Electrochemical Impedance Analysis for Fuel Cell

Preface

(1) Four-wheeled vehicle market

Global

1. Number of vehicles owned: 1,433,180,000 in 2019.
2. Production: 91,790,000 in 2019.
3. Sales: 91,300,000 in 2019.

P.R.C.

1. Number of vehicles owned: c.a. 260,000,000 in 2019 (18.1% of the global total).
2. Production: 25,721,000 in 2019 (28.0% of the global total)
3. Sales: 25,769,000 in 2019 (28.2% of the global total)

Japan

1. Number of vehicles owned: 78,416,591 in 2019 (5.5% of the global total).
2. Production: 9,680,000 in 2019 (10.5% of the global total).
3. Sales: 5,200,000 in 2019 (5.7% of the global total)
4. Used vehicle sales: 6,990,000 in 2019.

(2) Green vehicles

(i) BEV

μ-BEVs have recently come to be seen in Japan.

In P.R.C., c.a. 700,000,000 e-bikes are on the road.

So, the BEV shift has been successful in a small vehicle sector in P.R.C.

Japan may partially follow this trend.

However, ...

1. Aside from the low energy density of batteries, 200 Wh/kg or less (gasoline, 12,722 Wh/kg) ...
2. NIMS has announced that almost all existing Fe-reserve is going be used up by 2050, and that Li, Ni, and Mn are going to be used more than double the existing reserves.

(ii) FCV

1. The energy density of hydrogen can be 36,000 Wh/kg, three times larger than gasoline that is 12,722 Wh/kg. However, the volumetric energy density of hydrogen is 33% of gasoline, thus, the high-pressure tank is required.
2. The hydrogen-production cost-reduction has been considered challenging, however, electrolysis of water can reportedly cost JPY17-27/Nm^3 (cf. LNG can cost JPY13.3/Nm^3) by using the current electric power system network including regenerative energy with a small amount of decoupling capacity that would be supplied by batteries.

FCVs have so far been adopted for pro-use such as forklift, truck, bus et al. because of the refueling in a short time that is the MUST for professional-use.

(iii) FC-Stack/Battery power ratio

For the further FCV-spread, particularly in the passenger vehicle sector,

1. FC-stack cost, which is currently c.a. $200/kW, must be decreased.
2. One detour can be FC-stack/battery power ratio reconsideration. It tends to be thought that Toyota and Honda are superior to others, however, the other companies also have a chance.

(a) Toyota (FC-HEV)

Toyota has been using a 1.3-kWh Ni-MH battery pack that costs JPY130,000 + wages of JPY40,000-50,000, thus JPY170,000-180,000 in total.

The FC stack is 114 kW that is placed in the center of the chassis. The stack cost has been decreased to JPY660,000 (it has been expected to be decreased to JPY330,000 in 2025). Therefore, the total cost has become JPY840,000 (JPY510,000).

Well, 1.3-kWh battery is just as bulky as FC stack, though.

(b) Renault (FC range extender)

Renault uses a 33-kWh Li-ion battery pack and a 5-kW FC stack that can cost JPY450,000 and JPY29,000, respectively; thus, JPY479,000 in total.

(cf. 1) Nissan Leaf with a 30-kWh Li-ion battery pack. The battery-pack weight is 310 kg.

Considering the maneuverability and/or drivability, the motor-battery pair can generally be better than the motor-FC counter part. Toyota can offer the excellent drivability by mainly using the motor-FC pair with the assist by motor-battery-pair, though.

However, a battery pack can become heavy, or it can go up soon with a small and light one.

Then, what is the best FC/battery ratio in order to offer the best drivability and cost-effectiveness?

(c) Nissan e-power-based?

Nissan e-power (basically range extender) is more frequently battery-driven than Toyota hybrid system (THS):

(d) Honda i-MMD-based?

Honda i-MMD IC-HEV is also more frequently battery-driven than THS.

CLALITY Fuel Cell uses a large FC stack (104 kW):

Both of the Nissan e-power and Honda i-MMD use small Li-ion battery packs, around 1 kWh.

(e) Others?

The green energy sector in Japan have experienced a shift in interests from FCV spread to a large-scale green/blue fire power generation, however, the shift can also push the FCV spread, particularly in China, where the hydrogen obtained as the reformed gas is available at at the equivalent price of natural gas.

μ-FCV, which can run 100 km, is going to become available in 2021 at ¥1,000,000 by using a pet-bottle-size hydrogen cartridge that can be distributed through vending machines: STOR-H by AAQIUS - The new hydrogen standard; STORH presents his new Powertrain Kit - YouTube

(Supplementary 1)

• According to Yoshikawa et al. (『吉川大雄 他、「燃料電池自動車のシステム評価と走行特性」、日本機械学会論文集（B編）、2002年、68巻、665号、No.01-0143』), the FC-HEV equivalent to the max. power of 1500-cc HEV, of which batteries are used within SOC=40-70% (only regenerative-braking can charge the batteries up to SOC=80%) are as follows:

(Supplementary 2)

According to Sakai et al. (『酒井政信 他、「高精度内部抵抗センシング技術を用いた自動車用燃料電池湿潤制御システムの開発」、自動車技術会論文集、2015年、第46巻、p.1073-1078．』), the size- and cost-reduction of PEFC has been conducted by (1) increasing the current density and (2) lowering the humidity upon operation.

