{"id":11320,"date":"2021-10-05T10:00:09","date_gmt":"2021-10-05T18:00:09","guid":{"rendered":"https:\/\/www.linquip.com\/blog\/?p=11320"},"modified":"2023-02-06T02:16:30","modified_gmt":"2023-02-06T10:16:30","slug":"efficiency-of-fuel-cell","status":"publish","type":"post","link":"https:\/\/www.linquip.com\/blog\/efficiency-of-fuel-cell\/","title":{"rendered":"Efficiency of Fuel Cell: Calculation Formula &#038; Equation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.linquip.com\/blog\/efficiency-of-fuel-cell\/#Types_of_Fuel_Cell\" >Types of Fuel Cell<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.linquip.com\/blog\/efficiency-of-fuel-cell\/#The_Efficiency_of_Fuel_Cells\" >The Efficiency of Fuel Cells<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.linquip.com\/blog\/efficiency-of-fuel-cell\/#Calculating_Fuel_Cell_System_Efficiency\" >Calculating Fuel Cell System Efficiency<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.linquip.com\/blog\/efficiency-of-fuel-cell\/#Download_Efficiency_of_Fuel_Cell_PDF\" >Download Efficiency of Fuel Cell PDF<\/a><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-size: 14pt;\">The efficiency of fuel cell_ A <a href=\"https:\/\/www.linquip.com\/blog\/fuel-cells-advantages-and-disadvantages\/\">fuel cell<\/a> is a device that produces electricity by a chemical reaction. All fuel cells have two electrodes called the anode and cathode. The reactions that generate electricity occur at the electrodes.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Each fuel cell also has an electrolyte, which offers electrically charged particles and a catalyst that speeds the reactions at the electrodes.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">However, if waste heat is recovered in a cogeneration scheme, efficiencies of up to 85% can be achieved. The energy efficiency of a <a href=\"https:\/\/www.linquip.com\/equipment?q=Fuel%20Cell\"><strong>Fuel Cell<\/strong><\/a> is typically between 40 and 60 percent. Several <a href=\"https:\/\/www.linquip.com\/suppliers-companies?q=fuel-cell\"><strong>Suppliers and Companies<\/strong><\/a>, as well as various manufacturers and distributors, provide various types of fuel cells, and there are several types of <strong><u>Fuel Cells for Sale<\/u><\/strong> on Linquip.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">There is a comprehensive list of services on the Linquip website that covers all factory operations. Linquip vendors can assist you with this. Please contact <a href=\"https:\/\/www.linquip.com\/experts?q=fuel-cell\"><strong>Fuel Cell Experts in Linquip<\/strong><\/a> to learn more about how to connect with a diverse group of service providers who consistently deliver high-quality products.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Although less efficient compared to electric batteries, hydrogen fuel cells compare favorably with internal combustion engine technology, which extracts kinetic energy from the fuel at approximately 25 percent efficiency. A fuel cell, by contrast, can process hydrogen with air to generate electricity at up to 60 percent efficiency.<\/span><\/p>\n<figure id=\"attachment_11321\" aria-describedby=\"caption-attachment-11321\" style=\"width: 1090px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"size-full wp-image-11321\" src=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2.jpg\" alt=\"efficiency of fuel cell\" width=\"1090\" height=\"986\" title=\"\" srcset=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2.jpg 1090w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2-300x271.jpg 300w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2-1024x926.jpg 1024w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2-768x695.jpg 768w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2-696x630.jpg 696w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2-1068x966.jpg 1068w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/1-2-464x420.jpg 464w\" sizes=\"(max-width: 1090px) 100vw, 1090px\" \/><figcaption id=\"caption-attachment-11321\" class=\"wp-caption-text\">Hydrogen fuel cell (Reference: gmobility.eu)<\/figcaption><\/figure>\n<h2><strong>Types of Fuel Cell<br \/>\n<\/strong><\/h2>\n<p><span style=\"font-size: 14pt;\">Each fuel cell has two electrodes, an anode and cathode, and an electrolyte connecting them. Fuel cells have various electrolytes and electrodes, and their electrochemical processes occur at different temperature levels. As such, each kind of fuel cell (or fuel cell technology) has its inherent pros and cons, making them more proper for specific markets and applications.