications of the phosphoric acid type fuel cell used in calculating the coefficient are the same as those used in the evaluation of the characteristics of the fuel cell described later.
【００２５】低電流密度データからのβＯ(1) の決定；
低電流密度領域では拡散分極項 log( １−ｉ／（ＤＯ・
Ｐ）はゼロ（０）と考えると、（11）式は次式（12）の
ように簡略化される。Determination of βO (1) from low current density data;
In the low current density region, the diffusion polarization term log (1−i / (DO ·
Assuming that P) is zero (0), equation (11) is simplified as equation (12).
【００２６】[0026]
【数１０】 (Equation 10)
【００２７】電流密度一定、燃料極は純水素使用の条件
下で、生成水は全てカソード側に排出されるものと仮定
した場合、流入空気中の酸素分圧だけを変化させると、
二つの酸素分圧条件下での端子電圧差（Ｖ1 −Ｖ0 ）は
次式（13）より求められ、次のように記述される。 （Ｖ1 −Ｖ0 ）＝（φ/2＋3/4 ・βＯ(1))log(ＰO2.1/ ＰO2.0） （13） したがって、第１酸素分圧係数βＯ(1) は次式（14）で
求められることになる。 βＯ(1) ＝4/3 ・((Ｖ1 −Ｖ0 )/log(ＰO2.1/ ＰO2.0）−φ/2) （14）Assuming that all the generated water is discharged to the cathode side under the condition that the current density is constant and the fuel electrode uses pure hydrogen, if only the partial pressure of oxygen in the inflowing air is changed,
The terminal voltage difference (V 1 −V 0 ) under two oxygen partial pressure conditions is obtained from the following equation (13) and is described as follows. (V 1 −V 0 ) = (φ / 2 + 3/4 · βO (1)) log ( PO2.1 / PO2.0 ) (13) Therefore, the first oxygen partial pressure coefficient βO (1) is given by the following equation. It will be required in (14). βO (1) = 4/3 · ((V 1 −V 0 ) / log (PO 2.1 / PO 2.0 ) −φ / 2) (14)
【００２８】低電流密度データからのβＨ(1) の決定；
低電流密度側で任意の入口水素分圧を２条件とり、端子
電圧を測定すると、（12）式より２つの端子電圧差は次
式（15）で示されることになる。 （Ｖ1 −Ｖ0 ）＝（φ＋βＨ(1))log(ＰH2.1/ ＰH2.0） （15） さらに、βＨ(1) について展開すれば次式（16）とな
る。Determination of βH (1) from low current density data;
When the terminal voltage is measured under two conditions of an arbitrary inlet hydrogen partial pressure on the low current density side, the difference between the two terminal voltages is expressed by the following expression (15) from the expression (12). (V 1 -V 0) = ( φ + βH (1)) log (P H2.1 / P H2.0) (15) Further, the following equation (16) if developed for βH (1).
【００２９】[0029]
【数１１】 [Equation 11]
【００３０】カソード限界電流密度（ｉLC）を求める；
燃料極側に純水素を十分に流した状態で、空気極側流量
一定のもとに負荷電流を増加させてゆくと、電池電圧が
急激に低下し電圧０直線と直交するような電圧−電流密
度曲線が得られ、この電圧０直線との交点を限界電流密
度と定義できる。ただし、通常の空気を使用して、この
ようにして限界電流密度を決定するには非常に大きな電
流を取り出す必要があるため、酸素希釈条件で試験を実
施するのが便利である。また、セル面内での反応分布を
できるだけ均一にするために、酸素濃度が入口と出口で
余り大きくならないようにした。このようにして求めた
限界電流密度は、前記式（９）で示すように、酸素分圧
と温度の関数として求められる。Determine the cathode limiting current density (i LC );
If the load current is increased while the flow rate of the air electrode is constant while the pure hydrogen is sufficiently flowing to the fuel electrode, the voltage-current is such that the battery voltage drops sharply and is orthogonal to the voltage 0 straight line. A density curve is obtained, and an intersection with the voltage 0 straight line can be defined as a limit current density. However, in order to determine the limiting current density in this way using ordinary air, it is necessary to extract a very large current, so that it is convenient to carry out the test under oxygen dilution conditions. Also, in order to make the reaction distribution in the cell plane as uniform as possible, the oxygen concentration was not made too large at the inlet and the outlet. The limit current density thus obtained is obtained as a function of the oxygen partial pressure and the temperature, as shown in the above equation (9).