Main Topic: PEFC (Polymer Electrolyte Fuel Cell)

(1) PEFC Equivalent Circuit Model

According to Matsumoto, the equivalent circuit model of a PEFC is composed of

1. an Ra-Cd high-frequency component and
2. an Rr low-frequency component.

Here, Ra, Cd, and Rr denote the activation polarization resistance, electric double layer capacitance, and ionic/electronic resistance, respectively.

The Nyquist plot becomes a semi-circle: it is simple, so, a V-I plot is, instead, shown here.

Ra-Cd high-frequency component is mainly attributed from the activation polarization on water generation at the cathode. The H2O generation from O2 takes place after

1. the H+ diffusion through the electrolyte and ionomers from the anode to the cathode,
2. O2 permeation from the air to Pt catalysts at the cathode through the ionomers.

This process takes place at the solid-liquid-gas three-phase interface, thus, an electric double layer capacitance must be included in the model.

Rr low-frequency component is composed of

1. the resistance of H+ conduction through the electrolyte and the resistance of electron conduction through the separator, the gas-diffusion layer, and the catalyst layer, and
2. the resistance of the gas (mainly O2) diffusion. Note that the flooding mainly occurs at the cathode gas-diffusion layer and the cathode catalyst layer.

FC is usually operated at the maximum power. According to Yoshikawa et al., V-I and P-I curves becomes as follows:

『吉川大雄 他、「燃料電池自動車のシステム評価と走行特性」、日本機械学会論文集（B編）、2002年、68巻、665号、No.01-0143』

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• There is a case that FC is not operated at the maximum power. According to Manabe et al., the cold start has been achieved within 1 minute by (1) decreasing the moisture content to ~ 0% upon stop of a fuel cell system, (2) improved water-drainage from MEA upon the stop, and (3) temperature-rise rate maximization upon start of a fuel cell system by (a) reducing the heat capacity (by using the metal-based separator), by (b) pulling out a larger current than usual, and by (c) increasing oxygen concentration overpotential (by lowering air/fuel ratio *1). 『真鍋昇太等、「燃料電池ハイブリッド自動車における燃料電池急速暖気運転の開発」、自動車技術会論文集、2010年、第41巻、p.1379-1385．』
• *1: According to Naganuma, the lowest oxygen excess ratio (= O2-supplied/O2-reacted ratio) for the cold start is 1.03 that can suppress the H2 regeneration at the cathode (so-called pumping H2 generation). 『長沼良明等、「氷点下環境での燃料電池急速暖気制御の開発」、自動車技術会論文集、2013年、第44巻、p.1021-1026．』

(2) PEFC Durability

According to Osaka Gas, the main deterioration factors are

1. Electrolyte (ionomers) oxidation (decomposition), which results in the Ra-increase, resulting from the reaction with hydroxy radicals, HO・ and H2O・ which are the products of the reaction between the peroxide, H2O2, and the impurities such as Fe2+ and Cu2+, thus usually the radical quencher, Ce3+ or Mn2+, is added to the layer,
2. Anode catalyst deactivation (when the fuel does not contain CO, this does not take place.),
3. Cathode catalyst oxidation (then, dissolves)/reduction (then re-precipitates) resulting in the decrease in the specific surface area of catalyst particles and the carbon oxidation resulting in the cathode catalyst loss (Ra increases and Cd decreases), and
4. Cathode gas-diffusion deterioration, which results in the Rr-increase, mainly resulting from the water-repellent material loss (see the above-mentioned electrolyte oxidation).

In 2015, Toyota reported that the worst case scenario is 15% power decline per 15 years. The durability has been improved year by year because of new composition/structure catalysts, the new catalyst support, the operation scheme etc.

Supplementary on #3: "Cathode catalyst oxidation/reduction resulting in the decrease in the specific surface area." According to Sugawara (『菅原優、固体高分子形燃料電池模擬環境における白金の溶解機構、ま て り あ、第53巻、第4 号、(2014)、p165-p169．』),

• The PEFC stack voltage can reach 0.6-0.95 V upon FCV-driving, and can reach 1.5 V upon start if air exists at the anode.
• Platinum (Pt) can chemically dissolve at 0.8 V or higher, thus, when the oxidation of Pt at >= 0.8 V and the reduction at < 0.8 V take place over and over again, Pt particles will grow and decrease the specific surface area, resulting in the lower output current limit. Note that oxide surface layer of Pt grains are stable at >= 0.8 V; even so, repeated oxidation/reduction can increase the risk of the Pt particles' dissolution and re-growth.