<\/span><\/p>\n<h3><strong>Alkaline Fuel Cell <\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">Alkaline fuel cells (AFCs) were revealed in 1959 by Francis Thomas Bacon. They have a liquid alkaline electrolyte such as potassium hydroxide (KOH) in water and cathodes that are regularly made with platinum. Performing at 60-70<sup>o<\/sup>C (140-158<sup>o<\/sup>F), AFCs are one of the most efficient fuel cells that can reach up to 60% efficiency and approximately 87% combined heat and power.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Spaceships in the US and Russian\/Soviet used alkaline fuel cells to provide electricity and drinking water for astronauts. Other advantages of AFCs are their virtually instant performance without pre-heating, even at sub-zero temperatures, and their resistance to salt air and humidity. Also, AFCs are used as long-duration UPSs or\u00a0<a href=\"https:\/\/www.gencellenergy.com\/markets-applications\/backup-power\/\" target=\"_blank\" rel=\"noopener\">backup generators<\/a>\u00a0for powering telecom towers and urban buses.<\/span><\/p>\n<h3><strong>Proton Exchange Membrane Fuel Cell <\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">Proton exchange membrane fuel cells (PEM or PEMFC fuel cells) use platinum group-based electrodes and a water-based or mineral-acid-based polymer membrane as an electrolyte. The water-based fuel cells function at 80-100<sup>o<\/sup>C (176-212<sup>o<\/sup>F), and the mineral-acid-based PEMs, identified as high-temperature PEMs (or HTPEMs), function at up to 200<sup>o<\/sup>C (224<sup>o<\/sup>F). They need precise humidity conditions to work, and their acidic nature demands a platinum catalyst.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">PEM fuel cells are comparatively small and light-weight and are consequently the leading fuel cell technology applied in material handling applications such as forklifts and transportation applications, including buses, cars, and trucks. PEMFCs are the fastest-growing variety of fuel cells.<\/span><\/p>\n<h3><strong>Phosphoric Acid Fuel Cell <\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">This type was developed in the mid-1960s and field-tested in the 1970s; the Phosphoric acid fuel cells (PAFCs) are one of the most mature fuel cells and the first model to be commercially accepted. PAFCs use phosphoric acid as an electrolyte and an anode and cathode composed of a finely dispersed platinum catalyst on silicon carbide and carbon structure. Typically, they have been utilized for stationary power generation in buildings, hospitals, hotels, and utilities in the USA, Europe, and Asia.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">These systems have been technically prosperous and very reliable, with 40% plus efficiency levels and tens of thousands of working hours. Water management in this type is more straightforward than in PEMs, and they are more tolerant of contaminants in hydrogen. However, the emission of phosphoric acid is doubtful, and good ventilation is necessary. PAFCs are less powerful than other types in the same weight and volume and need much more platinum than other fuel cells, which increases their cost.<\/span><\/p>\n<figure id=\"attachment_11322\" aria-describedby=\"caption-attachment-11322\" style=\"width: 1018px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"size-full wp-image-11322\" src=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/2.png\" alt=\"efficiency of fuel cell\" width=\"1018\" height=\"934\" title=\"\" srcset=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/2.png 1018w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/2-300x275.png 300w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/2-768x705.png 768w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/2-696x639.png 696w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/2-458x420.png 458w\" sizes=\"(max-width: 1018px) 100vw, 1018px\" \/><figcaption id=\"caption-attachment-11322\" class=\"wp-caption-text\">Phosphoric Acid Fuel Cells (Reference: semanticscholar.org)<\/figcaption><\/figure>\n<h3><strong>Molten Carbonate Fuel Cells <\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">This type uses a molten carbonate electrolyte and operates at 650 <sup>o<\/sup>C, enabling them to function on unreformed fuels such as methanol, ethanol, biogas, natural gas, and coal. In addition, the absence of a catalyst produced from noble metals such as gold, silver, or platinum makes MCFCs be more cost-competitive with more conventional sources of power. The efficiency of fuel cells in MCFCs is close to 50%, increasing up to 80% when high-quality waste heat is reabsorbed.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">MCFCs need a large number of stainless steel and nickel parts that raise the materials cost, requiring specialized manufacturing techniques. Molten carbonate is also naturally corrosive. As the running temperature is so high, MCFCs need significant time to touch operating temperature and are slow in responding to sudden changes in electricity requirements. However, they are best suited for the preparation of constant power in large utilities.<\/span><\/p>\n<h3><strong>Solid Oxide Fuel Cells <\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">Solid oxide fuel cells are manufactured of a thin layer of ceramics. The ceramics in SOFCs are not electrically and ionically active until they are in the range of 500-1000 <sup>o<\/sup>C (1060-2120 <sup>o<\/sup>F). The high temperature enables them to oxidize almost any fuel, including gasoline, natural gas, diesel, biofuels, hydrogen, and even coal gas. The ceramic construction for providing stability and reliability makes SOFCs more costly than other fuel cells. The solid electrolyte is constructed from a ceramic material named Yttria-Stabilized Zirconia (YSZ). Considering the high running temperature, SOFCs need significant time to reach working temperature and are slow to respond to changes in electricity requirements.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">The table below presents the specification of the described fuel cells. (Reference: gencellenergy.com)<\/span><\/p>\n<table width=\"504\">\n<tbody>\n<tr>\n<td width=\"92\"><strong>FC Type<\/strong><\/td>\n<td width=\"93\"><strong>Proton Exchange<br \/>\n(PEM &amp; HTPEM)<\/strong><\/td>\n<td width=\"80\"><strong>Molten Carbonate (MCFC)<\/strong><\/td>\n<td width=\"89\"><strong>Alkaline<br \/>\n(AFC)<\/strong><\/td>\n<td width=\"78\"><strong>Phosphoric Acid (PAFC)<\/strong><\/td>\n<td width=\"71\"><strong>Solid Oxide (SOFC)<\/strong><\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Anode<\/strong><\/td>\n<td width=\"93\">Platinum<\/td>\n<td width=\"80\">Steel\/nickel<\/td>\n<td width=\"89\">Platinum or Carbon (GenCell)<\/td>\n<td width=\"78\">Platinum<\/td>\n<td width=\"71\">Ceramic<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Electrolyte<\/strong><\/td>\n<td width=\"93\">Polymer Membrane<\/td>\n<td width=\"80\">Molten Carbonate<\/td>\n<td width=\"89\">Potassium Hydroxide (KOH)<\/td>\n<td width=\"78\">Phosphoric Acid (H3PO4)<\/td>\n<td width=\"71\">Yttria-Stabilized Zirconia (YSZ)<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Electrolyte<br \/>\nType<\/strong><\/td>\n<td width=\"93\">Solid<\/td>\n<td width=\"80\">Solid<\/td>\n<td width=\"89\">Liquid<\/td>\n<td width=\"78\">Liquid<\/td>\n<td width=\"71\">Solid<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Fuel<\/strong><\/td>\n<td width=\"93\">\u2022 Hydrogen<\/td>\n<td width=\"80\">\u2022 Natural gas<br \/>\n\u2022 Methanol<br \/>\n\u2022 Ethanol<br \/>\n\u2022 Biogas<br \/>\n\u2022 Coal gas<\/td>\n<td width=\"89\">\u2022 Hydrogen<br \/>\n\u2022 Ammonia (GenCell)<\/td>\n<td width=\"78\">\u2022 Hydrogen<br \/>\n\u2022 Methanol<\/td>\n<td width=\"71\">\u2022 Natural gas<br \/>\n\u2022 Methanol<br \/>\n\u2022 Ethanol<br \/>\n\u2022 Biogas<br \/>\n\u2022 Coal gas<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Temperature<\/strong><\/td>\n<td width=\"93\">\u2022 80-100 \u00baC<br \/>\n(176-212 \u00baF)<br \/>\n\u2022 200 \u00baC (224 \u00baF)<\/td>\n<td width=\"80\">\u2022 650 \u00baC<br \/>\n(1202 \u00baF)<\/td>\n<td width=\"89\">\u2022 60-70 \u00baC<br \/>\n(140-158 \u00baF)<\/td>\n<td width=\"78\">\u2022 150-200 \u00baC<br \/>\n(336-448 \u00baF)<\/td>\n<td width=\"71\">\u2022 500-1000 \u00baC (1060-2120 \u00baF)<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Efficiency<\/strong><\/td>\n<td width=\"93\">30-40%<\/td>\n<td width=\"80\">50%<br \/>\n(80% CHP)<\/td>\n<td width=\"89\">60-70%<br \/>\n(80% CHP)<\/td>\n<td width=\"78\">40-50%<br \/>\n(80% CHP)<\/td>\n<td width=\"71\">60%<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Power<\/strong><\/td>\n<td width=\"93\">0.12-5 kW<\/td>\n<td width=\"80\">10 kW &#8211; 2 MW<\/td>\n<td width=\"89\">0.5\u2013200 kW<\/td>\n<td width=\"78\">100 &#8211; 400 kW<\/td>\n<td width=\"71\">0.01 \u2013 2000 kW<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Startup Time<\/strong><\/td>\n<td width=\"93\">&lt; 1 minute<\/td>\n<td width=\"80\">10 minutes<\/td>\n<td width=\"89\">&lt; 1 minute<\/td>\n<td width=\"78\">n\/a<\/td>\n<td width=\"71\">60 minutes<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Pros<\/strong><\/td>\n<td width=\"93\">\u2022 Quick startup<br \/>\n\u2022 Small<br \/>\n\u2022 Light-weight<\/td>\n<td width=\"80\">\u2022 Fuel variety<br \/>\n\u2022 Efficient<\/td>\n<td width=\"89\">\u2022 Quick startup<br \/>\n\u2022 Temperature resistant<br \/>\n\u2022 Low-cost ammonia liquid fuel<\/td>\n<td width=\"78\">\u2022 Stable<br \/>\n\u2022 Maturity<\/td>\n<td width=\"71\">\u2022 Fuel variety<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>Cons<\/strong><\/td>\n<td width=\"93\">\u2022 Sensitivity to humidity or dryness<br \/>\n\u2022 Sensitivity to salinity<br \/>\n\u2022 Sensitivity to low temperatures<\/td>\n<td width=\"80\">\u2022 Slow to respond<br \/>\n\u2022 Highly corrosive<\/td>\n<td width=\"89\">\u2022 Liquid catalyst adds weight<br \/>\n\u2022 Relatively large<\/td>\n<td width=\"78\">\u2022 Phosphoric acid vapor<br \/>\n\u2022 Less powerful<\/td>\n<td width=\"71\">\u2022 Long startup time<br \/>\n\u2022 Intense heat<\/td>\n<\/tr>\n<tr>\n<td width=\"92\"><strong>applications<\/strong><\/td>\n<td width=\"93\">\u2022 Cars<br \/>\n\u2022 Buses<br \/>\n\u2022 Trucks<\/td>\n<td width=\"80\">\u2022 Utilities<\/td>\n<td width=\"89\">\u2022 Backup generators (long-duration UPS)<br \/>\n\u2022 Primary power generators<br \/>\n\u2022 Off-grid telecom<\/td>\n<td width=\"78\">\u2022 Buildings<br \/>\n\u2022 Hotels<br \/>\n\u2022 Hospitals<br \/>\n\u2022 Utilities<\/td>\n<td width=\"71\">\u2022 Corporate power plants<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h3><strong>Direct Methanol Fuel Cells<\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">Most fuel cells operate with hydrogen, which can be supplied to the fuel cell system directly or can be provided within the fuel cell system by converting hydrogen-rich fuels such as methanol, ethanol, and hydrocarbon fuels. However, Direct Methanol Fuel Cells (DMFCs) are powered by pure methanol, which is regularly mixed with water and directly fed to the fuel cell anode.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Direct methanol fuel cells do not have fuel storage problems typical of some fuel cell systems as methanol has a higher energy density compared to hydrogen, though less than diesel fuel or gasoline. Methanol is also simpler to transport and supply using modern infrastructure because it is a liquid, similar to gasoline. DMFCs are often used to produce power for portable applications, the same as cell phones or laptop computers.<\/span><\/p>\n<h3><strong>Reversible Fuel Cells<br \/>\n<\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">Reversible fuel cells generate electricity from hydrogen and oxygen and produce heat and water as byproducts, similar to other fuel cells. However, reversible fuel cell systems can also utilize electricity from wind power, solar power, or other sources to break water into oxygen and hydrogen fuel by\u00a0<a href=\"https:\/\/www.energy.gov\/eere\/fuelcells\/hydrogen-production-electrolysis\" target=\"_blank\" rel=\"noopener\">electrolysis<\/a>\u00a0process. Reversible fuel cells can produce energy when needed, and during the high power generation from other technologies, reversible fuel cells can save the excess energy in the shape of hydrogen. This energy storage capacity could be a key enabler for alternate renewable energy technologies.<\/span><\/p>\n<figure id=\"attachment_11323\" aria-describedby=\"caption-attachment-11323\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"size-full wp-image-11323\" src=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/3-1.png\" alt=\"efficiency of fuel cell\" width=\"600\" height=\"600\" title=\"\" srcset=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/3-1.png 600w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/3-1-300x300.png 300w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/3-1-150x150.png 150w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/3-1-420x420.png 420w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><figcaption id=\"caption-attachment-11323\" class=\"wp-caption-text\">PEM Transparent Reversible Fuel Cell (Reference: horizoneducational.com)<\/figcaption><\/figure>\n<h2><span class=\"ez-toc-section\" id=\"The_Efficiency_of_Fuel_Cells\"><\/span><strong>The Efficiency of Fuel Cells<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-size: 14pt;\">The efficiency of fuel cells can be named as theoretical and practical, which vary in terms of action and equations.<\/span><\/p>\n<h3><strong>Theoretical Maximum Efficiency of Fuel Cel <\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">The energy efficiency of a system or method that converts energy is measured by the ratio of the amount of helpful energy (&#8220;output energy&#8221;) to the entire amount of energy (&#8220;input energy&#8221;) or by valuable output energy as a percentage of the whole input energy. In fuel cells, the output energy is electrical energy generated by the system. The input energy is the stored energy in the fuel.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">According to the US Department of Energy, the efficiency of fuel cells is generally between 40 and 60%. It is much higher compared to some other systems in energy generation. For instance, the typical internal combustion engine of a car is around 25% efficient. In Combined Heat and Power (CHP) systems, the heat delivered by the fuel cell is obtained, increasing the system&#8217;s efficiency to up to 85\u201390%.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">The theoretical maximum efficiency of power generation systems never reaches in practice. However, this calculation provides a comparison of various kinds of power generation systems. The theoretical maximum efficiency of a fuel cell approximates 100%, while this efficiency for internal combustion engines is roughly 58%.<\/span><\/p>\n<h3><strong>The efficiency of a Fuel Cell in Practice <\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">The practical efficiency of a fuel cell is less than the theoretical one and varies from case to case. In a fuel cell vehicle type, the tank-to-wheel efficiency is higher than 45% at low loads and presents average rates of about 36% when a driving cycle similar to the NEDC (<a href=\"https:\/\/en.wikipedia.org\/wiki\/New_European_Driving_Cycle\" target=\"_blank\" rel=\"noopener\">New European Driving Cycle<\/a>) is applied as a test procedure. The comparable NEDC efficiency for a Diesel vehicle is about 22%. In 2008 Honda published a fuel cell electric vehicle (the\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Honda_FCX_Clarity\" target=\"_blank\" rel=\"noopener\">Honda FCX Clarity<\/a>) with a fuel stack declaring a 60% tank-to-wheel efficiency.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Fuel cell vehicles operating on compressed hydrogen may have nearly a power-plant-to-wheel efficiency of 22% if the hydrogen is deposited as high-pressure gas and 17% if it is deposited as liquid hydrogen. Fuel cells can not save energy similar to a battery, except hydrogen. Still, in some utilization, such as stand-alone power plants based on discontinuous sources such as solar or wind power, they are coupled with electrolyzers and storage arrangements to form an energy storage scheme.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Since 2019, 90% of hydrogen was utilized for oil refining, chemicals, and fertilizer production, and almost 98% of hydrogen is provided by\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Steam_methane_reforming\" target=\"_blank\" rel=\"noopener\">steam methane reforming<\/a>, which releases carbon dioxide. The entire efficiency (electricity to hydrogen and reverse to electricity) of these plants (identified as round-trip efficiency), utilizing pure hydrogen and pure oxygen, can be in the range of 35 to 50 percent, based on gas density and other provisions. The electrolyzer\/fuel cell system can deposit unlimited quantities of hydrogen and is suited for long-term storage.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Solid-oxide fuel cells generate heat from the recombination of oxygen and hydrogen. The ceramic types can operate in 800 degrees Celsius. This heat can be recovered to be used in the system to increase the efficiency of fuel cells.<\/span><\/p>\n<figure id=\"attachment_11324\" aria-describedby=\"caption-attachment-11324\" style=\"width: 768px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"size-full wp-image-11324\" src=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/4.jpg\" alt=\"efficiency of fuel cell\" width=\"768\" height=\"604\" title=\"\" srcset=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/4.jpg 768w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/4-300x236.jpg 300w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/4-696x547.jpg 696w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/4-534x420.jpg 534w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/><figcaption id=\"caption-attachment-11324\" class=\"wp-caption-text\">Fuel cell power train (Reference: dsm.com)<\/figcaption><\/figure>\n<h2><strong>Calculating Fuel Cell System Efficiency<br \/>\n<\/strong><\/h2>\n<p><span style=\"font-size: 14pt;\">In a fuel cell reaction, the total energy is composed of both electrical and thermal energy identified as enthalpy (H). The Electrical energy is associated with the Gibbs free energy (G) and corresponds to the maximum usable electrical energy obtainable when hydrogen recombines with oxygen.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Irreversible energy in the system or entropy (S) is the &#8220;cost of doing business&#8221; and depends on the reaction&#8217;s temperature. The loss due to entropy is comparable with a bouncing ball losing energy when hitting the floor, as friction from the bouncing action creates a transfer of thermal energy to atoms in the bottom. The energy conveyed to those floor atoms dissipates and can not be recovered. Consequently, the change (\u0394) in certain quantities from a standard set of conditions follows the equation shown below:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta H=\\Delta G+T\\Delta S<\/span>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">The conventional method for calculating the efficiency of fuel cell power plants or other electrical generation devices is to divide the electricity generated by the Higher Heating Value (HHV) of the fuel employed. This is a reasonable way for calculating power plant efficiency because the power plant supervisor purchases fuel (natural gas is traded by heating value) and sells electricity.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><em>Electrical Efficiency= (Electricity Produced)\/(HHV of Fuel Used)<\/em><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\"><strong>\u00a0<\/strong>Accordingly, there is a maximum theoretical limit for the electrical efficiency achievable by a fuel cell system expressed by the Gibbs free energy divided by the heat of combustion of the fuel.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">For the hydrogen fuel cell, this value is:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">Gibbs free energy\/HHV = 237.2 kJ\/mole \u2215 285.8 kJ\/mol= 83%<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">The use of HHV here is in conformity with the method used in the United States to determine efficiency for internal combustion (IC) generators\/engine and gas generator\/turbine systems. However, some US developers of high-temperature fuel cells use the European convention and hydrogen&#8217;s lower heating value (LHV) for efficiency calculation.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">The maximum theoretical efficiency of a whole fuel cell system based on LHV of hydrogen is 94.5% or 228.6 kJ\/mole \u2215 241.8 kJ\/mol. As it is clear, using the LHV convention for measuring the efficiency of an electrical generator always generates numbers greater than those yielded by calculations employing the HHV for the same system. When requesting the electrical efficiency of an electric generator, it is essential to indicate whether it is based on the LHV or HHV calculation method.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Fuel cells can not reach these maximum electrical efficiency numbers due to internal resistance losses. For instance, a practical fuel cell working near its maximum power output might produce only 154 kJ of electricity per mole of hydrogen consumed. The rest of the heating value appears as heat produced by the fuel cell. The calculation for such a fuel cell is presented as 154 kJ\/mol\u2215 285.8 kJ\/mol= 54% efficient (HHV) in the practical process. 46% of the energy generated can be recovered from the fuel cell as co-generated heat.<\/span><\/p>\n<figure id=\"attachment_11325\" aria-describedby=\"caption-attachment-11325\" style=\"width: 1113px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"size-full wp-image-11325\" src=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1.jpg\" alt=\"efficiency of fuel cell\" width=\"1113\" height=\"810\" title=\"\" srcset=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1.jpg 1113w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1-300x218.jpg 300w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1-1024x745.jpg 1024w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1-768x559.jpg 768w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1-696x507.jpg 696w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1-1068x777.jpg 1068w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1-577x420.jpg 577w, https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/08\/5-1-324x235.jpg 324w\" sizes=\"(max-width: 1113px) 100vw, 1113px\" \/><figcaption id=\"caption-attachment-11325\" class=\"wp-caption-text\">Fuel cell auxiliary power unit (Reference: fchea.org)<\/figcaption><\/figure>\n<h3><strong>Voltage Efficiency of Fuel Cells and Stacks<br \/>\n<\/strong><\/h3>\n<p><span style=\"font-size: 14pt;\">The electrical system efficiency considerations discussed above are employed globally to whole fuel cell systems that involve many individual components, such as humidifiers, fuel processors, fuel cell stacks, power conditioners, and controls. Many experimenters and developers wish to evaluate the efficiency of the fuel cell stack separate from the system&#8217;s efficiency.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">For this reason, it is helpful to use the theory of voltage efficiency, which is described as the cell (or cell stack) operating voltage divided by the thermodynamic cell voltage.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><em>Voltage Efficiency= (Operating Voltage (V))\/(Thermodynamic Voltage (E))<\/em><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">The thermodynamic cell voltage can be determined using the Nernst equation and the Gibbs free energy:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">E=E^{0}-\\frac{RT}{nF}ln\\frac{[H_{2}O]}{[O_{2}]^{1\/2}[H_{2}]}<\/span>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">Where:<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 14pt;\">E\u00b0 = the thermodynamic voltage under standard conditions<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">E = the thermodynamic voltage under prevailing conditions<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">n = the number of electrons transferred (2 in this case)<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">F = Faraday constant (96,485 Coulomb mole-1)<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">R = the gas constant (8.314 J deg K-1 mole-1)<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">T = temperature in degrees Kelvin (25\u00b0C = 298 K)<\/span><\/li>\n<li><span style=\"font-size: 14pt;\">[ ] = the thermodynamic activity of the products and reactants. For gases, it can be approximated by partial pressure in the atmosphere .<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 14pt;\">As shown below, Gibbs free energy can be transformed into a thermodynamic voltage applying the formula as free energy is in joules per mole:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">Gibbs free energy (in standard conditions) = nFE\u00b0<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">The Gibbs free energy for the hydrogen-oxygen reaction, under standard conditions, is 237.2 kJ\/mol for the result of liquid water at 25\u00b0C. Consequently, the thermodynamic voltage for a hydrogen-oxygen fuel cell working at standard temperature and pressure is 1.229 volts.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">E^{0}= \\frac{237200J}{2(96485)J}=1.229 volts<\/span>\n<p>&nbsp;<\/p>\n<p><span style=\"font-size: 14pt;\">The Nernst equation is helpful for calculating the thermodynamic voltage at alternating pressures and reactant concentrations. Still, it should be regarded that the Gibbs free energy of the hydrogen\/oxygen reaction varies with temperature. To calculate the thermodynamic voltage of a cell at another temperature, it is required to find the Gibbs free energy for the reaction at that temperature in thermodynamic tables. For instance, the thermodynamic voltage is 0.998 volts for a high-temperature fuel cell running on hydrogen\/oxygen at atmospheric pressure and 1,000K.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">Experimenters and developers of higher-temperature fuel cells regularly use the free energy to form water vapor rather than liquid water in their calculations. We can find both in most thermodynamic tables. A suitable fuel cell with well-sealed parts and a properly operating electrolyte should display a voltage close to the thermodynamic voltage when it is not generating power (no-load).<\/span><\/p>\n<p><span style=\"font-size: 14pt;\">This is also recognized as the open-circuit voltage. Pinholes in the electrolyte that allow fuel and oxidant to process, for example, decrease the open-circuit voltage and indicate a problem. The approximate efficiency for a fuel cell stack that is generating electrical power can be determined by dividing the operating voltage by the thermodynamic voltage. Therefore, a polymer electrolyte membrane (PEM) fuel cell running at 0.800 volts under standard conditions has a 0.800 V \u2215 1.229 V = 65% voltage efficiency.<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Download_Efficiency_of_Fuel_Cell_PDF\"><\/span>Download Efficiency of Fuel Cell PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"su-button-center\"><a href=\"https:\/\/www.linquip.com\/blog\/wp-content\/uploads\/2021\/10\/linquip.com-Efficiency-of-Fuel-Cell-Calculation-Formula-Equation.pdf\" class=\"su-button su-button-style-default su-button-wide\" style=\"color:#FFFFFF;background-color:#2D89EF;border-color:#246ec0;border-radius:12px\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color:#FFFFFF;padding:0px 30px;font-size:22px;line-height:44px;border-color:#6cadf4;border-radius:12px;text-shadow:none\"> Download PDF<\/span><\/a><\/div>\n<h3><b>Buy Equipment or Ask for a Service<\/b><\/h3>\n<p><span style=\"font-size: 14pt;\">By using Linquip RFQ Service, you can expect\u00a0to receive quotations from various suppliers across multiple industries and regions.<\/span><\/p>\n<p style=\"text-align: center;\"><strong><a href=\"http:\/\/linquip.com\/get-quote?utm_source=blog&amp;utm_medium=content&amp;utm_campaign=product_list&amp;utm_term=product_list&amp;utm_content=rfq\" target=\"_blank\" rel=\"noopener\">Click Here to Request a Quotation From Suppliers and Service Providers<\/a><\/strong><\/p>\n<p><em><strong>Read More In Linquip<\/strong><\/em><\/p>\n<ul>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a title=\"Efficiency of Inverter\" href=\"https:\/\/www.linquip.com\/blog\/efficiency-of-inverter\/\" target=\"_blank\" rel=\"noopener\">Efficiency of Inverter<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/electric-heater-efficiency\/\" target=\"_blank\" rel=\"noopener\">Electric Heater Efficiency and Running Costs<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/space-heater-efficiency\/\" target=\"_blank\" rel=\"noopener\">Space Heater Efficiency For Various Types of Heaters<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/heater-efficiency\/\" target=\"_blank\" rel=\"noopener\">Heater Efficiency Calculation: Formula &amp; Equation<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/fan-efficiency\/\" target=\"_blank\" rel=\"noopener\">Fan Efficiency Calculation: Formula &amp; Equation<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/efficiency-of-wind-turbines\/\" target=\"_blank\" rel=\"noopener\">Efficiency of Wind Turbines<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/dc-motor-efficiency\/\" target=\"_blank\" rel=\"noopener\">DC Motor Efficiency: Calculation: Formula &amp; Equation<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/efficiency-of-diesel-generators\/\" target=\"_blank\" rel=\"noopener\">Efficiency of Diesel Generators Calculation: Formula &amp; Equation<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/energy-efficient-electric-heater\/\" target=\"_blank\" rel=\"noopener\">Energy Efficient Electric Heater: A Practical Guide<\/a><\/span><\/span><\/strong><\/li>\n<li><strong><span style=\"text-decoration: underline;\"><span style=\"font-size: 10pt; font-family: verdana, geneva, sans-serif;\"><a href=\"https:\/\/www.linquip.com\/blog\/generator-efficiency\/\" target=\"_blank\" rel=\"noopener\">What is Generator Efficiency? 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The reactions that generate electricity occur at the electrodes. Each fuel cell also has an electrolyte, which offers electrically charged particles and a catalyst that speeds &#8230;<\/p>\n","protected":false},"author":12,"featured_media":11329,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","footnotes":""},"categories":[323,21],"tags":[],"class_list":["post-11320","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-efficiency-calculation","category-electrical-component"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/posts\/11320","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/comments?post=11320"}],"version-history":[{"count":5,"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/posts\/11320\/revisions"}],"predecessor-version":[{"id":26286,"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/posts\/11320\/revisions\/26286"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/media\/11329"}],"wp:attachment":[{"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/media?parent=11320"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/categories?post=11320"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.linquip.com\/blog\/wp-json\/wp\/v2\/tags?post=11320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}