【００３１】酸素濃度変化のデータからのβＯ(2) の決
定 燃料極側には純水素を十分に流し、電流密度一定の条件
のもとに、酸素濃度２条件で端子電圧を測定し、その差
電圧を式（11）を利用し、さらにβＯ(2) について解い
て次式（17) 及び（18）を得る。Determination of βO (2) from Data of Oxygen Concentration Change Pure hydrogen is sufficiently supplied to the fuel electrode side, the terminal voltage is measured under two conditions of oxygen concentration under the condition of constant current density. The following equation (17) and (18) are obtained by solving the difference voltage with respect to βO (2) using equation (11).
【００３２】[0032]
【数１２】 (Equation 12)
【００３３】水素濃度変化のデータからの燃料極拡散項
の決定；電流密度を一定にしながら、水素濃度３条件で
測定し、１条件を基準として他２条件との差電圧を定義
する。その差電圧は次式（19）及び（20）で記述され
る。Determination of diffusion term of fuel electrode from data of change in hydrogen concentration; measurement is performed under three conditions of hydrogen concentration while keeping current density constant, and a difference voltage from two other conditions is defined based on one condition. The difference voltage is described by the following equations (19) and (20).
【００３４】[0034]
【数１３】 (Equation 13)
【００３５】未知数はβＨ(2) 及びＤＨなので、ニュー
トン・ラプソン法などによりこの連立方程式を解くこと
により求めることができる。ただし、燃料極の拡散分極
の影響は極端に小さいもので、正常な範囲内で作動して
いる電池に対しては、実際には考慮する必要はない。こ
のようにして、式（２）が求められる。Since the unknowns are βH (2) and DH, they can be obtained by solving this simultaneous equation by the Newton-Raphson method or the like. However, the influence of the diffusion polarization of the fuel electrode is extremely small, and it is not actually necessary to consider a battery operating within a normal range. Thus, equation (2) is obtained.
【００３６】擬似開回路電圧（Ｔ）の算出；式（11）の
未知係数は上記の過程で全て求められたので、端子電圧
を絶対的に記述するためには、次式（21）で示される擬
似開回路電圧の温度依存性を求める必要がある。Ｆ
（Ｔ）は、このように未知係数を全て求めた後の最後に
残った項、すなわち剰余項であるが、一般にいう開回路
電圧（電流をとらない時の電圧）に準じる性格のものと
して擬似開回路電圧と呼んでいる。 Ｆ（Ｔ) ＝ＥO ＋βＨ(1)log（ξA ）＋βＯ(1)log（ξC ） (21) ここで、水素濃度、酸素濃度、電流密度条件を多様に変
化させたデータをもとに、すでに求められた諸係数を用
いて、唯一未知数となっている（Ｆ（Ｔ）−ｒ・ｉ）を
計算することによりＦ（Ｔ）及び内部抵抗ｒを同様に求
めることができる。このようにして、端子電圧は前記式
（１）で決定できることになる。Calculation of pseudo open circuit voltage (T); Since the unknown coefficients in equation (11) are all obtained in the above process, to describe the terminal voltage absolutely, the following equation (21) is used. It is necessary to determine the temperature dependence of the pseudo open circuit voltage. F
(T) is the last remaining term after all the unknown coefficients have been obtained in this way, that is, the remainder term, which is pseudo-characteristic similar to the general open circuit voltage (voltage when no current is taken). Called open circuit voltage. Original F (T) = E O + βH (1) log (ξ A) + βO (1) log (ξ C) (21) where the hydrogen concentration, oxygen concentration, the data variously changing the current density conditions Then, by using the coefficients already obtained and calculating the only unknown (F (T) -ri), F (T) and the internal resistance r can be similarly obtained. Thus, the terminal voltage can be determined by the above equation (1).
【００３７】該端子電圧記述式（１）は、各係数が決定
さるが、これら決定された各係数の例を表１に示す。In the terminal voltage description equation (1), each coefficient is determined. Table 1 shows examples of the determined coefficients.
【００３８】[0038]
【表１】 [Table 1]
【００３９】表１中、第２水素分圧係数βＨ(2) 及び水
素拡散項係数ＤＨは、正常な範囲内で作動している電池
では、燃料極の拡散分極の影響が極端に小さく、無視で
きるものであった（表１中、neg.で示す）。したがって
式（１）は次式（22）として表わすことができる。In Table 1, the second hydrogen partial pressure coefficient βH (2) and the hydrogen diffusion term coefficient DH are extremely small for a cell operating within a normal range, and the influence of the diffusion polarization of the fuel electrode is extremely small. It was possible (indicated by neg. In Table 1). Therefore, equation (1) can be expressed as equation (22).
【００４０】[0040]
【数１４】 [Equation 14]
【００４１】本発明において用いられる燃料電池として
は、水素が反応する燃料極、酸素が消費される空気極、
これらの２つの電極に挟まれた電解質層から構成される
ものである。前記電解質としては、特に制限されず、リ
ン酸水溶液、アルカリ系電解質等が挙げられる。The fuel cell used in the present invention includes a fuel electrode where hydrogen reacts, an air electrode where oxygen is consumed,
It is composed of an electrolyte layer sandwiched between these two electrodes. The electrolyte is not particularly limited, and examples thereof include a phosphoric acid aqueous solution and an alkaline electrolyte.
【００４２】また、本発明において評価する電池特性と
しては、抵抗分極、活性化分極及び濃度電極に係わるも
のである。また、その対策としては抵抗分極の増加がみ
とめられた場合、電極及びセパレータ等のカーボン材
料の固有抵抗を下げるとともに、該カーボン材料の平滑
度を改善する。電解質マトリックス層を薄くするとと
もに、マトリックス層と触媒層のリン酸が不足しないよ
うにセル内にリン酸を貯蔵しておく等が挙げられる。ま
た、活性化分極の増加がみとめられた場合、白金等の
触媒種の活性度を上げる等が挙げられる。また、濃度分
極の増加がみとめられた場合、触媒がリン酸で過度に
覆われることのないように触媒層の撥水性を適切にする
こと。基板のガス透過性を良くすること等が挙げられ
る。The battery characteristics evaluated in the present invention relate to resistance polarization, activation polarization and concentration electrode. As a countermeasure, when an increase in resistance polarization is found, the specific resistance of a carbon material such as an electrode and a separator is reduced, and the smoothness of the carbon material is improved. For example, the thickness of the electrolyte matrix layer may be reduced, and phosphoric acid may be stored in the cell so that phosphoric acid in the matrix layer and the catalyst layer is not insufficient. Further, when an increase in activation polarization is observed, the activity of a catalyst species such as platinum may be increased. When an increase in concentration polarization is observed, the water repellency of the catalyst layer should be appropriately adjusted so that the catalyst is not excessively covered with phosphoric acid. Improving the gas permeability of the substrate may be mentioned.
【００４３】[0043]
【発明の効果】本発明によれば、抵抗分極、活性化分極
及び濃度分極を前記燃料電池の端子電圧記述式（１）又
は（22）を用いて定量的に把握することにより、燃料電
池の特性を把握でき、さらに燃料電池の開発、改良にお
いて効果的な指標を示すことができる。また、単セルの
燃料電池試験を実施することにより、実寸セルの挙動を
数値シミュレーションする場合の特性式として使用でき
る。According to the present invention, the resistance polarization, the activation polarization and the concentration polarization are quantitatively grasped by using the terminal voltage description formula (1) or (22) of the fuel cell, whereby the fuel cell is obtained. The characteristics can be grasped, and an effective index can be shown in the development and improvement of the fuel cell. Further, by performing a fuel cell test of a single cell, it can be used as a characteristic equation in the case of performing a numerical simulation of the behavior of an actual size cell.
【００４４】[0044]
【実施例】次に、本発明を実施例によりさらに具体的に
説明するが、これは、単に例示であって本発明を制限す
るものではない。 実施例１ 下記に示す燃料電池の試験装置を用い、前記式（22）に
基づいて、当該燃料電池の電池特性を評価した。その
際、式（22）中、前記式（21）で示される擬似開回路電
圧Ｆ（Ｔ）には交換電流密度に係わる過電圧分（式（2
1）中の第２項及び第３項）が含まれる。このままでは
燃料極（アノード）分と空気極（カソード）分の分離が
できないため、 log（ξA ）＝ log（ξC ）と仮定して
擬似開回路電圧に含まれる活性化分極の一部をアノード
とカソードに振り分けた。結果は、実測値との比較を図
１〜３に示し、電極特性の評価結果を図４〜図６に示し
た。EXAMPLES Next, the present invention will be described in more detail with reference to Examples, which are merely illustrative and do not limit the present invention. Example 1 Using the fuel cell test apparatus shown below, the cell characteristics of the fuel cell were evaluated based on the above equation (22). At this time, in the equation (22), the pseudo-open circuit voltage F (T) represented by the equation (21) is replaced with an overvoltage component (equation (2)
2) and 3) in 1) are included. Since this state will not be able to separate the fuel electrode (anode) min and an air electrode (cathode) fraction, a portion of the log (ξ A) = log ( ξ C) and assuming activation polarization included in the pseudo-open circuit voltage Sorted into anode and cathode. The results are shown in FIGS. 1 to 3 in comparison with the actually measured values, and the evaluation results of the electrode characteristics are shown in FIGS.
【００４５】（小型単燃料電池試験装置の基本仕様） 単燃料電池の大きさ：１０cm×１０cm 電解質 ：リン酸水溶液（リン酸濃度１０５％） 燃料極 ：白金触媒使用 空気極 ：白金合金触媒使用 電極有効面積：１００cm2 定格温度 ：２００℃（４７３Ｋ） 定格電流密度：３００mA／cm2 反応ガス 燃料側 ：水素（８０％）と炭酸ガス（２０％）の混
合ガス 空気側 ：空気 燃料利用率：８０％ 酸素利用率：６０％ 動作圧力 ：常圧(Basic Specifications of Small Single Fuel Cell Test Apparatus) Single fuel cell size: 10 cm × 10 cm Electrolyte: phosphoric acid aqueous solution (phosphoric acid concentration: 105%) Fuel electrode: using platinum catalyst Air electrode: using platinum alloy catalyst Electrode Effective area: 100cm 2 Rated temperature: 200 ° C (473K) Rated current density: 300mA / cm 2 Reactive gas Fuel side: Mixed gas of hydrogen (80%) and carbon dioxide gas (20%) Air side: Air Fuel utilization rate: 80 % Oxygen utilization: 60% Operating pressure: Normal pressure
【００４６】図１から本発明の特定記述式から予測した
予測値（実線部分）と実際の測定値（プロット部分）と
は極めてよく一致しており、相関係数はＲ2 ＝０．９８
９を示した。ただし、低電圧領域は限界電流密度に近い
領域で測定されたものであるため、測定値にもバラツキ
がある。図２から予測値と実測値は極めてよく一致し、
異なる温度における特性曲線がよく示されている。図３
においても限界電流密度付近でのずれを除いて、両者は
よく一致している。From FIG. 1, the predicted value (solid line portion) predicted from the specific description formula of the present invention and the actual measured value (plot portion) agree very well, and the correlation coefficient is R 2 = 0.98.
9 was shown. However, since the low voltage region is measured in a region close to the limit current density, the measured values also vary. From FIG. 2, the predicted value and the measured value agree very well,
The characteristic curves at different temperatures are well illustrated. FIG.
In both cases, both agree well except for a shift near the limit current density.
【００４７】図４〜図６において、ネルンスト損とは、
ネルンスト式中の分圧の濃度補正項に関連する損失をい
う。抵抗分極損は、図面作成上、半分毎に分け上下に記
載した。また、図４は温度４７３Ｋ、燃料利用率８０
％、酸素利用率６０％、図５は温度４３３Ｋ、燃料利用
率８０％、酸素利用率６０％、図６は温度４３３Ｋ、酸
素濃度８％、燃料利用率８０％、酸素利用率６０％の条
件である。図４〜図６から電流密度が大きくなる程、そ
れぞれの分極損が増大するが、そのうち、特に空気極活
性化分極の影響が大きい。この対策としては、白金等の
触媒の活性を上げ反応性を上げればよい。In FIGS. 4 to 6, Nernst loss means
Loss related to the concentration correction term of the partial pressure in the Nernst equation. The resistance polarization loss is divided into halves for drawing and described above and below. FIG. 4 shows a temperature of 473K and a fuel utilization of 80.
5, temperature of 433K, fuel utilization of 80%, oxygen utilization of 60%, and FIG. 6 shows temperature of 433K, oxygen concentration of 8%, fuel utilization of 80%, oxygen utilization of 60%. It is. 4 to 6, the polarization loss increases as the current density increases. Among them, the influence of the air electrode activation polarization is particularly large. As a countermeasure, the activity of the catalyst such as platinum may be increased to increase the reactivity.
【図１】本発明の評価方法と実測値の相関を示す図であ
る。FIG. 1 is a diagram showing a correlation between an evaluation method of the present invention and an actually measured value.
【図２】電圧−電流密度特性曲線における本発明の評価
方法と実測値の関係を示す図である。FIG. 2 is a diagram showing a relationship between an evaluation method of the present invention and an actually measured value in a voltage-current density characteristic curve.
【図３】電圧−電流密度特性曲線における本発明の評価
方法と実測値の関係を示す図である。FIG. 3 is a diagram showing a relationship between an evaluation method of the present invention and an actually measured value in a voltage-current density characteristic curve.
【図４】本発明の評価方法により求めた燃料電池の特性
図である。FIG. 4 is a characteristic diagram of a fuel cell obtained by the evaluation method of the present invention.
【図５】本発明の評価方法により求めた燃料電池の特性
図である。FIG. 5 is a characteristic diagram of a fuel cell obtained by the evaluation method of the present invention.
【図６】本発明の評価方法により求めた燃料電池の特性
図である。FIG. 6 is a characteristic diagram of a fuel cell obtained by the evaluation method of the present invention.
Claims (4)
る空気極、これら２つの電極に挟まれた電解質層から構
成される燃料電池において、次式（１）； 【数１】 （式中、Ｖは燃料電池端子電圧（mV) 、ｉは電流密度
（mA／cm2 ) 、ＰH20 は水蒸気分圧(atm) 、ＰH2は水素
分圧(atm) 、ＰO2は酸素分圧(atm) 、Ｔは反応温度
（Ｋ）、ａ及びｂは交流電流密度の分圧依存性に関する
定数、φは２．３ＲＴ／ｎＦ（ここで、Ｒはガス定数で
８．３１４Ｊ／mol 、ｎは反応に関与するする電子数ｎ
＝２、Ｆはファラデー定数を示す）、Ｆ（Ｔ）は擬似開
回路電圧、ｒは内部抵抗（Ω・cm2 ) 、βＨ(1) は第１
水素分圧係数、βＨ(2) は第２水素分圧係数、ＤＨは水
素拡散項係数、βＯ(1) は第１酸素分圧係数、βＯ(2)
は第２酸素分圧係数、ＤＯは酸素拡散項係数を示す。）
で表わされる特性式に基づいて電池特性を評価すること
を特徴とする燃料電池の評価方法。1. A fuel cell comprising a fuel electrode where hydrogen reacts, an air electrode where oxygen is consumed, and an electrolyte layer sandwiched between these two electrodes, the following formula (1): (Where V is fuel cell terminal voltage (mV), i is current density (mA / cm 2 ), P H20 is water vapor partial pressure (atm), P H2 is hydrogen partial pressure (atm), and P O2 is oxygen content. Pressure (atm), T is the reaction temperature (K), a and b are constants relating to the partial pressure dependency of the AC current density, φ is 2.3 RT / nF (where R is a gas constant of 8.314 J / mol, n is the number of electrons involved in the reaction n
= 2, F indicates the Faraday constant), F (T) is the pseudo open circuit voltage, r is the internal resistance (Ω · cm 2 ), βH (1) is the first
Hydrogen partial pressure coefficient, βH (2) is the second hydrogen partial pressure coefficient, DH is the hydrogen diffusion term coefficient, βO (1) is the first oxygen partial pressure coefficient, βO (2)
Denotes a second oxygen partial pressure coefficient, and DO denotes an oxygen diffusion term coefficient. )
A method for evaluating a fuel cell, comprising evaluating cell characteristics based on a characteristic expression represented by:
（０）、ａが１及びｂが３／４である請求項１記載の燃
料電池の評価方法。2. The method according to claim 1, wherein in equation (1), φlog (P H20 ) is zero (0), a is 1 and b is ／.
る空気極、これら２つの電極に挟まれた電解質層から構
成される燃料電池において、次式（22）； 【数２】 （式中、Ｖ、ｉ、ＰH2、ＰO2、Ｔ、φ、Ｆ（Ｔ) 、ｒ、
βＨ(1) 、βＯ(1) 、βＯ(2) 及びＤＯは前記と同
じ。）で表わされる特性式に基づいて電池特性を評価す
ることを特徴とする燃料電池の評価方法。3. A fuel cell comprising a fuel electrode where hydrogen reacts, an air electrode where oxygen is consumed, and an electrolyte layer sandwiched between these two electrodes, the following formula (22): ( Where V, i, P H2 , P O2 , T, φ, F (T), r,
βH (1), βO (1), βO (2) and DO are the same as above. 3.) A method for evaluating a fuel cell, comprising: evaluating cell characteristics based on a characteristic expression represented by:
濃度分極に係わるものである請求項１又は２記載の燃料
電池の評価方法。4. The method for evaluating a fuel cell according to claim 1, wherein the cell characteristics relate to resistance polarization, activation polarization or concentration polarization.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP8344653A JPH10172596A (en) | 1996-12-09 | 1996-12-09 | Fuel cell evaluation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP8344653A JPH10172596A (en) | 1996-12-09 | 1996-12-09 | Fuel cell evaluation method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH10172596A true JPH10172596A (en) | 1998-06-26 |
Family
ID=18370942
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|---|---|---|---|
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| Country | Link |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2000357526A (en) * | 1999-06-15 | 2000-12-26 | Nippon Telegr & Teleph Corp <Ntt> | Fuel cell power generating system and deterioration diagnostic method of its cell stack |
| JP2011257226A (en) * | 2010-06-08 | 2011-12-22 | Mazda Motor Corp | Detection method and detection device for residual capacity of battery |
| CN107576913A (en) * | 2017-08-16 | 2018-01-12 | 国网四川省电力公司电力科学研究院 | Hydrogen load operation analysis method in active distribution network |
| CN108052777A (en) * | 2018-01-15 | 2018-05-18 | 中国计量大学 | A kind of Fuel cell polarization internal resistance separation method based on model solution |
| CN112103537A (en) * | 2019-06-18 | 2020-12-18 | 丰田自动车株式会社 | Fuel cell system |
| CN115000464A (en) * | 2022-08-02 | 2022-09-02 | 中车工业研究院(青岛)有限公司 | Parameter regulation and control method, device, equipment and medium of PEMFC |
-
1996
- 1996-12-09 JP JP8344653A patent/JPH10172596A/en active Pending
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2000357526A (en) * | 1999-06-15 | 2000-12-26 | Nippon Telegr & Teleph Corp <Ntt> | Fuel cell power generating system and deterioration diagnostic method of its cell stack |
| JP2011257226A (en) * | 2010-06-08 | 2011-12-22 | Mazda Motor Corp | Detection method and detection device for residual capacity of battery |
| CN107576913A (en) * | 2017-08-16 | 2018-01-12 | 国网四川省电力公司电力科学研究院 | Hydrogen load operation analysis method in active distribution network |
| CN107576913B (en) * | 2017-08-16 | 2021-05-07 | 国网四川省电力公司电力科学研究院 | Hydrogen load operation analysis method in active power distribution network |
| CN108052777A (en) * | 2018-01-15 | 2018-05-18 | 中国计量大学 | A kind of Fuel cell polarization internal resistance separation method based on model solution |
| CN108052777B (en) * | 2018-01-15 | 2024-02-02 | 中国计量大学 | Fuel cell polarization internal resistance separation method based on model solving |
| CN112103537A (en) * | 2019-06-18 | 2020-12-18 | 丰田自动车株式会社 | Fuel cell system |
| CN112103537B (en) * | 2019-06-18 | 2024-03-19 | 丰田自动车株式会社 | Fuel cell system |
| CN115000464A (en) * | 2022-08-02 | 2022-09-02 | 中车工业研究院(青岛)有限公司 | Parameter regulation and control method, device, equipment and medium of PEMFC |
| CN115000464B (en) * | 2022-08-02 | 2022-10-25 | 中车工业研究院(青岛)有限公司 | Parameter regulation and control method, device, equipment and medium of PEMFC |
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