(3) PEFC Control

Materials mass-transfers are the rate-determining steps: it is obvious from the above-mentioned current-voltage curve and the equivalent circuit model.

(a) The typical working layout of a PEM fuel cell stack (Ragb et al, 2012)

1. In case the load draws more current from the fuel cell voltage developed by the stack is reduced due to the phenomena known as the polarization of PEMFC, this can significantly affect the performance. Therefore controllers need to be implemented in such a way that it can control the air and hydrogen flow rate so as to control the output voltage.
2. There is another performance related issue encountered in PEMFC stacks known as a slow cold start. At a lower temperature, it becomes difficult for starting the PEMFC stack quickly due to the slowed down fuel cell dynamics because of stacking. Apart from that stacking of a number of fuel cells also significantly increases the temperature. Uncontrolled higher temperature can ultimately result in softening and even destroying the membrane.
3. To generate higher current and power from the PEMFC stack it is required to keep the membrane sufficiently wet during the operating cycles. Fuel cells also generate water at the cathodes due to electrochemical reactions. Therefore it is required to precisely control the water flow to and from the PEMFC stack to avoid flooding of electrodes and scarcity of water in cells (Nehrir et al, 2009).

The design of control systems for the PEM fuel cells is meant to achieve control of the four major subsystems:

1. the reactants subsystem,
2. the thermal subsystem,
3. the water management subsystem,
4. the power conditioning subsystem and the power management subsystem.

(b) The PhD thesis by J. T. Pukrushpan, University of Michigan (2003).

1. The largest time constant is - 100 s on time-varying temperature, T(t).
2. The second largest is - 10 s on the inertia.
3. The third is - 1 s on reactants pressure, p(t).
4. The fourth, electrochemical reaction, is quite fast.

Thus, the main objective of the fuel cell control system becomes reactants supply.

1. Air supply is slower than hydrogen supply, then, hydrogen supply is controlled by receiving the cathode inlet manifold pressure as a pilot signal.
2. As such, the compressor drive voltage is controlled by receiving the air mass flow rate or the air pressure, the stack voltage, and the current withdrawn from the stack.
3. By withdrawing the current, the stack voltage decreases because of the oxygen depletion; therefore, the cathode must be quickly replenished with oxygen. Otherwise, the stack cannot continue to supply the electric power, and can be deteriorated.

In 2004, Pukrushpan et al. listed up the work required in the future as follows:

1. Each component model, such as compressor or blower, manifold, etc.
2. Stack humidity model, including flooding.
3. Spatially distributed partial pressures and temperature.
4. Hydrogen recirculation, which can cause the control delay because of the additional volume.

As of 2020, many technologies have been advanced.

For example,

• #1: トヨタFCV「MIRAI」に搭載 -- 小流量から大流量に対応した酸素供給エアーコンプレッサを新開発。豊田自動織機。

• #2: As mentioned before, 『酒井政信 他、「高精度内部抵抗センシング技術を用いた自動車用燃料電池湿潤制御システムの開発」、自動車技術会論文集、2015年、第46巻、p.1073-1078．』
• #3: As mentioned before, 『真鍋昇太等、「燃料電池ハイブリッド自動車における燃料電池急速暖気運転の開発」、自動車技術会論文集、2010年、第41巻、p.1379-1385．』

(c) Electric power management: J. M. A. Marquez et al., "Fuel Cell Control Strategies," Conference Paper, November 2006, DOI: 10.13140/RG.2.1.2613.4803

1. When a step load change happens, a 2.5 V drop in the output voltage is observed for a few hundreds of ms. This output voltage drop is related to a output power drop, that is produced because the compressor has a slow response.
2. Furthermore, this transitory period can damage the fuel cell operation. Therefore, it is important to limit the current variation if the fuel cell is working without another auxiliary source. If there is a auxiliary source, this source must supply the power peak.
3. In applications when the fuel cell works with slow variations in its current, its behavior can be described suitably by a stationary model, that is, the polarization curve. Therefore, this model is used, together with the converter model and the load model, to generate the whole plant model necessary to design the control system of the fuel cell operation point. ... A DC/DC converter steps up the low output fuel cell voltage to the standard automotive DC bus 42 V [1]. The control system must maintain the operating point when there are perturbations in state variables of the system.
4. As it is mentioned above, the fuel cell system is connected with a DC/DC converter. This converter regulates the output fuel cell voltage. The control signal is the converter duty cycle. To design the control system, it must be taken into account the no-linearity of the all system. The approximate linearization technique allows to obtain a state linear model which shows the perturbations around the operation point [3]. Figure 5 shows electrical connection scheme between fuel cell system and DC/DC converter, taking into account parasite leaks in inductor and capacitor elements.

by T. H.

Appendix

Pure-H2 FC, such as PEFC, can also be a solution for regenerative energy plus.

SOFC can be used for double-combined power generation with micro gas turbine.

I, kind of, expect STOR-H: